# Time Series Visualization with Altair

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Author(s): jdbcode

This tutorial provides methods for generating time series data in Earth Engine and visualizing it with the Altair library using drought and vegetation response as an example.

Topics include:

• Time series region reduction in Earth Engine
• Formatting a table in Earth Engine
• Transferring an Earth Engine table to a Colab Python kernel
• Converting an Earth Engine table to a pandas DataFrame
• Data representation with various Altair chart types

Note that this tutorial uses the Earth Engine Python API in a Colab notebook.

## Context

At the heart of this tutorial is the notion of data reduction and the need to transform data into insights to help inform our understanding of Earth processes and human's role in them. It combines a series of technologies, each best suited to a particular task in the data reduction process. Earth Engine is used to access, clean, and reduce large amounts of spatiotemporal data, pandas is used to analyze and organize the results, and Altair is used to visualize the results.

Note: This notebook demonstrates an analysis template and interactive workflow that is appropriate for a certain size of dataset, but there are limitations to interactive computation time and server-to-client data transfer size imposed by Colab and Earth Engine. To analyze even larger datasets, you may need to modify the workflow to export FeatureCollection results from Earth Engine as static assets and then use the static assets to perform the subsequent steps involving Earth Engine table formatting, conversion to pandas DataFrame, and charting with Altair.

## Materials

### Datasets

Climate

Vegetation proxies

### Region of interest

The region of interest for these examples is the Sierra Nevada ecoregion of California. The vegetation grades from mostly ponderosa pine and Douglas-fir at low elevations on the western side, to pines and Sierra juniper on the eastern side, and to fir and other conifers at higher elevations.

## General workflow

Preparation of every dataset for visualization follows the same basic steps:

1. Filter the dataset (server-side Earth Engine)
2. Reduce the data region by a statistic (server-side Earth Engine)
3. Format the region reduction into a table (server-side Earth Engine)
4. Convert the Earth Engine table to a DataFrame (server-side Earth Engine > client-side Python kernel)
5. Alter the DataFrame (client-side pandas)
6. Plot the DataFrame (client-side Altair)

The first dataset will walk through each step in detail. Following examples will provide less description, unless there is variation that merits note.

## Python setup

### Earth Engine API

1. Import the Earth Engine library.
2. Authenticate access (registration verification and Google account access).
3. Initialize the API.
import ee
ee.Authenticate()
ee.Initialize()


### Other libraries

Import other libraries used in this notebook.

• pandas: data analysis (including the DataFrame data structure)
• altair: declarative visualization library (used for charting)
• numpy: array-processing package (used for linear regression)
• folium: interactive web map
import pandas as pd
import altair as alt
import numpy as np
import folium


## Region reduction function

Reduction of pixels intersecting the region of interest to a statistic will be performed multiple times. Define a reusable function that can perform the task for each dataset. The function accepts arguments such as scale and reduction method to parameterize the operation for each particular analysis.

Note: most of the reduction operations in this tutorial use a large pixel scale so that operations complete quickly. In your own application, set the scale and other parameter arguments as you wish.

def create_reduce_region_function(geometry,
reducer=ee.Reducer.mean(),
scale=1000,
crs='EPSG:4326',
bestEffort=True,
maxPixels=1e13,
tileScale=4):
"""Creates a region reduction function.

Creates a region reduction function intended to be used as the input function
to ee.ImageCollection.map() for reducing pixels intersecting a provided region
to a statistic for each image in a collection. See ee.Image.reduceRegion()
documentation for more details.

Args:
geometry:
An ee.Geometry that defines the region over which to reduce data.
reducer:
Optional; An ee.Reducer that defines the reduction method.
scale:
Optional; A number that defines the nominal scale in meters of the
projection to work in.
crs:
Optional; An ee.Projection or EPSG string ('EPSG:5070') that defines
the projection to work in.
bestEffort:
Optional; A Boolean indicator for whether to use a larger scale if the
geometry contains too many pixels at the given scale for the operation
to succeed.
maxPixels:
Optional; A number specifying the maximum number of pixels to reduce.
tileScale:
Optional; A number representing the scaling factor used to reduce
aggregation tile size; using a larger tileScale (e.g. 2 or 4) may enable
computations that run out of memory with the default.

Returns:
A function that accepts an ee.Image and reduces it by region, according to
the provided arguments.
"""

def reduce_region_function(img):
"""Applies the ee.Image.reduceRegion() method.

Args:
img:
An ee.Image to reduce to a statistic by region.

