updating the documentation

This package allows a user to simulate geothermal doublets providing the following parameters: 

- Top depth

- Thickness (mean & standard deviation)

- Porosity

- Permeability (mean & standard deviation)

- Temperature (Optional: if not provided, a temperature gradient will be used)

- Top depth [m +ive downwards]

- Thickness [m]

- Porosity [0-1]

- Permeability [0-1]

- Temperature [°C] (Optional: if not provided, a temperature gradient will be used)

The code will simulate a Geothermal doublet, utilizing ThermoGIS with DoubletCalc1D as the engine to produce values of:

## Other statistical Implementations

The ThermoGIS methodology `calculate_doublet_performance_stochastic` assumes that we know the net-to-gross, porosity and depth of the aquifer perfectly and simulates a range of values only over permeability, thickness (and thus; transmissivity).

This is because transmissivity is usually the most important aquifer property when determining performance and for the ThermoGIS project we make country-wide maps with simulations of 1km x 1km for the Netherlands; this means choices have to be made when selecting what properties to sample over.

However, if conducting a local study you may well want to also incorporate statistical sampling across other reservoir properties, it is relatively easy (and insightful) to use pythermogis to generate samples and make your own stochastic framework.

The ThermoGIS methodology `calculate_doublet_performance_stochastic` assumes that we know the net-to-gross, porosity and depth of the aquifer and simulates doublets over a range of values for transmissivity (calculated from permeability and thickness).

There are two main reasons for selecting this statistical framework:

1. It is fast as we only sample over one parameter (and for the ThermoGIS website we have to run a lot of simulations)

2. Transmissivity is usually the most important reservoir property when determining performance

3. 

However, if conducting a local study you may well want to also incorporate statistical uncertainties across other reservoir properties, it is easy (and insightful) to use pythermogis to generate samples and make your own stochastic framework.

Here is a simple example where you define probability distributions on your input parameters and then run simulations across random combinations of those input parameters before deriving statistics from those samples:

```python

from pythermogis import calculate_doublet_performance, calculate_pos

from pythermogis import calculate_doublet_performance, calculate_pos, plot_exceedance

import xarray as xr

from matplotlib import pyplot as plt

from pathlib import Path

import numpy as np

from os import path

import numpy as np

# output directory to write output to

output_data_path = Path(path.dirname(__file__), "resources") / "test_output" / "exceedance_example"

axes[1, 1].legend()

plt.savefig(output_data_path / "exceedance_probabilities.png")

```

Firstly, we define how many simulations we want to run (1000 simulations takes approximately 10 seconds on an average laptop).

Then we define the range of values we want our simulations to test, here thickness, porosity and net-to-gross are defined as uniform distributions while permeability and depth are normal distributions.

We generate samples for each reservoir property and construct a Dataset with the dimension samples:

![Distributions](../images/reservoir_distributions.png)

*Figure: The sampled distributions for each reservoir property*

Then 1000 simulations are run and outputted to the simulations Dataset:

![Samples](../images/simulation_results.png)

*Figure: Distribution of simulation results across a few parameters of interest*

And then from these samples percentiles are calculated across each output parameter, from which exceedance probability graphs can be made:

![Samples](../images/exceedance_probabilities.png)

*Figure: Exceedance probabilities; for example this shows that their is a 30% chance that net-present-value is greater than 0*