# Observing Etna Eruption¶

This use case was prepared with support from European Space Agency.

## 1 Introduction¶

In early spring 2017, biggest Sicilian volcano - Etna - awakened and erupted several times. The Etna eruption started on January 23rd 2017 but intensified after February 27th and the activity continued till late April.

In this exercise we will demonstrate how such events can be observed using satellite images. We will utilize imagery acquired from satellites Sentinel 2 (s2) and Landsat 8 (l8). We will introduce the basic physical concepts that we need in order to understand the example but we will not go into theoretical details.

First, we need to set up two "technical" things:

1) The text and code you see here are written in Jupyter Notebook. You will need to "execute cells" to see satellite images. You can do that by clicking on the cell with code and then pressing "ctrl + Enter".

2) We will use Sentinel Hub to download the data. A provisional access is already provided for your convenience (i.e. a long number assigned to INSTANCE_ID variable) but it will support only limited number of requests to avoid abuse. If you want to play around and request more data, you will need to create your own account and replace the value of INSTANCE_ID with your own one. Check instructions to do so here.

Right below is a first cell that needs to be executed. Click on it and press: "ctrl + Enter".

In [23]:
INSTANCE_ID = 'cf8091e5-2837-463e-b45d-8dc0b121cad7'

# Set options
%matplotlib inline


A text "In [\*]" before a the cell indicates that the cell is being executed. When the "\*" turns into a number, e.g. "In [3]" it means that the cell was successfully executed and you can see the results of execution below the cell. Some cells do not return any results but just set up things that will be used latter.The execution of some cells might take a while, which is also indicated with an “hourglass icon” in the name of your browser's tab: </i>

Back to Etna now. We will download satellite data from the Sentinel Hub using sentinelhub-py. To prepare a request for downloading, we follow the example in sentinelhub-py documentation, where one can find the descriptions of all parameters. We adjusted the values so that we will download all "true color" images of Etna acquired between February 27th 2017 and April 18th 2017. The coordinates of bounding box of the area of interest (AOI) can be read from any online map, which displays the coordinates of current position of mouse (and defines coordinate system to which they refer). We used EO Browser.

In [24]:
from sentinelhub import (WmsRequest, WcsRequest, MimeType, CRS, BBox,
DataSource, CustomUrlParam, geo_utils)
import datetime
import numpy as np
import requests as  r

etna_bbox_web_mercator = [14.96, 37.70, 15.06, 37.78]
etna_bbox = BBox(bbox=etna_bbox_web_mercator, crs=CRS.WGS84)

true_color_request_s2 = WmsRequest(data_folder='data',
layer='TRUE-COLOR-S2-L1C',
bbox=etna_bbox,
time=('2017-02-27','2017-04-18'),
width=512,
maxcc=0.8,
instance_id=INSTANCE_ID,
custom_url_params={
CustomUrlParam.SHOWLOGO: False})

true_color_img_s2 = true_color_request_s2.get_data(save_data=True)
true_color_dates_s2 = true_color_request_s2.get_dates()

print('We downloaded %d images, each one acquired on a different date (i.e. \
time series). ' % len(true_color_img_s2))
print('Single image is of type {} and has a shape {}. First two dimensions \
bands.'.format(type(true_color_img_s2[-1]), true_color_img_s2[-1].shape))

We downloaded 11 images, each one acquired on a different date (i.e. time series).
Single image is of type <class 'numpy.ndarray'> and has a shape (516, 512, 3). First two dimensions indicate the size of downloaded image in pixels and the last is a number of downloaded bands.


Important: If the execution of the previous cell is not finished (i.e. the "In [\*]" still shows "\*") you won’t be able to continue. You might need to wait a while.

To have a means to display the downloaded images appropriately, we will prepare a function "plot_image", which will add labels and scale bar to the image. Run the cell below to display one of the images (we selected the 4th image in the time series, since it shows smoke and snow. You could choose any other image by changing the value of "display_image" variable).

In [25]:
from matplotlib_scalebar.scalebar import ScaleBar
import matplotlib.pyplot as plt

def plot_image(image, bbox, factor=1):
"""
Utility function for plotting RGB images.