Returns:
An ee.Feature that contains properties representing the image region
reduction results per band and the image timestamp formatted as
milliseconds from Unix epoch (included to enable time series plotting).
"""

stat = img.reduceRegion(
reducer=reducer,
geometry=geometry,
scale=scale,
crs=crs,
bestEffort=bestEffort,
maxPixels=maxPixels,
tileScale=tileScale)

return ee.Feature(geometry, stat).set({'millis': img.date().millis()})
return reduce_region_function


### Formatting

The result of the region reduction function above applied to an ee.ImageCollection produces an ee.FeatureCollection. This data needs to be transferred to the Python kernel, but serialized feature collections are large and awkward to deal with. This step defines a function to convert the feature collection to an ee.Dictionary where the keys are feature property names and values are corresponding lists of property values, which pandas can deal with handily.

1. Extract the property values from the ee.FeatureCollection as a list of lists stored in an ee.Dictionary using reduceColumns().
2. Extract the list of lists from the dictionary.
3. Add names to each list by converting to an ee.Dictionary where keys are property names and values are the corresponding value lists.

The returned ee.Dictionary is essentially a table, where keys define columns and list elements define rows.

# Define a function to transfer feature properties to a dictionary.
def fc_to_dict(fc):
prop_names = fc.first().propertyNames()
prop_lists = fc.reduceColumns(
reducer=ee.Reducer.toList().repeat(prop_names.size()),
selectors=prop_names).get('list')

return ee.Dictionary.fromLists(prop_names, prop_lists)


## Drought severity

In this section we'll look at a time series of drought severity as a calendar heat map and a bar chart.

### Import data

1. Load the gridded Palmer Drought Severity Index (PDSI) data as an ee.ImageCollection.
2. Load the EPA Level-3 ecoregion boundaries as an ee.FeatureCollection and filter it to include only the Sierra Nevada region, which defines the area of interest (AOI).
today = ee.Date(pd.to_datetime('today'))
pdsi = ee.ImageCollection('GRIDMET/DROUGHT').filterDate(date_range).select('pdsi')
aoi = ee.FeatureCollection('EPA/Ecoregions/2013/L3').filter(


Note: the aoi defined above will be used throughout this tutorial. In your own application, redefine it for your own area of interest.

### Reduce data

1. Create a region reduction function.
2. Map the function over the pdsi image collection to reduce each image.
3. Filter out any resulting features that have null computed values (occurs when all pixels in an AOI are masked).
reduce_pdsi = create_reduce_region_function(
geometry=aoi, reducer=ee.Reducer.mean(), scale=5000, crs='EPSG:3310')

pdsi_stat_fc = ee.FeatureCollection(pdsi.map(reduce_pdsi)).filter(
ee.Filter.notNull(pdsi.first().bandNames()))


STOP:

### Optional export

If your process is long-running, you'll want to export the pdsi_stat_fc variable as an asset using a batch task. Wait until the task finishes, import the asset, and continue on. Please see the Developer Guide section on exporting with the Python API.

Export to asset:

task = ee.batch.Export.table.toAsset(
collection=pdsi_stat_fc,
description='pdsi_stat_fc export',
assetId='users/YOUR_USER_NAME/pdsi_stat_fc_ts_vis_with_altair')



Import the asset after the export completes:

# pdsi_stat_fc = ee.FeatureCollection('users/YOUR_USER_NAME/pdsi_stat_fc_ts_vis_with_altair')


* Remove comments (#) to run the above cells.

CONTINUE:

### Server to client transfer

The ee.FeatureCollection needs to be converted to a dictionary and transferred to the Python kernel.

1. Apply the fc_to_dict function to convert from ee.FeatureCollection to ee.Dictionary.
2. Call getInfo() on the ee.Dictionary to transfer the data client-side.
pdsi_dict = fc_to_dict(pdsi_stat_fc).getInfo()


The result is a Python dictionary. Print a small part to see how it is formatted.

print(type(pdsi_dict), '\n')
for prop in pdsi_dict.keys():
print(prop + ':', pdsi_dict[prop][0:3] + ['...'])

<class 'dict'>

millis: [1048658400000, 1049090400000, 1049522400000, '...']
pdsi: [-1.5893803698264932, -1.6455390647106298, -1.6314651734141872, '...']
system:index: ['20030326', '20030331', '20030405', '...']


Convert the Python dictionary to a pandas DataFrame.

pdsi_df = pd.DataFrame(pdsi_dict)


Preview the DataFrame and check the column data types.

display(pdsi_df)
print(pdsi_df.dtypes)

millis            int64
pdsi            float64
system:index     object
dtype: object


Add date columns derived from the milliseconds from Unix epoch column. The pandas library provides functions and objects for timestamps and the DataFrame object allows for easy mutation.

Define a function to add date variables to the DataFrame: year, month, day, and day of year (DOY).

