-
Notifications
You must be signed in to change notification settings - Fork 0
/
MC_Example.Rmd
1199 lines (862 loc) · 59.2 KB
/
MC_Example.Rmd
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
---
title: "Example - Internal Only"
author: "Cory Whitney"
date: "`r Sys.Date()`"
csl: elsevier-harvard.csl
output:
html_document:
toc: true
toc_float: true
number_sections: true
fig_caption: true
bibliography: packages.bib
---
```{r, warning=FALSE, include=FALSE}
knitr::write_bib(c(.packages(), 'knitr', 'shiny', 'decisionSupport', 'base'), 'packages.bib')
```
# Decision model
Decision Analysis (DA) can be used to support practical decisions in the face of risk and uncertainty It can generate robust and science-based decision support by integrating data and expert knowledge on decisions and the systems they strive to influence. We demonstrate DA model development techniques to support the difficult task of deciding which interventions to choose, if any, given a collection of possible interventions to implement. The approach embraces complexity, makes recommendations that account for the imperfect state of available knowledge and identifies critical uncertainties that decision-supporting research should address. Such decision analysis is highly applicable in data-scarce environments.
The ```decisionSupport()``` function is part of the package ```decisionSupport``` [@R-decisionSupport] in the R programming environment [@R-base]. This package was used for a Monte-Carlo-based selection.
A number of specialized participatory approaches and modeling techniques helped us to construct and parameterize a model based on the knowledge of local expert stakeholders.
## Model structure
By coding a participatory conceptual model as a Monte Carlo simulation using the ```decisionSupport()``` function in the R package ```decisionSupport``` we were able to offer decision makers probable outcomes in terms of Net Present Value (NPV) and cash flow for the intervention decisions (including combined interventions) and to identify variables that most affected the overall outcome of the different decisions.
## Input table
The input table ```Example_input_table.csv``` contains the variables used in the model with distributions described by a 90% confidence interval, as well as the shape of the distribution.
```{r, echo = FALSE, results = 'asis'}
#format(scientific=FALSE)
options(scipen=999)
library(knitr)
library(kableExtra)
options(knitr.kable.NA = " ") #remove NA
options(knitr.table.format = "html")
#x<-as.data.frame(read.csv("Example_input_table.csv"))
#x[is.na(x)] <- "_" #replace NA with underscore
knitr::kable(read.csv("Example_input_table_decriptions.csv"), caption = "Table of expert estimates for all model variables. The column 'distribution' lists the distribution shapes used, including constant (const), 0-1 truncated normal (tnorm_0_1), positive normal (posnorm) and normal (norm)")%>%
kable_styling(full_width = T, font_size = 10)
```
```{r, include=FALSE}
library(decisionSupport)
make_variables<-function(est,n=1)
{ x<-random(rho=est, n=n)
for(i in colnames(x)) assign(i, as.numeric(x[1,i]),envir=.GlobalEnv)
}
make_variables(estimate_read_csv("Example_input_table.csv"))
```
# Implementing the model in R
To set up the analysis we first define the variable ```n_years``` to indicate the 30 year timeline for assessing the impacts of the intervention decision.
We define the probabilities of four ex-post risks (natural hazards, bad maintenance, and bad design) as possible impacts on the benefits probability, and three ex-ante risks (non-involvement of the local population, the institutions, and the donors) as possible impacts on the implementation of interventions.
## Chance events
Certain events can either occur or not, and values for dependent variables can depend on which of the cases occurs. The ```chance_event()``` function randomly simulates whether events occur and returns output values accordingly. The outputs can be single values or a series of values, with the option of introducing artificial variation into this dataset.
The identified ex-post and ex-ante risks were all assigned probability ranges from 0 to 1 and the ```chance_event()``` function was used to simulate a time series of their occurrence. The following lines of R code produce a series for the chance of the identified ex-ante or ex-post risk occurrences over 30 years (```n_years```). It simulates a random chance of the occurrence (value_if = 1) or not (value_if_not = 0) of the event.
### Chance events and ex-ante risks
We used the ```chance_event()``` function for simulation of ex-ante risks as impacts on the implementation of three interventions.
Probability distributions for the chance variables ```dredge_NonPopInvolv```, ```dredge_NonDonorsInvolv``` are defined in the input table ```Example_input_table.csv```.
#### Chance event of two ex-ante risks on the intervention
```{r}
dredge_NonPopInvolvEvent<-chance_event(dredge_NonPopInvolv,value_if = 1,value_if_not =0,n=1)
dredge_NonDonorsInvolvEvent<-chance_event(dredge_NonDonorsInvolv,1,value_if_not =0,n=1)
```
The ex-ante risk of lack of donor involvement was not considered valid for the dredging. This is because the main investment for the dredging intervention would be labor that, in principle, would be donated by the local communities.
#### Chance event of three ex-ante risks on the rock check dams intervention
```{r}
check_NonPopInvolvEvent<-chance_event(check_NonPopInvolv,value_if = 1,value_if_not =0,n=1)
check_NonInstInvolvEvent<-chance_event(check_NonInstInvolv,value_if = 1,value_if_not =0,n=1)
check_NonDonorsInvolvEvent<-chance_event(check_NonDonorsInvolv,value_if = 1,value_if_not = 0,n=1)
```
#### Chance event of three ex-ante risks on the buffer strips intervention
```{r}
buffer_NonPopInvolvEvent<-chance_event(buffer_NonPopInvolv,value_if = 1,value_if_not =0,n=1)
buffer_NonInstInvolvEvent<-chance_event(buffer_NonInstInvolv,value_if = 1,value_if_not = 0,n=1)
buffer_NonDonorsInvolvEvent<-chance_event(buffer_NonDonorsInvolv,value_if = 1,value_if_not = 0,n=1)
```
### Chance events and ex-post risks
We used the ```chance_event()``` function for simulation of the four ex-post risks as impacts on the benefits. Probability distributions for the chance variables ```NaturHazard```, ```BadMaintenance``` and ```BadDesign``` included in the code below, are all defined in the input table ```Example_input_table.csv```.
