# Resampling of swath data¶

Pyresample can be used to resample a swath dataset to a grid, a grid to a swath or a swath to another swath. Resampling can be done using nearest neighbour method, Guassian weighting, weighting with an arbitrary radial function.

## pyresample.image¶

The ImageContainerNearest and ImageContanerBilinear classes can be used for resampling of swaths as well as grids. Below is an example using nearest neighbour resampling.

```
>>> import numpy as np
>>> from pyresample import image, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> swath_con = image.ImageContainerNearest(data, swath_def, radius_of_influence=5000)
>>> area_con = swath_con.resample(area_def)
>>> result = area_con.image_data
```

For other resampling types or splitting the process in two steps use e.g. the functions in **pyresample.kd_tree** described below.

## pyresample.kd_tree¶

This module contains several functions for resampling swath data.

Note distance calculation is approximated with cartesian distance.

Masked arrays can be used as data input. In order to have undefined pixels masked out instead of
assigned a fill value set **fill_value=None** when calling the **resample_*** function.

### resample_nearest¶

Function for resampling using nearest neighbour method.

Example showing how to resample a generated swath dataset to a grid using nearest neighbour method:

```
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_nearest(swath_def, data,
... area_def, radius_of_influence=50000, epsilon=0.5)
```

If the arguments **swath_def** and **area_def** where switched (and **data** matched the dimensions of **area_def**) the grid of **area_def**
would be resampled to the swath defined by **swath_def**.

Note the keyword arguments:

**radius_of_influence**: The radius around each grid pixel in meters to search for neighbours in the swath.**epsilon**: The distance to a found value is guaranteed to be no further than (1 + eps) times the distance to the correct neighbour. Allowing for uncertanty decreases execution time.

If **data** is a masked array the mask will follow the neighbour pixel assignment.

If there are multiple channels in the dataset the **data** argument should be of the shape of the lons and lat arrays
with the channels along the last axis e.g. (rows, cols, channels). Note: the convention of pyresample < 0.7.4 is to pass
**data** in the form of (number_of_data_points, channels) is still accepted.

```
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> channel1 = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> channel2 = np.fromfunction(lambda y, x: y*x, (50, 10)) * 2
>>> channel3 = np.fromfunction(lambda y, x: y*x, (50, 10)) * 3
>>> data = np.dstack((channel1, channel2, channel3))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_nearest(swath_def, data,
... area_def, radius_of_influence=50000)
```

For nearest neighbour resampling the class **image.ImageContainerNearest** can be used as well as **kd_tree.resample_nearest**

### resample_gauss¶

Function for resampling using nearest Gussian weighting. The Gauss weigh function is defined as exp(-dist^2/sigma^2).
Note the pyresample sigma is **not** the standard deviation of the gaussian.
Example showing how to resample a generated swath dataset to a grid using Gaussian weighting:

```
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = kd_tree.resample_gauss(swath_def, data,
... area_def, radius_of_influence=50000, sigmas=25000)
```

If more channels are present in **data** the keyword argument **sigmas** must be a list containing a sigma for each channel.

If **data** is a masked array any pixel in the result data that has been “contaminated” by weighting of a masked pixel is masked.

Using the function **utils.fwhm2sigma** the sigma argument to the gauss resampling can be calculated from 3 dB FOV levels.

### resample_custom¶

Function for resampling using arbitrary radial weight functions.

Example showing how to resample a generated swath dataset to a grid using an arbitrary radial weight function:

```
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> wf = lambda r: 1 - r/100000.0
>>> result = kd_tree.resample_custom(swath_def, data,
... area_def, radius_of_influence=50000, weight_funcs=wf)
```

If more channels are present in **data** the keyword argument **weight_funcs** must be a list containing a radial function for each channel.

If **data** is a masked array any pixel in the result data that has been “contaminated” by weighting of a masked pixel is masked.

### Uncertainty estimates¶

Uncertainty estimates in the form of weighted standard deviation can be obtained from the **resample_custom** and **resample_gauss** functions.
By default the functions return the result of the resampling as a single numpy array. If the functions are given the keyword argument **with_uncert=True**
then the following list of numpy arrays will be returned instead: **(result, stddev, count)**. **result** is the usual result. **stddev** is the weighted standard deviation for each element in the result. **count** is the number of data values used in the weighting for each element in the result.