# Function to add date variables to DataFrame.
df['Timestamp'] = pd.to_datetime(df['millis'], unit='ms')
df['Year'] = pd.DatetimeIndex(df['Timestamp']).year
df['Month'] = pd.DatetimeIndex(df['Timestamp']).month
df['Day'] = pd.DatetimeIndex(df['Timestamp']).day
df['DOY'] = pd.DatetimeIndex(df['Timestamp']).dayofyear
return df


Note: the above function for adding date information to a DataFrame will be used throughout this tutorial.

Apply the add_date_info function to the PDSI DataFrame to add date attribute columns, preview the results.

pdsi_df = add_date_info(pdsi_df)


### Rename and drop columns

Often it is desirable to rename columns and/or remove unnecessary columns. Do both here and preview the DataFrame.

pdsi_df = pdsi_df.rename(columns={
'pdsi': 'PDSI'
}).drop(columns=['millis', 'system:index'])


Check the data type of each column.

pdsi_df.dtypes

PDSI                float64
Timestamp    datetime64[ns]
Year                  int64
Month                 int64
Day                   int64
DOY                   int64
dtype: object


At this point the DataFrame is in good shape for charting with Altair.

### Calendar heatmap

Chart PDSI data as a calendar heatmap. Set observation year as the x-axis variable, month as y-axis, and PDSI value as color.

Note that Altair features a convenient method for aggregating values within groups while encoding the chart (i.e., no need to create a new DataFrame). The mean aggregate transform is applied here because each month has three PDSI observations (year and month are the grouping factors).

Also note that a tooltip has been added to the chart; hovering over cells reveals the values of the selected variables.

alt.Chart(pdsi_df).mark_rect().encode(
x='Year:O',
y='Month:O',
color=alt.Color(
'mean(PDSI):Q', scale=alt.Scale(scheme='redblue', domain=(-5, 5))),
tooltip=[
alt.Tooltip('Year:O', title='Year'),
alt.Tooltip('Month:O', title='Month'),
alt.Tooltip('mean(PDSI):Q', title='PDSI')
]).properties(width=600, height=300)


The calendar heat map is good for interpretation of relative intra- and inter-annual differences in PDSI. However, since the PDSI variable is represented by color, estimating absolute values and magnitude of difference is difficult.

### Bar chart

Chart PDSI time series as a bar chart to more easily interpret absolute values and compare them over time. Here, the observation timestamp is represented on the x-axis and PDSI is represented by both the y-axis and color. Since each PDSI observation has a unique timestamp that can be plotted to the x-axis, there is no need to aggregate PDSI values as in the above chart. A tooltip is added to the chart; hover over the bars to reveal the values for each variable.

alt.Chart(pdsi_df).mark_bar(size=1).encode(
x='Timestamp:T',
y='PDSI:Q',
color=alt.Color(
'PDSI:Q', scale=alt.Scale(scheme='redblue', domain=(-5, 5))),
tooltip=[
alt.Tooltip('Timestamp:T', title='Date'),
alt.Tooltip('PDSI:Q', title='PDSI')
]).properties(width=600, height=300)


This temporal bar chart makes it easier to interpret and compare absolute values of PDSI over time, but relative intra- and inter-annual variability are arguably harder to interpret because the division of year and month is not as distinct as in the calendar heatmap above.

Take note of the extended and severe period of drought from 2012 through 2016. In the next section, we'll look for a vegetation response to this event.

## Vegetation productivity

NDVI is a proxy measure of photosynthetic capacity and is used in this tutorial to investigate vegetation response to the 2012-2016 drought identified in the PDSI bar chart above.

MODIS provides an analysis-ready 16-day NDVI composite that is well suited for regional investigation of temporal vegetation dynamics. The following steps reduce and prepare this data for charting in the same manner as the PDSI data above; please refer to previous sections to review details.

### Import and reduce

1. Load the MODIS NDVI data as an ee.ImageCollection.
2. Create a region reduction function.
3. Apply the function to all images in the time series.
4. Filter out features with null computed values.
ndvi = ee.ImageCollection('MODIS/006/MOD13A2').filterDate(date_range).select('NDVI')

reduce_ndvi = create_reduce_region_function(
geometry=aoi, reducer=ee.Reducer.mean(), scale=1000, crs='EPSG:3310')

ndvi_stat_fc = ee.FeatureCollection(ndvi.map(reduce_ndvi)).filter(
ee.Filter.notNull(ndvi.first().bandNames()))


STOP:

If your process is long-running, you'll want to export the ndvi_stat_fc variable as an asset using a batch task. Wait until the task finishes, import the asset, and continue on.