```{r}
HazardEvent<-chance_event(NaturHazard,value_if = 1,value_if_not =0,n=n_years)
BadMaintEvent<-chance_event(BadMaintenance,value_if = 1,value_if_not =0,n=n_years)
```
In the case of the ex-post risk of design problems (```BadDesign```) of the reservoir we used the option ```one_draw``` within the ```chance_event()``` function. ```one_draw``` is a boolean coefficient. By indicating that ```one_draw=TRUE``` the event occurrence ```BadDesign``` is determined only once with results applying to all elements of the results vector ```BadDesignEvent```.
```{r}
BadDesignEvent<-chance_event(BadDesign,value_if = 1,value_if_not =0,n=n_years, one_draw = TRUE)
```
## Variability in estimates
Many of the variables included in the model were considered to vary considerably over time and we chose to include this variation in the time series analyses. To do this we used the value varier function ```vv()``` to produce a time series that contains variation from a specified mean and coefficient of variation.
The probability distributions for the mean of the variable to be varied (the first argument in the ```vv()``` function) and the coefficient of variation (```var_CV```) are listed among the variables in ```Example_input_table.csv```. ```var_CV``` is assigned an upper and lower bound (5% and 20%).
The value varier function ```vv()``` was applied to the identified ex-ante risks on the irrigation area.
```{r}
Hazard_scaling_irrig_area<-1-HazardEvent*vv(Hazard_reduction_irrigated_area,var_CV,n=n_years)/100
BadMaint_scaling_irrig_area<-1-BadMaintEvent*vv(BadMaint_reduction_irrigated_area,var_CV,n=n_years)/100
BadDesign_scaling_irrig_area<-1-BadDesignEvent*vv(BadDesign_reduction_irrigated_area,var_CV,n=n_years)/100
```
### Simulation of common random draws
We also used ```vv()``` for simulation of common random draws for all intervention model runs.
#### Livestock
Livestock were calculated as Tropical Livestock Units (TLU), with the exclusion of the possibility of TLU inside the buffer zone if the buffer zone intervention was implemented. We used the ```vv()``` function to simulate expected variation in TLU and profits from TLU.
```{r}
TLU<-vv(TLU_no_buffer,var_CV,n_years)
TLU_profit<-vv(profit_per_TLU,var_CV,n_years)
```
#### Crops
Crops were grown in two different areas, one formal irrigation scheme downstream of the dam and one informal cropping area upstream of the dam.
![Map of the Lagdwenda reservoir in the Northern Volta Basin of Burkina Faso. The formal downstream irrigated cropping area (scheme 1) is outlined by the blue polygon at the bottom center. The informal upstream cropping area (scheme 2) is outlined by the blue polygon at the top.](Map.png){width=500px}
We used the ```vv()``` function to simulate expected variation crop benefits. Crop benefits were expected to vary with total cropping area (hectare) yields (ton per hectare) and profits (USD).
#### Crops in the buffer zone
**Fruits**
```{r}
precalc_buffer_fruit_benefits<-vv(buffer_fruit_area_ha,var_CV,n_years)*
vv(buffer_fruit_yield_t_ha,var_CV,n_years)*
vv(buffer_fruit_profit_USD_t,var_CV,n_years)
```
**Vegetables**
```{r}
precalc_buffer_vegetable_benefits<-vv(buffer_vegetable_area_ha,var_CV,n_years)*
vv(buffer_vegetable_yield_t_ha,var_CV,n_years)*
vv(buffer_vegetable_profit_USD_t,var_CV,n_years)
```
**Other rainfed crops**
```{r}
precalc_buffer_rainfed_crop_benefits<-vv(buffer_rainfed_crop_area_ha,var_CV,n_years)*
vv(buffer_rainfed_crop_yield_t_ha,var_CV,n_years)*
vv(buffer_rainfed_crop_profit_USD_t,var_CV,n_years)
```
#### Crops in the informal cropping area (upstream)
```{r}
precalc_scheme2_vegetable_yield_t_ha<-vv(scheme2_vegetable_yield_t_ha,var_CV,n_years)
precalc_scheme2_vegetable_profit_USD_t<-vv(scheme2_vegetable_profit_USD_t,var_CV,n_years)
precalc_scheme2_rice_yield_t_ha<-vv(scheme2_rice_yield_t_ha,var_CV,n_years)
precalc_scheme2_rice_profit_USD_t<-vv(scheme2_rice_profit_USD_t,var_CV,n_years)
```
#### Crops in the irrigation scheme (downstream)
**Vegetables**
```{r}
precalc_irrigation_scheme_vegetable_yield_t_ha<-vv(irrigation_scheme_vegetable_yield_t_ha,var_CV,n_years)
precalc_irrigation_scheme_vegetable_profit_USD_t<-vv(irrigation_scheme_vegetable_profit_USD_t,var_CV,n_years)
```
**Rice**
```{r}
precalc_irrigation_scheme_rice_yield_t_ha<-vv(irrigation_scheme_rice_yield_t_ha,var_CV,n_years)
precalc_irrigation_scheme_rice_profit_USD_t<-vv(irrigation_scheme_rice_profit_USD_t,var_CV,n_years)
precalc_proportion_irrigation_scheme_rice<-vv(proportion_irrigation_scheme_rice,var_CV,n_years)
```
#### Fish
We used the ```vv()``` function to simulate expected variation in benefits from fishing. The benefits from fishing were considered to vary according to ```var_CV```. Fish benefits were also expected to vary according to the possibility of natural hazards.
```{r}
precalc_fish_hazards<-HazardEvent*vv(Hazard_reduction_fish_perc/100,var_CV,n=n_years)
precalc_current_fish_value<-vv(current_annual_fish_value_USD,var_CV,n_years)
```
## Intervention loop
We defined an intervention loop centered around the three interventions (dredging, rock check dams, and buffer strips) and their various combinations.
```{r, eval=FALSE}
for (decision_dredging in c(FALSE,TRUE))
for (decision_check_dams in c(FALSE,TRUE))
for (decision_buffer_strips in c(FALSE,TRUE))
```
### Dredging
The model was programmed so that the implementation of dredging intervention would incur the costs of planning and doing the work, if it is not implemented then there would be no related costs.