The principle is to view the calculated value for each element in the result as a weighted average of values sampled from a statistical variable.
An estimate of the standard deviation of the distribution is calculated using the unbiased weighted estimator given as
**stddev = sqrt((V1 / (V1 ** 2 + V2)) * sum(wi * (xi - result) ** 2))** where **result** is the result of the resampling. **xi** is the value of a contributing neighbour
and **wi** is the corresponding weight. The coefficients are given as **V1 = sum(wi)** and **V2 = sum(wi ** 2)**. The standard deviation is only calculated for elements in
the result where more than one neighbour has contributed to the weighting. The **count** numpy array can be used for filtering at a higher number of contributing neigbours.

Usage only differs in the number of return values from **resample_gauss** and **resample_custom**. E.g.:

```
>>> result, stddev, count = pr.kd_tree.resample_gauss(swath_def, ice_conc, area_def,
... radius_of_influence=20000,
... sigmas=pr.utils.fwhm2sigma(35000),
... fill_value=None, with_uncert=True)
```

- Below is shown a plot of the result of the resampling using a real data set:
- The corresponding standard deviations:
- And the number of contributing neighbours for each element:

Notice the standard deviation is only calculated where there are more than one contributing neighbour.

### Resampling from neighbour info¶

The resampling can be split in two steps:

First get arrays containing information about the nearest neighbours to each grid point. Then use these arrays to retrive the resampling result.

This approch can be useful if several datasets based on the same swath are to be resampled. The computational heavy task of calculating the neighbour information can be done once and the result can be used to retrieve the resampled data from each of the datasets fast.

```
>>> import numpy as np
>>> from pyresample import kd_tree, geometry
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> valid_input_index, valid_output_index, index_array, distance_array = \
... kd_tree.get_neighbour_info(swath_def,
... area_def, 50000,
... neighbours=1)
>>> res = kd_tree.get_sample_from_neighbour_info('nn', area_def.shape, data,
... valid_input_index, valid_output_index,
... index_array)
```

Note the keyword argument **neighbours=1**. This specifies only to consider one neighbour for each
grid point (the nearest neighbour). Also note **distance_array** is not a required argument for
**get_sample_from_neighbour_info** when using nearest neighbour resampling

### Segmented resampling¶

Whenever a resampling function takes the keyword argument **segments** the number of segments to split the resampling process in can be specified. This affects the memory footprint of pyresample. If the value of **segments** is left to default pyresample will estimate the number of segments to use.

### Speedup using pykdtree¶

pykdtree can be used instead of scipy to gain significant speedup for large datasets. See Using multiple processor cores.

## pyresample.bilinear¶

Compared to nearest neighbour resampling, bilinear interpolation produces smoother results near swath edges of polar satellite data and edges of geostationary satellites.

The algorithm is implemented from http://www.ahinson.com/algorithms_general/Sections/InterpolationRegression/InterpolationIrregularBilinear.pdf

Below is shown a comparison between image generated with nearest neighbour resampling (top) and with bilinear interpolation (bottom):

Click images to see the full resolution versions.

The *perceived* sharpness of the bottom image is lower, but there is more detail present.

### resample_bilinear¶

Function for resampling using bilinear interpolation for irregular source grids.

```
>>> import numpy as np
>>> from pyresample import bilinear, geometry
>>> target_def = geometry.AreaDefinition('areaD',
... 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (500, 100))
>>> lons = np.fromfunction(lambda y, x: 3 + x * 0.1, (500, 100))
>>> lats = np.fromfunction(lambda y, x: 75 - y * 0.1, (500, 100))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> result = bilinear.resample_bilinear(data, source_def, target_def,
... radius=50e3, neighbours=32,
... nprocs=1, fill_value=0,
... reduce_data=True, segments=None,
... epsilon=0)
```

The **target_area** needs to be an area definition with **proj4_string**
attribute.

Keyword arguments which are passed to **kd_tree**:

**radius**: radius around each target pixel in meters to search for neighbours in the source data**neighbours**: number of closest locations to consider when selecting the four data points around the target location. Note that this value needs to be large enough to ensure “surrounding” the target!**nprocs**: number of processors to use for finding the closest pixels**fill_value**: fill invalid pixel with this value. If**fill_value=None**is used, masked arrays will be returned**reduce_data**: do/don’t do preliminary data reduction before calculating the neigbour info**segments**: number of segments to use in neighbour search**epsilon**: maximum uncertainty allowed in neighbour search

The example above shows the default value for each keyword argument.

### Resampling from bilinear coefficients¶

As for nearest neighbour resampling, also bilinear interpolation can be split in two steps.