Please see the above Optional export section for more details.

CONTINUE:

### Prepare DataFrame

1. Transfer data from the server to the client.
2. Convert the Python dictionary to a pandas DataFrame.
3. Preview the DataFrame and check data types.
ndvi_dict = fc_to_dict(ndvi_stat_fc).getInfo()
ndvi_df = pd.DataFrame(ndvi_dict)
display(ndvi_df)
print(ndvi_df.dtypes)

NDVI            float64
millis            int64
system:index     object
dtype: object

1. Remove the NDVI scaling.
3. Preview the DataFrame.
ndvi_df['NDVI'] = ndvi_df['NDVI'] / 10000


These NDVI time series data are now ready for plotting.

### DOY line chart

Make a day of year (DOY) line chart where each line represents a year of observations. This chart makes it possible to compare the same observation date among years. Use it to compare NDVI values for years during the drought and not.

Day of year is represented on the x-axis and NDVI on the y-axis. Each line represents a year and is distinguished by color. Note that this plot includes a tooltip and has been made interactive so that the axes can be zoomed and panned.

highlight = alt.selection(
type='single', on='mouseover', fields=['Year'], nearest=True)

base = alt.Chart(ndvi_df).encode(
x=alt.X('DOY:Q', scale=alt.Scale(domain=[0, 353], clamp=True)),
y=alt.Y('NDVI:Q', scale=alt.Scale(domain=[0.1, 0.6])),
color=alt.Color('Year:O', scale=alt.Scale(scheme='magma')))

points = base.mark_circle().encode(
opacity=alt.value(0),
tooltip=[
alt.Tooltip('Year:O', title='Year'),
alt.Tooltip('DOY:Q', title='DOY'),
alt.Tooltip('NDVI:Q', title='NDVI')

lines = base.mark_line().encode(
size=alt.condition(~highlight, alt.value(1), alt.value(3)))

(points + lines).properties(width=600, height=350).interactive()


The first thing to note is that winter dates (when there is snow in the Sierra Nevada ecoregion) exhibit highly variable inter-annual NDVI, but spring, summer, and fall dates are more consistent. With regard to drought effects on vegetation, summer and fall dates are the most sensitive time. Zooming into observations for the summer/fall days (224-272), you'll notice that many years have a u-shaped pattern where NDVI values decrease and then rise.

Another way to view these data is to plot the distribution of NDVI by DOY represented as an interquartile range envelope and median line. Here, these two charts are defined and then combined in the following snippet.

1. Define a base chart.
2. Define a line chart for median NDVI (note the use of aggregate median transform grouping by DOY).
3. Define a band chart using 'iqr' (interquartile range) to represent NDVI distribution grouping on DOY.
4. Combine the line and band charts.
base = alt.Chart(ndvi_df).encode(
x=alt.X('DOY:Q', scale=alt.Scale(domain=(150, 340))))

line = base.mark_line().encode(
y=alt.Y('median(NDVI):Q', scale=alt.Scale(domain=(0.47, 0.53))))

band = base.mark_errorband(extent='iqr').encode(
y='NDVI:Q')

(line + band).properties(width=600, height=300).interactive()


The summary statistics for the summer/fall days (224-272) certainly show an NDVI reduction, but there is also variability; some years exhibit greater NDVI reduction than others as suggested by the wide interquartile range during the middle of the summer. Assuming that NDVI reduction is due to water and heat limiting photosynthesis, we can hypothesize that during years of drought, photosynthesis (NDVI) will be lower than non-drought years. We can investigate the relationship between photosynthesis (NDVI) and drought (PDSI) using a scatter plot and linear regression.

## Dought and productivity relationship

A scatterplot is a good way to visualize the relationship between two variables. Here, PDSI (drought indicator) will be plotted on the x-axis and NDVI (vegetation productivity) on the y-axis. To achieve this, both variables must exist in the same DataFrame. Each row will be an observation in time and columns will correspond to PDSI and NDVI values. Currently, PDSI and NDVI are in two different DataFrames and need to be merged.

### Prepare DataFrames

Before they can be merged, each variable must be reduced to a common temporal observation unit to define correspondence. There are a number of ways to do this and each will define the relationship between PDSI and NDVI differently. Here, our temporal unit will be an annual observation set where NDVI is reduced to the intra-annual minimum from DOY 224 to 272 and PDSI will be the mean from DOY 1 to 272. We are proposing that average drought severity for the first three quarters of a year are related to minimum summer NDVI for a given year.