```{r, eval=FALSE}
if(decision_dredging)
{dredging<-TRUE
dredging_PlanningCost<-TRUE
dredging_Cost<-TRUE} else
{dredging<-FALSE
dredging_PlanningCost<-FALSE
dredging_Cost<-FALSE}
```
If the dredging intervention was chosen but the local populations did not get involved, the costs of planning the dredging would still be incurred, but the costs of dredging the channels would not, since the intervention would not go ahead. In the case of the dredging intervention the lack of institutional involvement was assumed to have no effect.
```{r, eval=FALSE}
if (dredge_NonPopInvolvEvent){ dredging<-FALSE ; dredging_Cost<-FALSE}
if (dredge_NonDonorsInvolvEvent){
dredging<-FALSE ; dredging_Cost<-FALSE ; dredging_PlanningCost<-FALSE}
```
### Rock check dams
The model was programmed so that the implementation of the rock check dam intervention incurs the costs of planning and doing the work, if it is not implemented then there would be no related costs.
```{r, eval=FALSE}
if(decision_check_dams)
{check_dams<-TRUE
check_dams_PlanningCost<-TRUE
check_dams_Cost<-TRUE} else
{check_dams<-FALSE
check_dams_PlanningCost<-FALSE
check_dams_Cost<-FALSE}
```
If the rock check dam intervention was chosen but either the local populations, institutions, or donors did not get involved, the costs of planning the rock check dams would still be incurred, but the costs of building the rock check dams would not as the intervention would not go ahead.
```{r, eval=FALSE}
if (check_NonPopInvolvEvent){check_dams<-FALSE ; check_dams_Cost<-FALSE}
if (check_NonInstInvolvEvent){check_dams<-FALSE ; check_dams_Cost<-FALSE}
if (check_NonDonorsInvolvEvent){check_dams<-FALSE ; dredging_Cost<-FALSE ; check_dams_PlanningCost<-FALSE}
```
### Buffer strips
The model was programmed so that the implementation of the buffer strips incur the costs of planning and doing the work, if it is not implemented then there would be no related costs.
```{r, eval=FALSE}
if(decision_buffer_strips)
{buffer_strips<-TRUE
buffer_strips_PlanningCost<-TRUE
buffer_strips_Cost<-TRUE} else
{buffer_strips<-FALSE
buffer_strips_PlanningCost<-FALSE
buffer_strips_Cost<-FALSE}
```
If the buffer strip intervention was chosen but either the local populations, institutions, or donors did not get involved, the costs of planning the buffer strips would still be incurred, but the costs of planting the buffer strips would not, since the intervention would not go ahead.
```{r, eval=FALSE}
if (buffer_NonPopInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE}
if (buffer_NonInstInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE}
if (buffer_NonDonorsInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE ; buffer_strips_PlanningCost<-FALSE}
```
### Costs of the interventions
All interventions had a number of costs that were identified by the local experts. The probability distributions for these are listed among the variables in ```Example_input_table.csv```.
####Costs of dredging
```{r, eval=FALSE}
if(dredging_Cost) {cost_dredging<-dredging_supervision_cost+dredging_admin_cost+dredging_transport_cost+
dredging_culvert_supervision_cost
} else cost_dredging<-0
```
####Costs of rock check dams
```{r, eval=FALSE}
if(check_dams_Cost) {cost_check_dams<-check_supervision_cost+check_training_cost+check_tech_devices_cost+check_material_cost+
check_rocks_cost+check_transport_cost
} else cost_check_dams<-0
```
####Costs of buffer strips
```{r, eval=FALSE}
if(buffer_strips_Cost) {cost_buffer_strips<-buffer_adaptation_cost+buffer_tech_devices_cost+buffer_nursery_cost+buffer_wells_cost+
buffer_training_cost+buffer_mngmt_oprt_cost+buffer_mngmt_follow_cost+buffer_mngmt_audit_cost
} else cost_buffer_strips<-0
```
####Costs of planning
```{r, eval=FALSE}
if(dredging_PlanningCost) {plan_cost_dredging<-dredging_study_cost+dredging_communication_cost+dredging_culvert_feasibility_cost
} else plan_cost_dredging<-0
if(check_dams_PlanningCost) {plan_cost_check_dams<-check_location_cost+check_feasibility_cost+check_topobatymetry_cost+check_communication_cost
} else plan_cost_check_dams<-0
if(buffer_strips_PlanningCost) {plan_cost_buffer_strips<-buffer_communication_cost+buffer_zoning_cost
} else plan_cost_buffer_strips<-0
```
####Costs of maintenance
```{r, eval=FALSE}
maintenance_cost<-rep(0,n_years)
```
The ```vv()``` function was used to simulate the expected variation in the cost of maintenance for the rock check dams and buffer strip interventions.
```{r, eval=FALSE}
if(check_dams) maintenance_cost<-maintenance_cost+vv(maintenance_check_dams,var_CV,n_years)
if(buffer_strips) maintenance_cost<-maintenance_cost+vv(maintenance_buffer_strips,var_CV,n_years)
```
####Costs of interventions
```{r, eval=FALSE}
intervention_cost<-maintenance_cost
intervention_cost[1]<-intervention_cost[1]+cost_dredging+cost_check_dams+cost_buffer_strips+
plan_cost_dredging+plan_cost_check_dams+plan_cost_buffer_strips
```
### Decline in irrigable area over time
Because Examples accumulate in the reservoir, the dam gradually loses its capacity to store water, which may become a binding constraint for irrigation in the foreseeable future. Because of this, in the irrigation scheme downstream, the total irrigable area (area that can be irrigated given the water stock in the reservoir) was expected to decline over time. This decline in irrigable area would, however, be delayed by the various interventions. This was modeled as a sigmoid using the ```gompertz_yield``` function to simulate these delays in loss of irrigable area over time.
The Gompertz equation is written as:
f(t)=a • e^(-b • e^(-c • t)).
