Rainwater Harvesting System

Summary

This experiment investigates rainwater harvesting system. Box-Behnken design to maximize water captured and minimize overflow by tuning tank size, gutter area, and first-flush diverter volume.

The design varies 3 factors: tank liters (L), ranging from 500 to 5000, gutter area m2 (m2), ranging from 50 to 200, and first flush L (L), ranging from 10 to 80. The goal is to optimize 2 responses: capture pct (%) (maximize) and overflow pct (%) (minimize). Fixed conditions held constant across all runs include annual rainfall mm = 900, usage L day = 50.

A Box-Behnken design was chosen because it efficiently fits quadratic models with 3 continuous factors while avoiding extreme corner combinations — requiring only 15 runs instead of the 8 needed for a full factorial at two levels.

Quadratic response surface models were fitted to capture potential curvature and factor interactions. The RSM contour plots below visualize how pairs of factors jointly affect each response.

Key Findings

For capture pct, the most influential factors were first flush L (40.2%), gutter area m2 (31.6%), tank liters (28.3%). The best observed value was 73.6 (at tank liters = 2750, gutter area m2 = 125, first flush L = 45).

For overflow pct, the most influential factors were first flush L (42.3%), tank liters (35.5%), gutter area m2 (22.2%). The best observed value was 17.1 (at tank liters = 2750, gutter area m2 = 125, first flush L = 45).

Recommended Next Steps

Run confirmation experiments at the predicted optimal settings to validate the model.
Consider whether any fixed factors should be varied in a future study.

Experimental Setup

Factors

Factor	Low	High	Unit
`tank_liters`	500	5000	L
`gutter_area_m2`	50	200	m2
`first_flush_L`	10	80	L

Fixed: annual_rainfall_mm = 900, usage_L_day = 50

Responses

Response	Direction	Unit
`capture_pct`	↑ maximize	%
`overflow_pct`	↓ minimize	%

Configuration

use_cases/128_rainwater_harvesting/config.json

{
  "metadata": {
    "name": "Rainwater Harvesting System",
    "description": "Box-Behnken design to maximize water captured and minimize overflow by tuning tank size, gutter area, and first-flush diverter volume"
  },
  "factors": [
    {
      "name": "tank_liters",
      "levels": [
        "500",
        "5000"
      ],
      "type": "continuous",
      "unit": "L"
    },
    {
      "name": "gutter_area_m2",
      "levels": [
        "50",
        "200"
      ],
      "type": "continuous",
      "unit": "m2"
    },
    {
      "name": "first_flush_L",
      "levels": [
        "10",
        "80"
      ],
      "type": "continuous",
      "unit": "L"
    }
  ],
  "fixed_factors": {
    "annual_rainfall_mm": "900",
    "usage_L_day": "50"
  },
  "responses": [
    {
      "name": "capture_pct",
      "optimize": "maximize",
      "unit": "%"
    },
    {
      "name": "overflow_pct",
      "optimize": "minimize",
      "unit": "%"
    }
  ],
  "settings": {
    "operation": "box_behnken",
    "test_script": "use_cases/128_rainwater_harvesting/sim.sh"
  }
}

Experimental Matrix

The Box-Behnken Design produces 15 runs. Each row is one experiment with specific factor settings.

Run	`tank_liters`	`gutter_area_m2`	`first_flush_L`
1	2750	50	10
2	2750	125	45
3	5000	125	80
4	5000	125	10
5	2750	125	45
6	2750	125	45
7	500	125	80
8	5000	50	45
9	2750	50	80
10	5000	200	45
11	500	125	10
12	2750	200	80
13	500	50	45
14	500	200	45
15	2750	200	10

Step-by-Step Workflow

1

Preview the design

Terminal

$ doe info --config use_cases/128_rainwater_harvesting/config.json

2

Generate the runner script

Terminal

$ doe generate --config use_cases/128_rainwater_harvesting/config.json \
    --output use_cases/128_rainwater_harvesting/results/run.sh --seed 42

3

Execute the experiments

Terminal

$ bash use_cases/128_rainwater_harvesting/results/run.sh

4

Analyze results

Terminal

$ doe analyze --config use_cases/128_rainwater_harvesting/config.json

5

Get optimization recommendations

Terminal

$ doe optimize --config use_cases/128_rainwater_harvesting/config.json

6

Multi-objective optimization

With 2 competing responses, use --multi to find the best compromise via Derringer–Suich desirability.

