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# Quadtree Grid-based Forecast Evaluation

This example demonstrates how to create a quadtree based single resolution-grid and multi-resolution grid. Multi-resolution grid is created using earthquake catalog, in which seismic density determines the size of a grid cell. In creating a multi-resolution grid we select a threshold (\(N_{max}\)) as a maximum number of earthquake in each cell. In single-resolution grid, we simply select a zoom-level (L) that determines a single resolution grid. The number of cells in single-resolution grid are equal to \(4^L\). The zoom-level L=11 leads to 4.2 million cells, nearest to 0.1x0.1 grid.

We use these grids to create and evaluate a time-independent forecast. Grid-based forecasts assume the variability of the forecasts is Poissonian. Therefore, poisson-based evaluations should be used to evaluate grid-based forecasts defined using quadtree regions.

- Overview:
- Define spatial grids
Multi-resolution grid

Single-resolution grid

- Load forecasts
Multi-resolution forecast

Single-resolution forecast

Load evaluation catalog

Apply Poissonian evaluations for both grid-based forecasts

Visualize evaluation results

## Load required libraries

Most of the core functionality can be imported from the top-level `csep`

package. Utilities are available from the
`csep.utils`

subpackage.

```
import numpy
import pandas
from csep.core import poisson_evaluations as poisson
from csep.utils import time_utils, plots
from csep.core.regions import QuadtreeGrid2D
from csep.core.forecasts import GriddedForecast
from csep.utils.time_utils import decimal_year_to_utc_epoch
from csep.core.catalogs import CSEPCatalog
```

## Load Training Catalog for Multi-resolution grid

We define a multi-resolution quadtree using earthquake catalog. We load a training catalog in CSEP and use that catalog to create a multi-resolution grid.
Sometimes, we do not the catalog in exact format as requried by pyCSEP. So we can read a catalog using Pandas and convert it
into the format accepable by PyCSEP. Then we instantiate an object of class CSEPCatalog by calling function `csep.core.regions.CSEPCatalog.from_dataframe()`

```
dfcat = pandas.read_csv('cat_train_2013.csv')
column_name_mapper = {
'lon': 'longitude',
'lat': 'latitude',
'mag': 'magnitude',
'index': 'id'
}
# maps the column names to the dtype expected by the catalog class
dfcat = dfcat.reset_index().rename(columns=column_name_mapper)
# create the origin_times from decimal years
dfcat['origin_time'] = dfcat.apply(lambda row: decimal_year_to_utc_epoch(row.year), axis=1)
# create catalog from dataframe
catalog_train = CSEPCatalog.from_dataframe(dfcat)
print(catalog_train)
```

```
Name: None
Start Date: 1976-01-01 00:00:00+00:00
End Date: 2013-01-01 00:00:00+00:00
Latitude: (-77.16000366, 87.01999664)
Longitude: (-180.0, 180.0)
Min Mw: 5.150024414
Max Mw: 9.08350563
Event Count: 28465
```

## Define Multi-resolution Gridded Region

Now use define a threshold for maximum number of earthquake allowed per cell, i.e. Nmax
and call `csep.core.regions.QuadtreeGrid_from_catalog()`

to create a multi-resolution grid.
For simplicity we assume only single magnitude bin, i.e. all the earthquakes greater than and equal to 5.95

```
mbins = numpy.array([5.95])
Nmax = 25
r_multi = QuadtreeGrid2D.from_catalog(catalog_train, Nmax, magnitudes=mbins)
print('Number of cells in Multi-resolution grid :', r_multi.num_nodes)
```

```
Number of cells in Multi-resolution grid : 3502
```

## Define Single-resolution Gridded Region

Here as an example we define a single resolution grid at zoom-level L=6. For this purpose
we call `csep.core.regions.QuadtreeGrid2D_from_single_resolution()`

to create a single resolution grid.

```
# For simplicity of example, we assume only single magnitude bin,
# i.e. all the earthquakes greater than and equal to 5.95
mbins = numpy.array([5.95])
r_single = QuadtreeGrid2D.from_single_resolution(6, magnitudes=mbins)
print('Number of cells in Single-Resolution grid :', r_single.num_nodes)
```

```
Number of cells in Single-Resolution grid : 4096
```