- Calculate interpolation coefficients, input data reduction matrix and mapping matrix
- Use this information to resample several datasets between these two areas/swaths

Only the first step is computationally expensive operation, so by
re-using this information the overall processing time is reduced
significantly. This is also done internally by the
**resample_bilinear** function, but separating these steps makes it
possible to cache the coefficients if the same transformation is done
over and over again. This is very typical in operational
geostationary satellite image processing. Note that the output shape is now
defined so that the result is reshaped to correct shape. This reshaping
is done internally in **resample_bilinear**.

```
>>> import numpy as np
>>> from pyresample import bilinear, geometry
>>> target_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)',
... 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> source_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> t_params, s_params, input_idxs, idx_ref = \
... bilinear.get_bil_info(source_def, target_def, radius=50e3, nprocs=1)
>>> res = bilinear.get_sample_from_bil_info(data.ravel(), t_params, s_params,
... input_idxs, idx_ref,
... output_shape=target_def.shape)
```

## pyresample.ewa¶

Pyresample makes it possible to resample swath data to a uniform grid using an Elliptical Weighted Averaging algorithm or EWA for short. This algorithm behaves differently than the KDTree based resampling algorithms that pyresample provides. The KDTree-based algorithms process each output grid pixel by searching for all “nearby” input pixels and applying a certain interpolation (nearest neighbor, gaussian, etc). The EWA algorithm processes each input pixel mapping it to one or more output pixels. Once each input pixel has been analyzed the intermediate results are averaged to produce the final gridded result.

The EWA algorithm also has limitations on how the input data is structured compared to the generic KDTree algorithms. EWA assumes that data in the array is organized geographically; adjacent data in the array is adjacent data geographically. The algorithm uses this to configure parameters based on the size and location of the swath pixels.

The EWA algorithm consists of two steps: ll2cr and fornav. The algorithm was originally part of the MODIS Swath to Grid Toolbox (ms2gt) created by the NASA National Snow & Ice Data Center (NSIDC). Its default parameters work best with MODIS L1B data, but it has been proven to produce high quality images from VIIRS and AVHRR data with the right parameters.

Note

This code was originally part of the Polar2Grid project. This documentation and the API documentation for this algorithm may still use references or concepts from Polar2Grid until everything can be updated.

### Gridding¶

The first step is called ‘ll2cr’ which stands for “longitude/latitude to column/row”. This step maps the pixel location (lon/lat space) into area (grid) space. Areas in pyresample are defined by a PROJ.4 projection specification. An area is defined by the following parameters:

- Grid Name
- PROJ.4 String (either lat/lon or metered projection space)
- Width (number of pixels in the X direction)
- Height (number of pixels in the Y direction)
- Cell Width (pixel size in the X direction in grid units)
- Cell Height (pixel size in the Y direction in grid units)
- X Origin (upper-left X coordinate in grid units)
- Y Origin (upper-left Y coordinate in grid units)

### Resampling¶

The second step of EWA remapping is called “fornav”, short for “forward navigation”. This EWA algorithm processes one input scan line at a time. The algorithm weights the effect of an input pixel on an output pixel based on its location in the scan line and other calculated coefficients. It can also handle swaths that are not scan based by specifying rows_per_scan as the number of rows in the entire swath. How the algorithm treats the data can be configured with various keyword arguments, see the API documentation for more information. Both steps provide additional information to inform the user how much data was used in the result. The first returned value of ll2cr tells you how many of the input swath pixels overlap the grid. The first returned value of fornav tells you how many grid points have valid data values in them.

### Example¶

Note

EWA resampling in pyresample is still in an alpha stage. As development continues, EWA resampling may be called differently.

```
>>> import numpy as np
>>> from pyresample.ewa import ll2cr, fornav
>>> area_def = geometry.AreaDefinition('areaD', 'Europe (3km, HRV, VTC)', 'areaD',
... {'a': '6378144.0', 'b': '6356759.0',
... 'lat_0': '50.00', 'lat_ts': '50.00',
... 'lon_0': '8.00', 'proj': 'stere'},
... 800, 800,
... [-1370912.72, -909968.64,
... 1029087.28, 1490031.36])
>>> data = np.fromfunction(lambda y, x: y*x, (50, 10))
>>> lons = np.fromfunction(lambda y, x: 3 + x, (50, 10))
>>> lats = np.fromfunction(lambda y, x: 75 - y, (50, 10))
>>> swath_def = geometry.SwathDefinition(lons=lons, lats=lats)
>>> # ll2cr converts swath longitudes and latitudes to grid columns and rows
>>> swath_points_in_grid, cols, rows = ll2cr(swath_def, area_def)
>>> # if the data is scan based, specify how many data rows make up one scan
>>> rows_per_scan = 5
>>> # fornav resamples the swath data to the gridded area
>>> num_valid_points, gridded_data = fornav(cols, rows, area_def, data, rows_per_scan=rows_per_scan)
```