Terminal

$ doe optimize --config use_cases/128_rainwater_harvesting/config.json --multi

7

Generate the HTML report

Terminal

$ doe report --config use_cases/128_rainwater_harvesting/config.json \
    --output use_cases/128_rainwater_harvesting/results/report.html

Features Exercised

Feature	Value
Design type	`box_behnken`
Factor types	`continuous` (all 3)
Arg style	`double-dash`
Responses	2 (capture_pct ↑, overflow_pct ↓)
Total runs	15

Analysis Results

Generated from actual experiment runs using the DOE Helper Tool.

Response: capture_pct

Top factors: first_flush_L (40.2%), gutter_area_m2 (31.6%), tank_liters (28.3%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
tank_liters	2	322.0142	161.0071	0.658	0.5438
gutter_area_m2	2	460.0717	230.0359	0.940	0.4299
first_flush_L	2	827.8042	413.9021	1.691	0.2440
Lack	of	Fit	6	783.1192	130.5199
Pure	Error	2	489.4467
Error	8	1272.5659	244.7233
Total	14	2882.4560	205.8897

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Half-Normal Plot of Effects

Model Diagnostics

Response: overflow_pct

Top factors: first_flush_L (42.3%), tank_liters (35.5%), gutter_area_m2 (22.2%).

ANOVA

Source	DF	SS	MS	F	p-value
Source	DF	SS	MS	F	p-value
tank_liters	2	259.8667	129.9334	0.933	0.4324
gutter_area_m2	2	127.0042	63.5021	0.456	0.6494
first_flush_L	2	511.2399	255.6200	1.835	0.2209
Lack	of	Fit	6	359.9451	59.9909
Pure	Error	2	278.6400
Error	8	638.5851	139.3200
Total	14	1536.6960	109.7640

Pareto Chart

Main Effects Plot

Normal Probability Plot of Effects

Normal probability plot for overflow_pct

Half-Normal Plot of Effects

Model Diagnostics

Response Surface Plots

3D surfaces fitted with quadratic RSM. Red dots are observed data points.

capture pct gutter area m2 vs first flush L

capture pct tank liters vs first flush L

capture pct tank liters vs gutter area m2

overflow pct gutter area m2 vs first flush L

overflow pct tank liters vs first flush L

overflow pct tank liters vs gutter area m2

Multi-Objective Optimization

When responses compete, Derringer–Suich desirability finds the best compromise. Each response is scaled to a 0–1 desirability, then combined via a weighted geometric mean.

Overall Desirability

D = 0.9545

Per-Response Desirability

Response	Weight	Desirability	Predicted	Dir
`capture_pct`	1.5	0.9545	73.60 0.9545 73.60 %	↑
`overflow_pct`	1.0	0.9545	17.10 0.9545 17.10 %	↓

Recommended Settings

Factor	Value
`tank_liters`	500 L
`gutter_area_m2`	50 m2
`first_flush_L`	45 L

Source: from observed run #10

Trade-off Summary

Sacrifice = how much worse than single-objective best.

Response	Predicted	Best Observed	Sacrifice
`overflow_pct`	17.10	17.10	+0.00

Top 3 Runs by Desirability

Run	D	Factor Settings
#4	0.8470	tank_liters=500, gutter_area_m2=200, first_flush_L=45
#15	0.7941	tank_liters=500, gutter_area_m2=125, first_flush_L=80

Model Quality

Response	R²	Type
`overflow_pct`	0.4966	linear

Full Multi-Objective Output

doe optimize --multi
============================================================
MULTI-OBJECTIVE OPTIMIZATION
Method: Derringer-Suich Desirability Function
============================================================