## Load forecast of multi-resolution grid

An example time-independent forecast had been created for this grid and provided the example forecast data set along with the main repository. We load the time-independent global forecast which has time horizon of 1 year. The filepath is relative to the root directory of the package. You can specify any file location for your forecasts.

```
forecast_data = numpy.loadtxt('example_rate_zoom=EQ10L11.csv')
#Reshape forecast as Nx1 array
forecast_data = forecast_data.reshape(-1,1)
forecast_multi_grid = GriddedForecast(data = forecast_data, region = r_multi, magnitudes = mbins, name = 'Example Multi-res Forecast')
#The loaded forecast is for 1 year. The test catalog we will use to evaluate is for 6 years. So we can rescale the forecast.
print(f"expected event count before scaling: {forecast_multi_grid.event_count}")
forecast_multi_grid.scale(6)
print(f"expected event count after scaling: {forecast_multi_grid.event_count}")
```

```
expected event count before scaling: 116.18568954606255
expected event count after scaling: 697.1141372763753
```

## Load forecast of single-resolution grid

We have already created a time-independent global forecast with time horizon of 1 year and provided with the reporsitory. The filepath is relative to the root directory of the package. You can specify any file location for your forecasts.

```
forecast_data = numpy.loadtxt('example_rate_zoom=6.csv')
#Reshape forecast as Nx1 array
forecast_data = forecast_data.reshape(-1,1)
forecast_single_grid = GriddedForecast(data = forecast_data, region = r_single,
magnitudes = mbins, name = 'Example Single-res Forecast')
# The loaded forecast is for 1 year. The test catalog we will use is for 6 years. So we can rescale the forecast.
print(f"expected event count before scaling: {forecast_single_grid.event_count}")
forecast_single_grid.scale(6)
print(f"expected event count after scaling: {forecast_single_grid.event_count}")
```

```
expected event count before scaling: 116.18568954606256
expected event count after scaling: 697.1141372763753
```

## Load evaluation catalog

We have a test catalog stored here. We can read the test catalog as a pandas frame and convert it into a format that is acceptable to PyCSEP Then we instantiate an object of catalog

```
dfcat = pandas.read_csv('cat_test.csv')
column_name_mapper = {
'lon': 'longitude',
'lat': 'latitude',
'mag': 'magnitude'
}
# maps the column names to the dtype expected by the catalog class
dfcat = dfcat.reset_index().rename(columns=column_name_mapper)
# create the origin_times from decimal years
dfcat['origin_time'] = dfcat.apply(lambda row: decimal_year_to_utc_epoch(row.year), axis=1)
# create catalog from dataframe
catalog = CSEPCatalog.from_dataframe(dfcat)
print(catalog)
```

```
Name: None
Start Date: 2014-01-01 00:00:00+00:00
End Date: 2019-01-01 00:00:00+00:00
Latitude: (-63.26, 74.39)
Longitude: (-179.23, 179.66)
Min Mw: 5.95047692260089
Max Mw: 8.27271203001144
Event Count: 651
```

## Compute Poisson spatial test and Number test

Simply call the `csep.core.poisson_evaluations.spatial_test()`

and `csep.core.poisson_evaluations.number_test()`

functions to evaluate the forecast using the specified
evaluation catalog. The spatial test requires simulating from the Poisson forecast to provide uncertainty. The verbose
option prints the status of the simulations to the standard output.

Note: But before we use evaluation catalog, we need to link gridded region with observed catalog. Since we have two different grids here, so we do it separately for both grids.

```
#For Multi-resolution grid, linking region to catalog.
catalog.region = forecast_multi_grid.region
spatial_test_multi_res_result = poisson.spatial_test(forecast_multi_grid, catalog)
number_test_multi_res_result = poisson.number_test(forecast_multi_grid, catalog)
#For Single-resolution grid, linking region to catalog.
catalog.region = forecast_single_grid.region
spatial_test_single_res_result = poisson.spatial_test(forecast_single_grid, catalog)
number_test_single_res_result = poisson.number_test(forecast_single_grid, catalog)
```

## Plot spatial test results

We provide the function `csep.utils.plotting.plot_poisson_consistency_test()`

to visualize the evaluation results from
consistency tests.

```
stest_result = [spatial_test_single_res_result, spatial_test_multi_res_result]
ax_spatial = plots.plot_poisson_consistency_test(stest_result,
plot_args={'xlabel': 'Spatial likelihood'})
ntest_result = [number_test_single_res_result, number_test_multi_res_result]
ax_number = plots.plot_poisson_consistency_test(ntest_result,
plot_args={'xlabel': 'Number of Earthquakes'})
```

**Total running time of the script:** (0 minutes 3.274 seconds)