In this formula “a” is the maximum asymptotic ‘yield’ value (provided as an input, in our case “max-harvest=1”) and “b” and “c” are two parameters that can be identified from a set of two equations with two unknowns. Concretely, rather than estimating them directly, we define the equation for two points in time, with user-estimated inputs, and then solve the equations for “b” and “c”. This means, we say that
f(t1)=e^(-b • e^(-c • t1))=f1
and
f(t2)=e^(-b • e^(-c • t2))=f2
t1, t2, f1 and f2 are inputs (“a” is missing here, because we specify f1 and f2 as percentage of “a”, so that it drops out). These two equations with two unknowns can be solved mathematically to obtain “b” and “c”. That is what the Gompertz function does.
```{r, eval=FALSE}
gompertz_time1_time_until_irrigated_area_declines<-
sum(c(baseline_time_until_irrig_area_declines,
dredging*dredging_delay_of_irrig_area_decline,
check_dams*check_dam_delay_of_irrig_area_decline,
buffer_strips*buffer_strip_delay_of_irrig_area_decline))
gompertz_time2_time_until_irrigated_area_halved<-
sum(c(gompertz_time1_time_until_irrigated_area_declines,
baseline_start_losses_to_half_irrig_area_lost,
dredging*dredging_delay_of_irrig_area_halved,
check_dams*check_dam_delay_of_irrig_area_halved,
buffer_strips*buffer_strip_delay_of_irrig_area_halved))
```
The Gompertz function for loss of irrigable area in the downstream irrigation area was applied using the variables defined above. The irrigable area was likely to be highest in the first few years, thus we called for the highest value in the first year ```max-harvest=1```. Following this, irrigation area would gradually decrease, starting from ``gompertz_time1_time_until_irrigated_area_declines`` until the irrigation area was lost by half ```gompertz_time1_time_until_irrigated_area_declines ```.
```{r, eval=FALSE}
irrig_scheme1_area_share<-
1-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=gompertz_time1_time_until_irrigated_area_declines,
time_to_second_yield_estimate=gompertz_time2_time_until_irrigated_area_halved,
first_yield_estimate_percent=10,
second_yield_estimate_percent=50,
n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
```
We define a vector of the irrigation area over time from the output of the ```gompertz_yield``` function.
```{r, eval=FALSE}
irrig_scheme1_area_share<-irrig_scheme1_area_share[1:30]
irrig_scheme1_area<-current_irrig_area*irrig_scheme1_area_share
```
### Irrigation pipe blockage and clearing
Downstream the reservoir, water supply is achieved through a system of pipes underneath the dam’s barrier that allow the irrigation scheme to be watered. Examples regularly disrupt this system, blocking the pipes and preventing water from flowing into the agricultural area. Therefore, interventions that reduce sedimentation prevent the obstruction of pipes and generate benefits by securing irrigation use in the scheme. We used the ```gompertz_yield``` function to represent the decline in the irrigated area over time. The blockage was likely to be low for a few years after starting the irrigation, following which blockages would gradually increase until the irrigation pipes were no longer operational.
```{r, eval=FALSE}
gompertz_time2_time_until_pipe_blockage_occurs_every_second_year<-
sum(c(baseline_time_until_pipes_blocked_every_second_year,
dredging*dredging_delay_of_pipes_blocked_every_second_year,
check_dams*check_dam_delay_of_pipes_blocked_every_second_year,
buffer_strips*buffer_strip_delay_of_pipes_blocked_every_second_year))
```
We used the ```gompertz_yield``` function to define the risk of pipe blockage.
```{r, eval=FALSE}
risk_blockage<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=0,
time_to_second_yield_estimate=gompertz_time2_time_until_pipe_blockage_occurs_every_second_year,
first_yield_estimate_percent=100*current_risk_of_pipe_blockage,
second_yield_estimate_percent=50,
n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
risk_blockage[which(risk_blockage>1)]<-1
risk_blockage[which(risk_blockage<0)]<-0
```
We defined the ```time_to_second_yield_estimate``` for the ```gompertz_yield``` function by adding together the amount of time that the different interventions delay the pipe blockage given their occurrence.
```{r, eval=FALSE}
gompertz_time2_time_until_chance_cleared_50percent<-
sum(c(baseline_time_until_chance_cleared_50percent,
dredging*dredging_delay_of_time_until_chance_cleared_50percent,
check_dams*check_dam_delay_of_time_until_chance_cleared_50percent,
buffer_strips*buffer_strip_delay_of_time_until_chance_cleared_50percent))
```
We used the ```gompertz_yield``` function to define the chance of pipes being cleared.
```{r, eval=FALSE}
chance_cleared<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=0,
time_to_second_yield_estimate=gompertz_time2_time_until_chance_cleared_50percent,
first_yield_estimate_percent=100*current_chance_of_blocked_pipe_cleared,
second_yield_estimate_percent=50,
n_years=n_years, var_CV = 10,
no_yield_before_first_estimate = TRUE)
```
We then bound the chance of being cleared to between '0' and '1'.
```{r, eval=FALSE}
chance_cleared[which(chance_cleared>1)]<-1
chance_cleared[which(chance_cleared<0)]<-0
```
#### Creation of intermediate variables
We then created intermediate variables to calculate the area potentially irrigated, in the formal irrigation scheme, given the risk that pipes are blocked and/or cleared.
```{r, eval=FALSE}
pipe_clogging<-sapply(1:n_years,function(x) rbinom(1,1,risk_blockage[x]))
pipe_cleared<-sapply(1:n_years,function(x) rbinom(1,1,chance_cleared[x]))
pipe_blocked <- pipe_clogging
for (i in 2:length(pipe_blocked))
if (pipe_clogging[i] == 0)
if (pipe_blocked[i - 1] == 1)
if (!pipe_cleared[i] == 1) pipe_blocked[i] <- 1
```
We used the ```vv()``` function to simulate the ex-ante risks of formal irrigation area lost to pipe blockage.
```{r, eval=FALSE}
irrig_scheme1_irrigated_area_ex_ante<-irrig_scheme1_area*(1-pipe_blocked*vv(pipe_blocked_area_lost_perc/100,var_CV,n_years))
irrigated_area_scheme1<-irrig_scheme1_irrigated_area_ex_ante*
Hazard_scaling_irrig_area*BadMaint_scaling_irrig_area*
BadDesign_scaling_irrig_area
```
We then calculated the benefits from rice cultivation on the shore of the reservoir.
