# WaterModels Result Data Format

## The Result Data Dictionary

WaterModels uses a dictionary to organize the results of a `solve_`

command. The dictionary uses strings as key values so it can be serialized to JSON for algorithmic data exchange. The data dictionary organization is designed to be consistent with The Network Data Dictionary.

At the top level, the results data dictionary is structured as follows:

```
{
"optimizer": <string>, # name of the solver used to solve the model
"termination_status": <type>, # optimizer status at termination
"dual_status": <type>, # optimizer dual status at termination
"primal_status": <type>, # optimizer primal status at termination
"solve_time": <float>, # reported solve time (in seconds)
"objective": <float>, # the final evaluation of the objective function
"objective_lb": <float>, # the final lower bound of the objective function (if available)
"solution": {...} # complete solution information (details below)
}
```

## Solution Data

The `"solution"`

subdictionary provides detailed information about the problem solution produced by the `solve_`

command. The solution is organized similarly to The Network Data Dictionary with the same nested structure and parameter names, when available. For example, for a single-network problem, `result["solution"]["pipe"]["1"]`

reports all the solution values associated with the pipe at index `"1"`

, e.g.,

```
{
"qn": 0.0,
"qp": 2.0,
"dhn": 0.0,
"q": 2.0,
"dhp": 0.033770,
"y": 1.0
}
```

Similarly, for a multinetwork problem, as an example, `result["nw"]["3"]["pump"]["2"]`

reports the solution values associated with the pump at pump index `"2"`

and time index `"3"`

, e.g.,

```
{
"qn": 0.0,
"c": 0.16850289352749692,
"g": 0.8372647243015188,
"P": 0.00016374541106904265,
"status": 1.0,
"qp": 0.36694422549881334,
"q": 0.36694422549881334,
"E": 1.8023959936938814e-6,
"y": 1.0
}
```

### Solution Data Schema

By default, all solution data are reported in per-unit (non-dimensionalized) units. Below are common outputs of the implemented optimization models, which are sometimes based on flow directionality:

```
{
"multiinfrastructure": <bool> # Whether or not the solution data is part of a broader multi-infrastructure solution.
"multinetwork": <bool> # Whether or not the network data describes a multinetwork (e.g., a time series of networks).
"per_unit": <bool>, # Whether the data is in per-unit (non-dimensionalized) or SI units.
"base_flow": <float>, # Base for non-dimensionalizing volumetric flow rate. SI units are cubic meters per second.
"base_head": <float>, # Base for non-dimensionalizing total hydraulic head head. SI units are meters.
"base_length": <float>, # Base for non-dimensionalizing length. SI units are meters.
"base_mass": <float>, # Base for non-dimensionalizing mass. SI units are kilograms.
"base_time": <float>, # Base for non-dimensionalizing time. SI units are seconds.
"node": {
"1": {
"h": <float>, # Total hydraulic head of the node. SI units are meters.
"p": <float> # Pressure head of the node. SI units are meters.
},
"2": {
...
},
...
},
"demand": {
"1": {
"q": <float> # Demanded volumetric flow rate at the demand point. SI units are cubic meters per second.
},
"2": {
...
},
...
},
"reservoir": {
"1": {
"q": <float> # Outgoing volumetric flow rate from the reservoir. SI units are cubic meters per second.
},
"2": {
...
},
...
},
"tank": {
"1": {
"V": <float>, # Volume of water contained by the tank. SI units are cubic meters.
"q": <float> # Outgoing volumetric flow rate from the reservoir. SI units are cubic meters per second.
},
"2": {
...
},
...
},
"pipe": {
"1": {
"q": <float>, # Volumetric flow rate transported through the pipe. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"dhp": <float>, # Total hydraulic head decrease in the positive direction of flow. SI units are meters.
"dhn": <float>, # Total hydraulic head decrease in the negative direction of flow. SI units are meters.
"y": <float> # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
},
"2": {
...
},
...
},
"des_pipe": {
"1": {
"q": <float>, # Volumetric flow rate transported through the design pipe. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"dhp": <float>, # Total hydraulic head decrease in the positive direction of flow. SI units are meters.
"dhn": <float>, # Total hydraulic head decrease in the negative direction of flow. SI units are meters.
"y": <float>, # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
"status": <float> # Pipe construction status, i.e., one if the pipe is constructed and zero otherwise.
},
"2": {
...
},
...
},
"short_pipe": {
"1": {
"q": <float>, # Volumetric flow rate transported through the short pipe. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"y": <float> # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
},
"2": {
...
},
...
},
"pump": {
"1": {
"q": <float>, # Volumetric flow rate transported through the pump. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"y": <float>, # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
"g": <float>, # Head gain (increase) from "node_fr" to "node_to" resulting from the pump. SI units are meters.
"c": <float>, # Cost of operating the pump over the time index (step) of interest. Standard units are currency.
"P": <float>, # Power consumed by the pump over the time index (step) of interest. SI units are Watts.
"E": <float>, # Energy consumption of the pump over the time index (step) of interest. SI units are Joules.
"status": <float> # Status of the pump, i.e., one if the pump is active and zero otherwise.
},
"2": {
...
},
...
},
"valve": {
"1": {
"q": <float>, # Volumetric flow rate transported through the valve. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"y": <float> # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
"status": <float> # Status of the valve, i.e., one if the valve is opened and zero otherwise.
},
"2": {
...
},
...
},
"regulator": {
"1": {
"q": <float>, # Volumetric flow rate transported through the regulator. SI units are cubic meters per second.
"qp": <float>, # Volumetric flow rate transported in the positive direction. SI units are cubic meters per second.
"qn": <float>, # Volumetric flow rate transported in the negative direction. SI units are cubic meters per second.
"y": <float> # Flow direction, i.e., one if flow is transported _from_ "node_fr" and zero otherwise.
"status": <float> # Status of the regulator, i.e., one if the regulator is active and zero otherwise.
},
"2": {
...
},
...
}
}
```

## Transforming Solution Data

Because the data dictionary and the solution dictionary have the same structure, the InfrastructureModels `update_data!`

helper function can be used to update a data dictionary with values from a solution, e.g.,

```
import InfrastructureModels
InfrastructureModels.update_data!(
data["nw"]["3"]["pump"]["1"],
result["solution"]["nw"]["3"]["pump"]["1"]
)
```

Note that, by default, all results are reported in a per-unit (non-dimensionalized) system. Additional data from WaterModels can be used to convert such data back to their dimensionalized forms. For example, the code block below translates a per-unit pump flow rate to SI units, then the more conventional units of liters per second.

```
# Get a pump volumetric flow rate solution in the per-unit system.
flow_per_unit = result["solution"]["nw"]["3"]["pump"]["1"]["q"]
# Get the per-unit scalar used to convert back to SI units.
base_flow = data["base_flow"]
# Compute the volumetric flow rate in SI units (cubic meters per second).
base_flow * flow_per_unit
# Compute the volumetric flow rate in liters per second.
base_flow * flow_per_unit * 1000.0
```

Note also that per-unit base quantities are also reported in the solution data dictionary for convenience, e.g.,

```
# Should return `true`.
result["solution"]["base_flow"] == data["base_flow"]
```

For convenience, solution data can be transformed to SI units using

`make_si_units!(result["solution"])`