1. Filter the NDVI DataFrame to observations that occur between DOY 224 and 272.
2. Reduce the DOY-filtered subset to intra-annual minimum NDVI.
ndvi_doy_range = [224, 272]

ndvi_df_sub = ndvi_df[(ndvi_df['DOY'] >= ndvi_doy_range[0])
& (ndvi_df['DOY'] <= ndvi_doy_range[1])]

ndvi_df_sub = ndvi_df_sub.groupby('Year').agg('min')


Note: in your own application you may find that a different DOY range is more suitable, change the ndvi_doy_range as needed.

1. Filter the PDSI DataFrame to observations that occur between DOY 1 and 272.
2. Reduce the values within a given year to the mean of the observations.
pdsi_doy_range = [1, 272]

pdsi_df_sub = pdsi_df[(pdsi_df['DOY'] >= pdsi_doy_range[0])
& (pdsi_df['DOY'] <= pdsi_doy_range[1])]

pdsi_df_sub = pdsi_df_sub.groupby('Year').agg('mean')


Note: in your own application you may find that a different DOY range is more suitable, change the pdsi_doy_range as needed.

1. Perform a join on 'Year' to combine the two reduced DataFrames.
2. Select only the columns of interest: 'Year', 'NDVI', 'PDSI'.
3. Preview the DataFrame.
ndvi_pdsi_df = pd.merge(
ndvi_df_sub, pdsi_df_sub, how='left', on='Year').reset_index()

ndvi_pdsi_df = ndvi_pdsi_df[['Year', 'NDVI', 'PDSI']]



NDVI and PDSI are now included in the same DataFrame linked by Year. This format is suitable for determining a linear relationship and drawing a line of best fit through the data.

Including a line of best fit can be a helpful visual aid. Here, a 1D polynomial is fit through the xy point cloud defined by corresponding NDVI and PDSI observations. The resulting fit is added to the DataFrame as a new column 'Fit'.

1. Add a line of best fit between PDSI and NDVI by determining the linear relationship and predicting NDVI based on PDSI for each year.
ndvi_pdsi_df['Fit'] = np.poly1d(
np.polyfit(ndvi_pdsi_df['PDSI'], ndvi_pdsi_df['NDVI'], 1))(
ndvi_pdsi_df['PDSI'])



### Scatter plot

The DataFrame is ready for plotting. Since this chart is to include points and a line of best fit, two charts need to be created, one for the points and one for the line. The results are combined into the final plot.

base = alt.Chart(ndvi_pdsi_df).encode(
x=alt.X('PDSI:Q', scale=alt.Scale(domain=(-5, 5))))

points = base.mark_circle(size=60).encode(
y=alt.Y('NDVI:Q', scale=alt.Scale(domain=(0.4, 0.6))),
color=alt.Color('Year:O', scale=alt.Scale(scheme='magma')),
tooltip=[
alt.Tooltip('Year:O', title='Year'),
alt.Tooltip('PDSI:Q', title='PDSI'),
alt.Tooltip('NDVI:Q', title='NDVI')
])

fit = base.mark_line().encode(
y=alt.Y('Fit:Q'),
color=alt.value('#808080'))

(points + fit).properties(width=600, height=300).interactive()


As you can see, there seems to be some degree of positive correlation between PDSI and NDVI (i.e., as wetness increases, vegetation productivity increases; as wetness decreases, vegetation productivity decreases). Note that some of the greatest outliers are 2016, 2017, 2018 - the three years following recovery from the long drought. It is also important to note that there are many other factors that may influence the NDVI signal that are not being considered here.

## Patch-level vegetation mortality

At a regional scale there appears to be a relationship between drought and vegetation productivity. This section will look more closely at effects of drought on vegetation at a patch level, with a specific focus on mortality. Here, a Landsat time series collection is created for the period 1984-present to provide greater temporal context for change at a relatively precise spatial resolution.

### Find a point of interest

Use aerial imagery from the National Agriculture Imagery Program (NAIP) in an interactive Folium map to identify a location in the Sierra Nevada ecoregion that appears to have patches of dead trees.

1. Run the following code block to render an interactive Folium map for a selected NAIP image.
2. Zoom and pan around the image to identify a region of recently dead trees (standing silver snags with no fine branches or brown/grey snags with fine branches).
3. Click the map to list the latitude and longitude for a patch of interest. Record these values for use in the following section (the example location used in the following section is presented as a yellow point).
# Define a method for displaying Earth Engine image tiles to folium map.
map_id_dict = ee.Image(ee_image_object).getMapId(vis_params)
folium.raster_layers.TileLayer(
tiles=map_id_dict['tile_fetcher'].url_format,
attr='Map Data &copy; <a href="https://earthengine.google.com/">Google Earth Engine, USDA National Agriculture Imagery Program</a>',
name=name,
overlay=True,