:param image: image to be plotted
:type image: numpy array
:param bbox: bounding box object, which will be used to set the
extent of the plot
:type bbox: sentinelhub.common.bbox
:param factor: factor
:type factor: int
"""
fig = plt.subplots(nrows=1, ncols=1, figsize=(9, 9))

bbox_polygon = bbox.get_polygon()

if np.issubdtype(image.dtype, np.floating):
plt.imshow(np.minimum(image * factor, 1), extent=[
bbox_polygon[0][0], bbox_polygon[2][0],
bbox_polygon[0][1], bbox_polygon[2][1]])
else:
plt.imshow(image, extent=[bbox_polygon[0][0],
bbox_polygon[2][0],
bbox_polygon[0][1],
bbox_polygon[2][1]])

if bbox.get_crs() == CRS.WGS84 :
plt.xlabel('longitude [°]')
plt.ylabel('latitude [°]')
else:
plt.xlabel('easting  [m]')
plt.ylabel('northing [m]')

width = image.shape[1]
height = image.shape[2]
resx, resy = geo_utils.bbox_to_resolution(bbox,
width,
height)
scalebar = ScaleBar((width*resx)/(bbox_polygon[2][0]
-bbox_polygon[0][0]),
'm',
location='lower right',
box_alpha=0.9)

display_image = 4
plot_image(true_color_img_s2[display_image], etna_bbox)
plt.title('Etna, true color image acquired with Sentinel 2 on '+ str(
true_color_dates_s2[display_image].date()));
print()


This is how Etna looks like from space! This visualization is called a true color composite because the scene appears as it would be seen by a human observer (i.e. snow and clouds appear white, soil appears dark, etc.). To be honest, it is difficult to interpret this concrete image. We notice different white surfaces, which might be either snow, smoke or clouds. If we look more carefully we can notice a shadow on the right lower corner indicating that there is a mountain in the image. Knowing that this is Etna, we can recognize a crater and smoke fuming out of the crater. Lava is dark thus it is impossible to distinguish it from soil or see it through the smoke.

But we know lava is much hotter than soil. Could we make use of the lava's "hotness" to see it?

## 2 Some Background¶

### 2.1 Wien's Displacement Law¶

Every object, which is hotter than absolute zero (0° Kelvin), emits electromagnetic radiation - the hotter the object, the higher the frequency at which the most of radiation is emitted (i.e. the shorter the wavelength $\lambda$). This relationship is described by Wien's displacement law:

\begin{equation*} \lambda_{max}=\frac{b}{T} \end{equation*}

where:

• $\lambda_{max}$ is λ, at which the blackbody with temperature $T$ emits the most of electromagnetic energy
• $b = 2.9*10^{-3}$ is Wien's displacement constant
• $T$ is temperature of the blackbody

We will illustrate this in a figure below but before that let's talk about "satellite's bands".

### 2.2 Satellite's Bands¶

Another concept that we need to familiarize ourselves with is the concept of satellite bands. Sensors carried by satellites like Sentinel-2 or Landsat 8 can image our Earth in different parts of the electromagnetic spectrum. The light that we see as humans can generally be thought of as having three components or bands: red, blue and green. Remember the true color image from earlier? That is a representation of the images acquired in red, blue and green bands of the satellite. These bands roughly match our own human vision and the image therefore appears in the same way as it would be seen by a human observer in space. But satellites can see much more of the electromagnetic spectrum than we humans can. For example, Sentinel-2 is also observing the near infrared and shortwave infrared parts of the electromagnetic spectrum. These correspond to much longer wavelengths than the visible light. Below is a table of Sentinel-2's and Landsat 8 bands, their central wavelength and spatial resolutions.

In [26]:
from IPython.core.display import HTML

# Satellite Bands with their wavelengths
# S2 bands, (band name, S2A central wavelength, S2A bandwidth, ...)
bands_s2 =[ ("B01", 442.7, 21, 442.2, 21, 60),
("B02", 492.4, 66, 492.1, 66, 10),
("B03", 559.8, 36, 559.0, 36, 10),
("B04", 664.6, 31, 664.9, 31, 10),
("B05", 704.1, 15, 703.8, 16, 20),
("B06", 740.5, 15, 739.1, 15, 20),
("B07", 782.8, 20, 779.7, 20, 20),
("B08", 832.8, 106, 832.9, 106, 10),
("B8a", 864.7, 21, 864.0, 22, 20),
("B09", 945.1, 20, 943.2, 21, 60),
("B10", 1373.5, 31, 1376.9, 30, 60),
("B11", 1613.7, 91, 1610.4, 94, 20),
("B12", 2202.4, 175, 2185.7, 185, 20)]