Overall desirability: D = 0.9545

Response                  Weight Desirability    Predicted  Direction
---------------------------------------------------------------------
capture_pct                  1.5       0.9545       73.60 %   ↑
overflow_pct                 1.0       0.9545       17.10 %   ↓

Recommended settings:
  tank_liters = 500 L
  gutter_area_m2 = 50 m2
  first_flush_L = 45 L
  (from observed run #10)

Trade-off summary:
  capture_pct: 73.60 (best observed: 73.60, sacrifice: +0.00)
  overflow_pct: 17.10 (best observed: 17.10, sacrifice: +0.00)

Model quality:
  capture_pct: R² = 0.4727 (linear)
  overflow_pct: R² = 0.4966 (linear)

Top 3 observed runs by overall desirability:
  1. Run #10 (D=0.9545): tank_liters=500, gutter_area_m2=50, first_flush_L=45
  2. Run #4 (D=0.8470): tank_liters=500, gutter_area_m2=200, first_flush_L=45
  3. Run #15 (D=0.7941): tank_liters=500, gutter_area_m2=125, first_flush_L=80

Full Analysis Output

doe analyze
=== Main Effects: capture_pct ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
first_flush_L           17.9964       3.7049            40.2%
gutter_area_m2          14.1500       3.7049            31.6%
tank_liters             12.6750       3.7049            28.3%

=== ANOVA Table: capture_pct ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
tank_liters                  2     322.0142     161.0071      0.658     0.5438
gutter_area_m2               2     460.0717     230.0359      0.940     0.4299
first_flush_L                2     827.8042     413.9021      1.691     0.2440
Lack of Fit                  6     783.1192     130.5199      0.533     0.7670
Pure Error                   2     489.4467     244.7233
Error                        8    1272.5659     244.7233
Total                       14    2882.4560     205.8897

=== Summary Statistics: capture_pct ===

tank_liters:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  2750                7    50.4286    17.7788    25.9000    73.6000
  500                 4    57.2000     8.3407    46.1000    65.8000
  5000                4    44.5250    12.3184    28.8000    57.0000

gutter_area_m2:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  125                 7    48.5286    13.4979    25.9000    65.8000
  200                 4    59.6000    14.1112    41.3000    73.6000
  50                  4    45.4500    15.6189    28.8000    60.5000

first_flush_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  10                  4    61.8250     9.9312    51.0000    73.6000
  45                  7    43.8286    14.1609    25.9000    60.5000
  80                  4    51.4500    13.6085    35.6000    67.1000

=== Main Effects: overflow_pct ===
Factor                   Effect    Std Error   % Contribution
--------------------------------------------------------------
first_flush_L           13.5143       2.7051            42.3%
tank_liters             11.3500       2.7051            35.5%
gutter_area_m2           7.0750       2.7051            22.2%

=== ANOVA Table: overflow_pct ===
Source                      DF           SS           MS          F    p-value
-----------------------------------------------------------------------------
tank_liters                  2     259.8667     129.9334      0.933     0.4324
gutter_area_m2               2     127.0042      63.5021      0.456     0.6494
first_flush_L                2     511.2399     255.6200      1.835     0.2209
Lack of Fit                  6     359.9451      59.9909      0.431     0.8209
Pure Error                   2     278.6400     139.3200
Error                        8     638.5851     139.3200
Total                       14    1536.6960     109.7640

=== Summary Statistics: overflow_pct ===

tank_liters:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  2750                7    33.0286    12.5800    17.1000    52.4000
  500                 4    28.1250     4.5945    24.0000    32.3000
  5000                4    39.4750     9.3803    31.1000    49.6000

gutter_area_m2:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  125                 7    34.8714     9.6809    24.0000    52.4000
  200                 4    28.6500    12.7921    17.1000    45.3000
  50                  4    35.7250    10.9006    24.3000    49.6000

first_flush_L:
  Level               N       Mean        Std        Min        Max
  ------------------------------------------------------------
  10                  4    25.9000     6.8103    17.1000    31.9000
  45                  7    39.4143    10.9260    24.3000    52.4000
  80                  4    30.5250     7.5288    20.3000    38.4000