These were set to '0' if buffer strips were implemented.
```{r, eval=FALSE}
if (buffer_strips)
buffer_strip_cultivation<-TRUE else buffer_strip_cultivation<-FALSE
```
We then defined the time until the benefits from rice cultivation on the shore of the reservoir were gone by adding the baseline case to the benefits from rock check dams.
```{r, eval=FALSE}
scheme2_time_until_benefits_gone<-
scheme2_time_until_dredging_benefits_gone_baseline+
check_dams*check_dams_added_scheme2_area_benefit_time
```
We then used the ```gompertz_yield``` function to calculate the benefits from rice cultivation on the shore of the reservoir. These were set to '0' if buffer strips were implemented.
```{r, eval=FALSE}
scheme2_area_scaler<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=1,
time_to_second_yield_estimate=scheme2_time_until_benefits_gone,
first_yield_estimate_percent=100,
second_yield_estimate_percent=0,
n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
```
We used the output of the ```gompertz_yield``` function to calculate the area of the informal cropping area.
```{r, eval=FALSE}
scheme2_area_ha<-scheme2_area_no_dredging_ha*(1+
dredging*scheme2_area_scaler*dredging_bump_scheme2_area_perc/100)
```
With the exception of a small bump in yields from the dredging intervention, the total area of rice cultivation in the informal cropping scheme was expected to remain unchanged. This is because the water needed for rice cultivation is easily accessible in the rainy season.
The ```vv()``` function was used to simulate the variability in the rice benefits from the informal cropping area. In the case that the buffer strip intervention was implemented we expected no informal cropping area, as this would be within the buffer zone.
```{r, eval=FALSE}
scheme2_rice_benefits<-as.numeric(!buffer_strips)*
vv(scheme2_area_ha,var_CV,n_years)*
precalc_scheme2_rice_yield_t_ha*
precalc_scheme2_rice_profit_USD_t
```
The time until irrigation areas begin to decline in the informal cropping area as well as the time at which they have declined by half were defined for use in the ```gompertz_yield``` function.
```{r, eval=FALSE}
gompertz_time1_time_until_irrigated_area2_declines<-sum(c(baseline_time_until_irrig_area2_declines,
dredging*dredging_delay_of_irrig_area2_decline,
check_dams*check_dam_delay_of_irrig_area2_decline))
gompertz_time2_time_until_irrigated_area2_halved<-
sum(c(gompertz_time1_time_until_irrigated_area2_declines,
baseline_start_losses_to_half_irrig_area2_lost,
dredging*dredging_delay_of_irrig_area2_halved,
check_dams*check_dam_delay_of_irrig_area2_halved))
```
The ```gompertz_yield``` function was used to simulate the decline of the informal cropping area overtime.
```{r, eval=FALSE}
irrig_scheme2_area_share<-
1-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=gompertz_time1_time_until_irrigated_area2_declines,
time_to_second_yield_estimate=gompertz_time2_time_until_irrigated_area2_halved,
first_yield_estimate_percent=0,
second_yield_estimate_percent=50, n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
```
The outputs (declines in cropping area) from the ```gompertz_yield``` function were used to calculate the informal cropping area by multiplying by the original estimated informal cropping area ```scheme2_area_ha``` defined in the input table ```Example_input_table.csv```.
```{r, eval=FALSE}
scheme2_vegetable_area_ha<-scheme2_area_ha*irrig_scheme2_area_share
```
These were then used to calculate the benefits of crop production in the informal cropping area.
```{r, eval=FALSE}
scheme2_vegetable_benefits<-as.numeric(!buffer_strips)*
vv(scheme2_vegetable_area_ha,var_CV,n_years)*
precalc_scheme2_vegetable_yield_t_ha*
precalc_scheme2_vegetable_profit_USD_t
buffer_fruit_benefits<-as.numeric(buffer_strips)*precalc_buffer_fruit_benefits
buffer_vegetable_benefits<-as.numeric(buffer_strips)*precalc_buffer_vegetable_benefits
buffer_rainfed_crop_benefits<-as.numeric(buffer_strips)*precalc_buffer_rainfed_crop_benefits
rainy_season_rice_area_scheme1<-
irrigated_area_scheme1*precalc_proportion_irrigation_scheme_rice
rainy_season_vegetable_area_scheme1<-irrigated_area_scheme1-rainy_season_rice_area_scheme1
irrigation_season_rainy_season_benefits_scheme1<-rainy_season_rice_area_scheme1*
precalc_irrigation_scheme_rice_yield_t_ha*
precalc_irrigation_scheme_rice_profit_USD_t+
rainy_season_vegetable_area_scheme1*
precalc_irrigation_scheme_vegetable_yield_t_ha*
precalc_irrigation_scheme_vegetable_profit_USD_t
irrigation_season_dry_season_benefits_scheme1<-irrigated_area_scheme1*
precalc_irrigation_scheme_vegetable_yield_t_ha*
precalc_irrigation_scheme_vegetable_profit_USD_t
```
The total benefits of crop production were defined by adding all the benefits of agricultural production in the formal and informal cropping area and in the buffer zone.
```{r, eval=FALSE}
crop_production<-scheme2_rice_benefits+
scheme2_vegetable_benefits+
buffer_fruit_benefits+
buffer_vegetable_benefits+
buffer_rainfed_crop_benefits+
irrigation_season_rainy_season_benefits_scheme1+
irrigation_season_dry_season_benefits_scheme1
```
The amount of time to the fish population beginning to decline and the time it takes for the fish population to decline by half were defined for use in the ```gompertz_yield``` function.
```{r, eval=FALSE}
time_to_start_fish_decline<-sum(c(time_to_start_fish_decline_baseline,
dredging_delay_start_fish_decline,
check_dams_delay_start_fish_decline,
buffer_strips_delay_start_fish_decline))
time_to_fish_population_halved<-sum(c(time_to_start_fish_decline,
time_to_halve_fish_population_baseline,
dredging_delay_in_time_to_halve_fish_population,
check_dams_delay_in_time_to_halve_fish_population,
buffer_strips_delay_in_time_to_halve_fish_population))
```
The ```gompertz_yield``` function was used to simulate the decline in benefits from fishing overtime.