#L8 bands, (band name, min band wavelength, max band wavelength)
bands_l8 = [("B01", 435, 451, 30),
("B02", 452, 512, 30),
("B03", 533, 590, 30),
("B04", 636, 673, 30),
("B05", 851, 879, 30),
("B06", 1566, 1651, 30),
("B07", 2107, 2294, 30),
("B08", 503, 676, 15),
("B09", 1363, 1384, 30),
("B10", 10600, 11190, 100),
("B11", 11500, 12510, 100)]

display(HTML(
'<h3>Sentinel-2</h3><table><tr><th>Band</th><th>Central wavelength [nm]</th><th>Spatial Resolution [m]</th></tr><tr>{}</tr></table>'.format(
'</tr><tr>'.join(
'<td>{}</td>'.format('</td><td>'.join(str(_) for _ in (row[0],row[1],row[5]))) for row in bands_s2)
)
))

display(HTML(
'<h3>Landsat 8</h3><table><tr><th>Band</th><th>Central wavelength [nm]</th><th>Spatial Resolution [m]</th></tr><tr>{}</tr></table>'.format(
'</tr><tr>'.join(
'<td>{}</td>'.format('</td><td>'.join(str(_) for _ in (row[0],(row[1]+row[2])/2,row[3] ))) for row in bands_l8)
)
))


### Sentinel-2

BandCentral wavelength [nm]Spatial Resolution [m]
B01442.760
B02492.410
B03559.810
B04664.610
B05704.120
B06740.520
B07782.820
B08832.810
B8a864.720
B09945.160
B101373.560
B111613.720
B122202.420

### Landsat 8

BandCentral wavelength [nm]Spatial Resolution [m]
B01443.030
B02482.030
B03561.530
B04654.530
B05865.030
B061608.530
B072200.530
B08589.515
B091373.530
B1010895.0100
B1112005.0100

By plotting radiation curves for objects with different temperatures we can present the "displacements" of their maximum. S2 and L8 bands can also be visualized so that their position in spectrum can be compared to radiation curves.

In [31]:
# @hidden_cell
import scipy.constants as sc
import ipywidgets as widgets
from IPython.display import display, HTML

# Constants
h = sc.Planck
c = sc.speed_of_light
kb = sc.Boltzmann
e = np.exp(1)
b = sc.Wien

hc_kb = h*c/kb

def planck_law (w, T):
#factor1 = 2 * h * c**2 / w**5
factor1 = 2 * h * np.power(c,2) / np.power(w,5)
factor2 = 1 / ( np.power(e,( hc_kb / (w*T))) - 1 )
return factor1 * factor2

def wien_law (T):
alfa_max = b / T
return alfa_max

def draw_curve (ax, wavelengths, T, color):
ax.plot(list(wavelengths), planck_law (wavelengths* 10**(-9),
T), color=color)
xmax = wien_law (T) * 10**(9)
ymax = planck_law (wien_law(T), T)
if ax.get_xlim()[1] > xmax:
ax.plot(xmax, ymax, 'o', color=color)
ax.text(xmax*1.03, ymax*1.01, str(T-273) + "°C", fontsize=14, color=color)

def draw_spectrum (custom_temperature, draw_curves, draw_RGB, draw_s2, draw_l8):
fig, ax = plt.subplots (2, 1, figsize=(16, 12))

# Generate data
wavelengths = np.linspace(100, 13000, 400) #(start, stop, number) in nm

# Set some global characteristics of the plots
ax[0].set_title("Overview plot")
ax[1].set_title("Detailed plot for wavelengths up to 2500 nm")
ax[1].set_xlim(0, 13000);
ax[1].set_xlim(0, 2500);

# The same thing will be drawn in all subplots but we set different limits
# for x axes for each subplot to achive "zoom in" effect.
for a in ax:
if custom_temperature:
draw_curve (a, wavelengths, custom_temperature + 273, '#ff1a1a')

if draw_curves:
for T in [6000, 5000, 4000, 3000, 1000, 300]:
draw_curve (a, wavelengths, T + 273, '#000000')

if draw_RGB:
a.axvspan(590, 750, facecolor='r', alpha=0.2)
a.axvspan(495, 590, facecolor='g', alpha=0.2)
a.axvspan(400, 495, facecolor='b', alpha=0.2)

if draw_s2:
for band in bands_s2:
a.axvspan((band[1] - band[2]/2) , (band[1] + band[2]/2),
facecolor='#2ca02c', alpha=0.4)

if draw_l8:
for band in bands_l8[:]:
a.axvspan( band[1], band[2], facecolor="#3366ff", alpha=0.4)

a.set_xlabel('Wavelength [nm]')
a.set_ylabel(r'Spectral radiance [W·sr$^\mathsf{-1}$·m$^\mathsf{-3}$]')