Optimization Recommendations

doe optimize
=== Optimization: capture_pct ===
Direction: maximize

Best observed run: #10
  tank_liters = 2750
  gutter_area_m2 = 125
  first_flush_L = 45
  Value: 73.6

RSM Model (linear, R² = 0.3398, Adj R² = 0.1597):
  Coefficients:
    intercept                      +50.6600
    tank_liters                    -6.1000
    gutter_area_m2                 -1.5500
    first_flush_L                  -9.1000

RSM Model (quadratic, R² = 0.4701, Adj R² = -0.4838):
  Coefficients:
    intercept                      +56.5667
    tank_liters                    -6.1000
    gutter_area_m2                 -1.5500
    first_flush_L                  -9.1000
    tank_liters*gutter_area_m2     +1.0000
    tank_liters*first_flush_L      -1.2000
    gutter_area_m2*first_flush_L   -1.8500
    tank_liters^2                  +0.8417
    gutter_area_m2^2               -2.4583
    first_flush_L^2                -9.4583

  Curvature analysis:
    first_flush_L                  coef=-9.4583  concave (has a maximum)
    gutter_area_m2                 coef=-2.4583  concave (has a maximum)
    tank_liters                    coef=+0.8417  convex (has a minimum)

  Notable interactions:
    gutter_area_m2*first_flush_L   coef=-1.8500  (antagonistic)
    tank_liters*first_flush_L      coef=-1.2000  (antagonistic)
    tank_liters*gutter_area_m2     coef=+1.0000  (synergistic)

  Predicted optimum (from linear model, at observed points):
    tank_liters = 500
    gutter_area_m2 = 125
    first_flush_L = 10
    Predicted value: 65.8600

  Surface optimum (via L-BFGS-B, linear model):
    tank_liters = 500
    gutter_area_m2 = 50
    first_flush_L = 10
    Predicted value: 67.4100

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. first_flush_L  (effect: 18.4, contribution: 54.2%)
  2. tank_liters  (effect: 12.2, contribution: 35.8%)
  3. gutter_area_m2  (effect: 3.4, contribution: 10.0%)

=== Optimization: overflow_pct ===
Direction: minimize

Best observed run: #10
  tank_liters = 2750
  gutter_area_m2 = 125
  first_flush_L = 45
  Value: 17.1

RSM Model (linear, R² = 0.2906, Adj R² = 0.0972):
  Coefficients:
    intercept                      +33.4400
    tank_liters                    +4.0875
    gutter_area_m2                 -0.2375
    first_flush_L                  +6.2500

RSM Model (quadratic, R² = 0.5329, Adj R² = -0.3079):
  Coefficients:
    intercept                      +26.6000
    tank_liters                    +4.0875
    gutter_area_m2                 -0.2375
    first_flush_L                  +6.2500
    tank_liters*gutter_area_m2     -1.5500
    tank_liters*first_flush_L      -0.2750
    gutter_area_m2*first_flush_L   +1.4750
    tank_liters^2                  +1.6000
    gutter_area_m2^2               +1.5000
    first_flush_L^2                +9.7250

  Curvature analysis:
    first_flush_L                  coef=+9.7250  convex (has a minimum)
    tank_liters                    coef=+1.6000  convex (has a minimum)
    gutter_area_m2                 coef=+1.5000  convex (has a minimum)

  Notable interactions:
    tank_liters*gutter_area_m2     coef=-1.5500  (antagonistic)
    gutter_area_m2*first_flush_L   coef=+1.4750  (synergistic)

  Predicted optimum (from linear model, at observed points):
    tank_liters = 5000
    gutter_area_m2 = 125
    first_flush_L = 80
    Predicted value: 43.7775

  Surface optimum (via L-BFGS-B, linear model):
    tank_liters = 500
    gutter_area_m2 = 200
    first_flush_L = 10
    Predicted value: 22.8650

  Model quality: Weak fit — consider adding center points or using a different design.

Factor importance:
  1. first_flush_L  (effect: 15.8, contribution: 63.4%)
  2. tank_liters  (effect: 8.2, contribution: 32.9%)
  3. gutter_area_m2  (effect: 0.9, contribution: 3.7%)