```{r, eval=FALSE}
fish_benefit_scaler<-
1-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=time_to_start_fish_decline,
time_to_second_yield_estimate=time_to_fish_population_halved,
first_yield_estimate_percent=0,
second_yield_estimate_percent=50, n_years=n_years, var_CV = 10,
no_yield_before_first_estimate = TRUE)
```
The outputs from the ```gompertz_yield``` function were used to calculate the risk adjusted benefits from fishing in the reservoir.
```{r, eval=FALSE}
risk_adjusted_fish_benefits<-fish_benefit_scaler*(1-precalc_fish_hazards)
```
The risk adjusted benefits from fishing were then used to calculate the benefits from fishing in the reservoir.
```{r, eval=FALSE}
Fish_benefits<-precalc_current_fish_value*risk_adjusted_fish_benefits
```
Benefits from additional livestock rearing through access to the reservoir were calculated by subtracting the TLU change if the buffer strip intervention is implemented. Buffer strips were expected to restrict access to the reservoir for livestock and thus reduce TLU.
```{r, eval=FALSE}
if(buffer_strips) TLU_intervention<-
TLU*(1+change_TLU_buffer_perc/100)
else TLU_intervention<-TLU
```
Benefits from additional livestock rearing through access to the reservoir were calculated as total TLU multiplied by profit per unit.
```{r, eval=FALSE}
livestock_benefits<-TLU_intervention*TLU_profit
```
Total benefits were then calculated as the benefits of crop production plus benefits of fishing and benefits of keeping livestock.
```{r, eval=FALSE}
total_benefits<-crop_production+Fish_benefits+livestock_benefits
```
Finally the net benefits were calculated by subtracting the intervention costs from the total benefits.
```{r, eval=FALSE}
net_benefits<-total_benefits-intervention_cost
if(decision_dredging & decision_check_dams & decision_buffer_strips) result_dredge_check_buff<-net_benefits
if(decision_dredging & decision_check_dams & !decision_buffer_strips) result_dredge_check_nbuff<-net_benefits
if(decision_dredging & !decision_check_dams & decision_buffer_strips) result_dredge_ncheck_buff<-net_benefits
if(decision_dredging & !decision_check_dams & !decision_buffer_strips) result_dredge_ncheck_nbuff<-net_benefits
if(!decision_dredging & decision_check_dams & decision_buffer_strips) result_ndredge_check_buff<-net_benefits
if(!decision_dredging & decision_check_dams & !decision_buffer_strips) result_ndredge_check_nbuff<-net_benefits
if(!decision_dredging & !decision_check_dams & decision_buffer_strips) result_ndredge_ncheck_buff<-net_benefits
if(!decision_dredging & !decision_check_dams & !decision_buffer_strips) result_ndredge_ncheck_nbuff<-net_benefits
```
The ```discount``` function was used to adjust the net benefits for time preference. With the attribute ```calculate_NPV()```, the function automatically calculates the Net Present Value (the sum of discounted values)
```{r, eval=FALSE}
NPV_dredge_check_buff<-discount(result_dredge_check_buff,discount_rate,calculate_NPV = TRUE)
NPV_dredge_check_nbuff<-discount(result_dredge_check_nbuff,discount_rate,calculate_NPV = TRUE)
NPV_dredge_ncheck_buff<-discount(result_dredge_ncheck_buff,discount_rate,calculate_NPV = TRUE)
NPV_dredge_ncheck_nbuff<-discount(result_dredge_ncheck_nbuff,discount_rate,calculate_NPV = TRUE)
NPV_ndredge_check_buff<-discount(result_ndredge_check_buff,discount_rate,calculate_NPV = TRUE)
NPV_ndredge_check_nbuff<-discount(result_ndredge_check_nbuff,discount_rate,calculate_NPV = TRUE)
NPV_ndredge_ncheck_buff<-discount(result_ndredge_ncheck_buff,discount_rate,calculate_NPV = TRUE)
NPV_ndredge_ncheck_nbuff<-discount(result_ndredge_ncheck_nbuff,discount_rate,calculate_NPV = TRUE)
```
The final lines of the function call for a list of NPV and cash flow for all interventions and combinations of interventions.
```{r, eval=FALSE}
return(list(NPV_dredge_check_buff=NPV_dredge_check_buff-NPV_ndredge_ncheck_nbuff,
NPV_dredge_check_nbuff=NPV_dredge_check_nbuff-NPV_ndredge_ncheck_nbuff,
NPV_dredge_ncheck_buff=NPV_dredge_ncheck_buff-NPV_ndredge_ncheck_nbuff,
NPV_dredge_ncheck_nbuff=NPV_dredge_ncheck_nbuff-NPV_ndredge_ncheck_nbuff,
NPV_ndredge_check_buff=NPV_ndredge_check_buff-NPV_ndredge_ncheck_nbuff,
NPV_ndredge_check_nbuff=NPV_ndredge_check_nbuff-NPV_ndredge_ncheck_nbuff,
NPV_ndredge_ncheck_buff=NPV_ndredge_ncheck_buff-NPV_ndredge_ncheck_nbuff))
```
# R function (decision model)
The full R function (decision model) for the Example intervention decision is given below. It calculates the Net Present Value (NPV) and cash flow for the implementation of the three identified Example management options. The decision model function is named ```Example_calc```. This function receives values for all the variables specified in the input table ```Example_input_table.csv```.