# Widgets
style = {'description_width': 'initial'}
text_temp = widgets.BoundedIntText(
value=5500,
min=-10,
max=10000,
step=1,
description='Add red curve for temperature [°C]:',
disabled=False,
style=style
)

toggle_curves = widgets.Checkbox(
value=True,
disabled=False
)

toggle_s2 = widgets.Checkbox(
value=False,
description='S2 bands',
disabled=False
)

toggle_l8 = widgets.Checkbox(
value=False,
description='L8 bands',
disabled=False
)

toggle_RGB = widgets.Checkbox(
value=True,
description='Visible part of spectrum',
disabled=False
)

# Make the plot interactive
widgets.interact(draw_spectrum,
custom_temperature=text_temp,
draw_curves=toggle_curves,
draw_RGB=toggle_RGB,
draw_s2=toggle_s2,
draw_l8=toggle_l8);


Both figures above show radiation curves of blackbodies at different temperatures (black) and visible part of the spectrum (blue, green and read colors in background). The curves are presentation of Planck's Law. Dots represent maximum of each curve. Note how curves with lower temperatures have maximum at longer wavelengths (= what Wien Displacement Law says). The Sun's temperature is approximately 5500 °C and its radiation has a peak around 500 nm, which corresponds to visible part of the spectrum. Whereas Earth's radiation peaks around 10000 nm, it does not emit visible light thus we cannot see it with naked eye unless it is illuminated by the Sun (or some other source of visible light).

#### 2.2.1 Play with the graph¶

1) Try to insert typical temperatures of some objects in the textbox and click outside of it. Try, e.g.:

• 10000 °C approx. temperature of Sirius, the brightest star
• 5500 °C approx. temperature of the Sun
• 450 °C - 1000 °C approx. temperature of lava right after eruption
• 200 °C temperature in the oven when the bread is baked
• 0 °C temperature at which water freezes

The radiation curve for blackbody with the selected temperature will be added to the graph in red color. If needed turn off "Radiation curves" so that the graph limits will adjust to the red curve and observe how the maximum of the curve moves relative to wavelengths depending on the temperature.

2) Checkboxes below can be used to turn off/on specific information. Try turning on/off S2 and L8 bands to see in which part of the spectrum satellites detect the radiation.

3) Try to turn off "Radiation Curves" and insert 700 °C (approx. temperature of lava) in the textbox. Turn on S2 and L8 bands. The first figure will adjust the limits of axes and it will be easier to observe where the maximum of radiated energy for 700 °C is relative to satellite bands.

Most of the objects on Earth surface can be imaged by Sentinel-2 and Landsat 8 only because they reflect Sun's radiation, which has a peak in visible part of electromagnetic spectrum. Would we still be able to see anything in the satellite images if we turned the Sun off (or if the satellites captured images by night)?

Well, very little but yes, we would still see "hot-enough" objects on Earth surface, which emit radiation with "short-enough" wavelengths, which can be captured by the bands sensitive to the longest wavelengths. In case of Sentinel-2 such bends are 11 and 12 and for Landsat 8 such bands are 6, 7, 10 and 11. Fortunately for us, lava erupted from Etna in 2017 was "hot-enough".

## 3 Visualizing Etna's Eruption¶

### 3.1 Sentinel-2 Images¶

To utilize these concepts, we will create a visualization based on data acquired in infra-red part of electromagnetic spectrum (https://sentinel.esa.int/web/sentinel/user-guides/sentinel-2-msi/resolutions/spatial). We will use:

• Band 04 (B04), which measures radiation of electromagnetic waves with wavelengths around 665 nm
• Band 11 (B11), which measures radiation of electromagnetic waves with wavelengths around 1610 nm
• Band 12 (B12), which measures radiation of electromagnetic waves with wavelengths around 2190 nm

To visualize these data, we will use red color for image acquired with B12, green color for image acquired with B11 and blue color for image acquired with B04. Let check how that looks like:

In [32]:
bands_request_s2 = WmsRequest(data_folder='data',
layer='BANDS-S2-L1C',
bbox=etna_bbox,
time=('2017-02-27','2017-04-18'),
width=512,
image_format=MimeType.TIFF_d32f,
maxcc=0.8,
instance_id=INSTANCE_ID,
custom_url_params={
CustomUrlParam.SHOWLOGO: False})

bands_img_s2 = bands_request_s2.get_data(save_data=True)
bands_dates_s2 = bands_request_s2.get_dates()

#Note: Numbers 12, 11, 3 do not indicate bands but indexes of bands_img_s2 array.
plot_image(bands_img_s2[display_image][:, :, [12, 11, 3]],
etna_bbox, 2.5)
plt.title('Etna, B12, B11, B04 bands composite, acquired with Sentinel-2 \
on '+ str(bands_dates_s2[display_image].date()))
print()