# Add an Earth Engine layer drawing method to folium.

# Import a NAIP image for the area and date of interest.
naip_img = ee.ImageCollection('USDA/NAIP/DOQQ').filterDate(
'2016-01-01',
'2017-01-01').filterBounds(ee.Geometry.Point([-118.6407, 35.9665])).first()

# Display the NAIP image to the folium map.
m = folium.Map(location=[35.9665, -118.6407], tiles='Stamen Terrain', zoom_start=16)

# Add the point of interest to the map.
folium.Circle(
location=[35.9665, -118.6407],
color='yellow',
fill=False,

# Add the AOI to the map.
folium.GeoJson(
aoi.getInfo(),
name='geojson',
style_function=lambda x: {'fillColor': '#00000000', 'color': '#000000'},

# Add a lat lon popup.

# Display the map.
display(m)


### Prepare Landsat collection

Landsat surface reflectance data need to be prepared before being reduced. The steps below will organize data from multiple sensors into congruent collections where band names are consistent, cloud and cloud shadows have been masked out, and the normalized burn ratio (NBR) transformation is calculated and returned as the image representative (NBR is a good indicator of forest disturbance). Finally, all sensor collections will be merged into a single collection and annual composites calculated based on mean annual NBR using a join.

1. Define Landsat observation date window inputs based on NDVI curve plotted previously and set latitude and longitude variables from the map above.
start_day = 224
end_day = 272

latitude = 35.9665
longitude = -118.6407


Note: in your own application it may be necessary to change these values.

1. Prepare a Landsat surface reflectance collection 1984-present. Those unfamiliar with Landsat might find the following acronym definitions and links helpful.

• OLI (Landsat's Operational Land Imager sensor)
• ETM+ (Landsat's Enhanced Thematic Mapper Plus sensor)
• TM (Landsat's Thematic Mapper sensor)
• NBR. (Normalized Burn Ratio: a spectral vegetation index)
• Understanding Earth Engine joins
# Make lat. and long. vars an ee.Geometry.Point.
point = ee.Geometry.Point([longitude, latitude])

# Define a function to get and rename bands of interest from OLI.
def rename_oli(img):
return (img.select(
ee.List(['B2', 'B3', 'B4', 'B5', 'B6', 'B7', 'pixel_qa']),
ee.List(['Blue', 'Green', 'Red', 'NIR', 'SWIR1', 'SWIR2', 'pixel_qa'])))

# Define a function to get and rename bands of interest from ETM+.
def rename_etm(img):
return (img.select(
ee.List(['B1', 'B2', 'B3', 'B4', 'B5', 'B7', 'pixel_qa']),
ee.List(['Blue', 'Green', 'Red', 'NIR', 'SWIR1', 'SWIR2', 'pixel_qa'])))

qa = img.select('pixel_qa')

# Define a function to add year as an image property.
def set_year(img):
year = ee.Image(img).date().get('year')
return img.set('Year', year)

# Define a function to calculate NBR.
def calc_nbr(img):
return img.normalizedDifference(ee.List(['NIR', 'SWIR2'])).rename('NBR')

# Define a function to prepare OLI images.
def prep_oli(img):
orig = img
img = rename_oli(img)
img = calc_nbr(img)
img = img.copyProperties(orig, orig.propertyNames())
return set_year(img)

# Define a function to prepare TM/ETM+ images.
def prep_etm(img):
orig = img
img = rename_etm(img)
img = calc_nbr(img)
img = img.copyProperties(orig, orig.propertyNames())
return set_year(img)

# Import image collections for each Landsat sensor (surface reflectance).
tm_col = ee.ImageCollection('LANDSAT/LT05/C01/T1_SR')
etm_col = ee.ImageCollection('LANDSAT/LE07/C01/T1_SR')
oli_col = ee.ImageCollection('LANDSAT/LC08/C01/T1_SR')

# Filter collections and prepare them for merging.
oli_col = oli_col.filterBounds(point).filter(
ee.Filter.calendarRange(start_day, end_day, 'day_of_year')).map(prep_oli)

etm_col = etm_col.filterBounds(point).filter(
ee.Filter.calendarRange(start_day, end_day, 'day_of_year')).map(prep_etm)

tm_col = tm_col.filterBounds(point).filter(
ee.Filter.calendarRange(start_day, end_day, 'day_of_year')).map(prep_etm)

# Merge the collections.
landsat_col = oli_col.merge(etm_col).merge(tm_col)

# Get a distinct year collection.
distinct_year_col = landsat_col.distinct('Year')

# Define a filter that identifies which images from the complete collection
# match the year from the distinct year collection.
join_filter = ee.Filter.equals(leftField='Year', rightField='Year')