```{r, eval=FALSE}
Example_calc<-function(x, varnames)
{
### 4 ex-post risks, impacts on the benefits
HazardEvent<-chance_event(NaturHazard,1,0,n=n_years)
BadMaintEvent<-chance_event(BadMaintenance,1,0,n=n_years)
BadDesignEvent<-chance_event(BadDesign,1,0,n=n_years, one_draw = TRUE)
Hazard_scaling_irrig_area<-
1-HazardEvent*vv(Hazard_reduction_irrigated_area,var_CV,n=n_years)/100
BadMaint_scaling_irrig_area<-
1-BadMaintEvent*vv(BadMaint_reduction_irrigated_area,var_CV,n=n_years)/100
BadDesign_scaling_irrig_area<-
1-BadDesignEvent*vv(BadDesign_reduction_irrigated_area,var_CV,n=n_years)/100
### 3 ex-ante risks, impacts on the implementation of interventions
dredge_NonPopInvolvEvent<-chance_event(dredge_NonPopInvolv,1,0,n=1)
dredge_NonDonorsInvolvEvent<-chance_event(dredge_NonDonorsInvolv,1,0,n=1)
check_NonPopInvolvEvent<-chance_event(check_NonPopInvolv,1,0,n=1)
check_NonInstInvolvEvent<-chance_event(check_NonInstInvolv,1,0,n=1)
check_NonDonorsInvolvEvent<-chance_event(check_NonDonorsInvolv,1,0,n=1)
buffer_NonPopInvolvEvent<-chance_event(buffer_NonPopInvolv,1,0,n=1)
buffer_NonInstInvolvEvent<-chance_event(buffer_NonInstInvolv,1,0,n=1)
buffer_NonDonorsInvolvEvent<-chance_event(buffer_NonDonorsInvolv,1,0,n=1)
##calculation of common random draws for all intervention model runs
TLU<-vv(TLU_no_buffer,var_CV,n_years)
TLU_profit<-vv(profit_per_TLU,var_CV,n_years)
precalc_buffer_fruit_benefits<-vv(buffer_fruit_area_ha,var_CV,n_years)*
vv(buffer_fruit_yield_t_ha,var_CV,n_years)*
vv(buffer_fruit_profit_USD_t,var_CV,n_years)
precalc_buffer_vegetable_benefits<-vv(buffer_vegetable_area_ha,var_CV,n_years)*
vv(buffer_vegetable_yield_t_ha,var_CV,n_years)*
vv(buffer_vegetable_profit_USD_t,var_CV,n_years)
precalc_buffer_rainfed_crop_benefits<-vv(buffer_rainfed_crop_area_ha,var_CV,n_years)*
vv(buffer_rainfed_crop_yield_t_ha,var_CV,n_years)*
vv(buffer_rainfed_crop_profit_USD_t,var_CV,n_years)
precalc_scheme2_vegetable_yield_t_ha<-vv(scheme2_vegetable_yield_t_ha,var_CV,n_years)
precalc_scheme2_vegetable_profit_USD_t<-vv(scheme2_vegetable_profit_USD_t,var_CV,n_years)
precalc_scheme2_rice_yield_t_ha<-vv(scheme2_rice_yield_t_ha,var_CV,n_years)
precalc_scheme2_rice_profit_USD_t<-vv(scheme2_rice_profit_USD_t,var_CV,n_years)
precalc_irrigation_scheme_vegetable_yield_t_ha<-
vv(irrigation_scheme_vegetable_yield_t_ha,var_CV,n_years)
precalc_irrigation_scheme_vegetable_profit_USD_t<-
vv(irrigation_scheme_vegetable_profit_USD_t,var_CV,n_years)
precalc_irrigation_scheme_rice_yield_t_ha<-
vv(irrigation_scheme_rice_yield_t_ha,var_CV,n_years)
precalc_irrigation_scheme_rice_profit_USD_t<-
vv(irrigation_scheme_rice_profit_USD_t,var_CV,n_years)
precalc_proportion_irrigation_scheme_rice<-
vv(proportion_irrigation_scheme_rice,var_CV,n_years)
precalc_fish_hazards<-HazardEvent*vv(Hazard_reduction_fish_perc/100,var_CV,n=n_years)
precalc_current_fish_value<-vv(current_annual_fish_value_USD,var_CV,n_years)
for (decision_dredging in c(FALSE,TRUE))
for (decision_check_dams in c(FALSE,TRUE))
for (decision_buffer_strips in c(FALSE,TRUE))
{
### Intervention 1: dredging
if(decision_dredging)
{dredging<-TRUE
dredging_PlanningCost<-TRUE
dredging_Cost<-TRUE} else
{dredging<-FALSE
dredging_PlanningCost<-FALSE
dredging_Cost<-FALSE}
if (dredge_NonPopInvolvEvent){ dredging<-FALSE ; dredging_Cost<-FALSE}
# Non institutional involvement is assumed to have no effect #
if (dredge_NonDonorsInvolvEvent){ dredging<-FALSE ; dredging_Cost<-FALSE ; dredging_PlanningCost<-FALSE}
### Intervention 2: check_dams
if(decision_check_dams)
{check_dams<-TRUE
check_dams_PlanningCost<-TRUE
check_dams_Cost<-TRUE} else
{check_dams<-FALSE
check_dams_PlanningCost<-FALSE
check_dams_Cost<-FALSE}
if (check_NonPopInvolvEvent){check_dams<-FALSE ; check_dams_Cost<-FALSE}
if (check_NonInstInvolvEvent){check_dams<-FALSE ; check_dams_Cost<-FALSE}
if (check_NonDonorsInvolvEvent){check_dams<-FALSE ; dredging_Cost<-FALSE ; check_dams_PlanningCost<-FALSE}
### Intervention 3: buffer_strips
if(decision_buffer_strips)
{buffer_strips<-TRUE
buffer_strips_PlanningCost<-TRUE
buffer_strips_Cost<-TRUE} else
{buffer_strips<-FALSE
buffer_strips_PlanningCost<-FALSE
buffer_strips_Cost<-FALSE}
if (buffer_NonPopInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE}
if (buffer_NonInstInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE}
if (buffer_NonDonorsInvolvEvent){buffer_strips<-FALSE ; buffer_strips_Cost<-FALSE ; buffer_strips_PlanningCost<-FALSE}
###Costs
if(dredging_Cost) {cost_dredging<-
dredging_supervision_cost+dredging_admin_cost+dredging_transport_cost+
dredging_culvert_supervision_cost
} else cost_dredging<-0
if(check_dams_Cost) {cost_check_dams<-
check_supervision_cost+check_training_cost+check_tech_devices_cost+
check_material_cost+
check_rocks_cost+check_transport_cost
} else cost_check_dams<-0
if(buffer_strips_Cost) {cost_buffer_strips<-
buffer_adaptation_cost+buffer_tech_devices_cost+buffer_nursery_cost+
buffer_wells_cost+
buffer_training_cost+buffer_mngmt_oprt_cost+buffer_mngmt_follow_cost+
buffer_mngmt_audit_cost
} else cost_buffer_strips<-0
if(dredging_PlanningCost) {plan_cost_dredging<-
dredging_study_cost+dredging_communication_cost+
dredging_culvert_feasibility_cost
} else plan_cost_dredging<-0
if(check_dams_PlanningCost) {plan_cost_check_dams<-
check_location_cost+check_feasibility_cost+check_topobatymetry_cost+
check_communication_cost
} else plan_cost_check_dams<-0
if(buffer_strips_PlanningCost) {plan_cost_buffer_strips<-buffer_communication_cost+buffer_zoning_cost
} else plan_cost_buffer_strips<-0
maintenance_cost<-rep(0,n_years)
if(check_dams) maintenance_cost<-maintenance_cost+vv(maintenance_check_dams,var_CV,n_years)
if(buffer_strips) maintenance_cost<-maintenance_cost+vv(maintenance_buffer_strips,var_CV,n_years)
intervention_cost<-maintenance_cost
intervention_cost[1]<-intervention_cost[1]+cost_dredging+cost_check_dams+cost_buffer_strips+
plan_cost_dredging+plan_cost_check_dams+plan_cost_buffer_strips
###irrigation scheme 1 - area decline and delay by interventions
gompertz_time1_time_until_irrigated_area_declines<-
sum(c(baseline_time_until_irrig_area_declines,
dredging*dredging_delay_of_irrig_area_decline,
check_dams*check_dam_delay_of_irrig_area_decline,
buffer_strips*buffer_strip_delay_of_irrig_area_decline))
gompertz_time2_time_until_irrigated_area_halved<-
sum(c(gompertz_time1_time_until_irrigated_area_declines,
baseline_start_losses_to_half_irrig_area_lost,
dredging*dredging_delay_of_irrig_area_halved,
check_dams*check_dam_delay_of_irrig_area_halved,
buffer_strips*buffer_strip_delay_of_irrig_area_halved))
irrig_scheme1_area_share<-1-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=gompertz_time1_time_until_irrigated_area_declines,
time_to_second_yield_estimate=gompertz_time2_time_until_irrigated_area_halved,
first_yield_estimate_percent=10,
second_yield_estimate_percent=50, n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
irrig_scheme1_area_share<-irrig_scheme1_area_share[1:30]
irrig_scheme1_area<-current_irrig_area*irrig_scheme1_area_share
###irrigation scheme 1 - risk of blockage and pipe clearing
gompertz_time2_time_until_pipe_blockage_occurs_every_second_year<-
sum(c(baseline_time_until_pipes_blocked_every_second_year,
dredging*dredging_delay_of_pipes_blocked_every_second_year,
check_dams*check_dam_delay_of_pipes_blocked_every_second_year,
buffer_strips*buffer_strip_delay_of_pipes_blocked_every_second_year))
risk_blockage<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=0,
time_to_second_yield_estimate=gompertz_time2_time_until_pipe_blockage_occurs_every_second_year,
first_yield_estimate_percent=100*current_risk_of_pipe_blockage,
second_yield_estimate_percent=50,
n_years=n_years, var_CV = 0,
no_yield_before_first_estimate = TRUE)
risk_blockage[which(risk_blockage>1)]<-1
risk_blockage[which(risk_blockage<0)]<-0
gompertz_time2_time_until_chance_cleared_50percent<-
sum(c(baseline_time_until_chance_cleared_50percent,
dredging*dredging_delay_of_time_until_chance_cleared_50percent,
check_dams*check_dam_delay_of_time_until_chance_cleared_50percent,
buffer_strips*buffer_strip_delay_of_time_until_chance_cleared_50percent))
chance_cleared<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=0,
time_to_second_yield_estimate=gompertz_time2_time_until_chance_cleared_50percent,
first_yield_estimate_percent=100*current_chance_of_blocked_pipe_cleared,
second_yield_estimate_percent=50,
n_years=n_years, var_CV = 10,
no_yield_before_first_estimate = TRUE)
chance_cleared[which(chance_cleared>1)]<-1
chance_cleared[which(chance_cleared<0)]<-0
### Creation of intermediate variables
pipe_clogging<-sapply(1:n_years,function(x) rbinom(1,1,risk_blockage[x]))
pipe_cleared<-sapply(1:n_years,function(x) rbinom(1,1,chance_cleared[x]))
pipe_blocked <- pipe_clogging
for (i in 2:length(pipe_blocked))
if (pipe_clogging[i] == 0)
if (pipe_blocked[i - 1] == 1)
if (!pipe_cleared[i] == 1) pipe_blocked[i] <- 1
irrig_scheme1_irrigated_area_ex_ante<-
irrig_scheme1_area*(1-pipe_blocked*vv(pipe_blocked_area_lost_perc/100,var_CV,n_years))
### Impact of ex-post risks on irrigated area
irrigated_area_scheme1<-irrig_scheme1_irrigated_area_ex_ante*
Hazard_scaling_irrig_area*BadMaint_scaling_irrig_area*
BadDesign_scaling_irrig_area
### Benefits from rice cultivation on the shore of the reservoir (==0 if buffer strips implemented)
if (buffer_strips)
buffer_strip_cultivation<-TRUE else buffer_strip_cultivation<-FALSE
scheme2_time_until_benefits_gone<-scheme2_time_until_dredging_benefits_gone_baseline+
check_dams*check_dams_added_scheme2_area_benefit_time
scheme2_area_scaler<-gompertz_yield(max_harvest=1,
time_to_first_yield_estimate=1,
time_to_second_yield_estimate=scheme2_time_until_benefits_gone,
first_yield_estimate_percent=100,
second_yield_estimate_percent=0,