# Define a join.
join = ee.Join.saveAll('year_matches')

# Apply the join and convert the resulting FeatureCollection to an
# ImageCollection.
join_col = ee.ImageCollection(
join.apply(distinct_year_col, landsat_col, join_filter))

# Define a function to apply mean reduction among matching year collections.
def reduce_by_join(img):
year_col = ee.ImageCollection.fromImages(ee.Image(img).get('year_matches'))
return year_col.reduce(ee.Reducer.mean()).rename('NBR').set(
'system:time_start',
ee.Image(img).date().update(month=8, day=1).millis())

# Apply the reduce_by_join function to the list of annual images in the
# properties of the join collection.
landsat_col = join_col.map(reduce_by_join)


The result of the above code block is an image collection with as many images as there are years present in the merged Landsat collection. Each image represents the annual mean NBR constrained to observations within the given date window.

### Prepare DataFrame

1. Create a region reduction function; use ee.Reducer.first() as the reducer since no spatial aggregation is needed (we are interested in the single pixel that intersects the point). Set the region as the geometry defined by the lat. and long. coordinates identified in the above map.
2. Apply the function to all images in the time series.
3. Filter out features with null computed values.
reduce_landsat = create_reduce_region_function(
geometry=point, reducer=ee.Reducer.first(), scale=30, crs='EPSG:3310')

nbr_stat_fc = ee.FeatureCollection(landsat_col.map(reduce_landsat)).filter(
ee.Filter.notNull(landsat_col.first().bandNames()))

1. Transfer data from the server to the client.
Note: if the process times out, you'll need to export/import the nbr_stat_fc feature collection as described in the Optional export section.

2. Convert the Python dictionary to a pandas DataFrame.

3. Preview the DataFrame and check data types.

nbr_dict = fc_to_dict(nbr_stat_fc).getInfo()
nbr_df = pd.DataFrame(nbr_dict)
print(nbr_df.dtypes)

NBR             float64
millis            int64
system:index     object
dtype: object

2. Preview the DataFrame.
nbr_df = add_date_info(nbr_df)


### Line chart

Display the Landsat NBR time series for the point of interest as a line plot.

alt.Chart(nbr_df).mark_line().encode(
x=alt.X('Timestamp:T', title='Date'),
y='NBR:Q',
tooltip=[
alt.Tooltip('Timestamp:T', title='Date'),
alt.Tooltip('NBR:Q')
]).properties(width=600, height=300).interactive()


As you can see from the above time series of NBR observations, a dramatic decrease in NBR began in 2015, shortly after the severe and extended drought began. The decline continued through 2017, when a minor recovery began. Within the context of the entire time series, it is apparent that the decline is outside of normal inter-annual variability and that the reduction in NBR for this site is quite severe. The lack of major recovery response in NBR in 2017-19 (time of writing) indicates that the event was not ephemeral; the loss of vegetation will have a lasting impact on this site. The corresponding onset of drought and reduction in NBR provides further evidence that there is a relationship between drought and vegetation response in the Sierra Nevada ecoregion.

## Past and future climate

The previous data visualizations suggest there is a relationship between drought and vegetation stress and mortality in the Sierra Nevada ecoregion.

This section will look at how climate is projected to change in the future, which can give us a sense for what to expect with regard to drought conditions and speculate about its impact on vegetation.

We'll look at historical and projected temperature and precipitation. Projected data are represented by NEX-DCP30, and historical observations by PRISM.

### Future climate

NEX-DCP30 data contain 33 climate models projected to the year 2100 using several scenarios of greenhouse gas concentration pathways (RCP). Here, we'll use the median of all models for RCP 8.5 (the worst case scenario) to look at potential future temperature and precipitation.

#### Import and prepare collection

1. Filter the collection by date and scenario.
2. Calculate 'mean' temperature from median min and max among 33 models.
dcp_col = (ee.ImageCollection('NASA/NEX-DCP30_ENSEMBLE_STATS')
.select(['tasmax_median', 'tasmin_median', 'pr_median'])
.filter(
ee.Filter.And(ee.Filter.eq('scenario', 'rcp85'),
ee.Filter.date('2019-01-01', '2070-01-01'))))

def calc_mean_temp(img):
return (img.select('tasmax_median')
.divide(ee.Image.constant(2.0))
.rename(['Temp-mean', 'Precip-rate'])
.copyProperties(img, img.propertyNames()))

dcp_col = dcp_col.map(calc_mean_temp)


#### Prepare DataFrame

1. Create a region reduction function.
2. Apply the function to all images in the time series.
3. Filter out features with null computed values.
reduce_dcp30 = create_reduce_region_function(
geometry=point, reducer=ee.Reducer.first(), scale=5000, crs='EPSG:3310')

dcp_stat_fc = ee.FeatureCollection(dcp_col.map(reduce_dcp30)).filter(
ee.Filter.notNull(dcp_col.first().bandNames()))

1. Transfer data from the server to the client. Note: if the process times out, you'll need to export/import the dcp_stat_fc feature collection as described in the Optional export section.
2. Convert the Python dictionary to a pandas DataFrame.
3. Preview the DataFrame and check the data types.
dcp_dict = fc_to_dict(dcp_stat_fc).getInfo()
dcp_df = pd.DataFrame(dcp_dict)
display(dcp_df)
print(dcp_df.dtypes)

Precip-rate     float64
Temp-mean       float64
millis            int64
system:index     object
dtype: object

2. Preview the DataFrame.
dcp_df = add_date_info(dcp_df)

1. Convert precipitation rate to mm.
2. Convert Kelvin to celsius.
3. Add the model name as a column.
4. Remove the 'Precip-rate' column.
dcp_df['Precip-mm'] = dcp_df['Precip-rate'] * 86400 * 30
dcp_df['Temp-mean'] = dcp_df['Temp-mean'] - 273.15
dcp_df['Model'] = 'NEX-DCP30'
dcp_df = dcp_df.drop('Precip-rate', 1)

/tmpfs/src/tf_docs_env/lib/python3.7/site-packages/ipykernel_launcher.py:4: FutureWarning: In a future version of pandas all arguments of DataFrame.drop except for the argument 'labels' will be keyword-only
after removing the cwd from sys.path.


### Past climate

PRISM data are climate datasets for the conterminous United States. Grid cells are interpolated based on station data assimilated from many networks across the country. The datasets used here are monthly averages for precipitation and temperature. They provide a record of historical climate.

#### Reduce collection and prepare DataFrame

1. Import the collection and filter by date.
2. Reduce the collection images by region and filter null computed values.
3. Convert the feature collection to a dictionary and transfer it client-side.
Note: if the process times out, you'll need to export/import the prism_stat_fc feature collection as described in the Optional export section.

4. Convert the dictionary to a DataFrame.

5. Preview the DataFrame.

prism_col = (ee.ImageCollection('OREGONSTATE/PRISM/AN81m')
.select(['ppt', 'tmean'])
.filter(ee.Filter.date('1979-01-01', '2019-12-31')))

reduce_prism = create_reduce_region_function(
geometry=point, reducer=ee.Reducer.first(), scale=5000, crs='EPSG:3310')

prism_stat_fc = (ee.FeatureCollection(prism_col.map(reduce_prism))
.filter(ee.Filter.notNull(prism_col.first().bandNames())))

prism_dict = fc_to_dict(prism_stat_fc).getInfo()
prism_df = pd.DataFrame(prism_dict)

display(prism_df)
print(prism_df.dtypes)

millis            int64
ppt             float64
system:index     object
tmean           float64
dtype: object

3. Rename columns to be consistent with the NEX-DCP30 DataFrame.
4. Preview the DataFrame.
prism_df = add_date_info(prism_df)
prism_df['Model'] = 'PRISM'
prism_df = prism_df.rename(columns={'ppt': 'Precip-mm', 'tmean': 'Temp-mean'})


### Combine DataFrames

At this point the PRISM and NEX-DCP30 DataFrames have the same columns, the same units, and are distinguished by unique entries in the 'Model' column. Use the concat function to concatenate these DataFrames into a single DataFrame for plotting together in the same chart.

climate_df = pd.concat([prism_df, dcp_df], sort=True)
climate_df


### Charts

Chart the past and future precipitation and temperature together to get a sense for where climate has been and where it is projected to go under RCP 8.5.

#### Precipitation

base = alt.Chart(climate_df).encode(
x='Year:O',
color='Model')

line = base.mark_line().encode(
y=alt.Y('median(Precip-mm):Q', title='Precipitation (mm/month)'))

band = base.mark_errorband(extent='iqr').encode(
y=alt.Y('Precip-mm:Q', title='Precipitation (mm/month)'))

(band + line).properties(width=600, height=300)


#### Temperature

line = alt.Chart(climate_df).mark_line().encode(
x='Year:O',
y='median(Temp-mean):Q',
color='Model')

band = alt.Chart(climate_df).mark_errorband(extent='iqr').encode(
x='Year:O',
y=alt.Y('Temp-mean:Q', title='Temperature (°C)'), color='Model')

(band + line).properties(width=600, height=300)


Future climate projections suggest that precipitation will decrease and temperature will increase for the selected point of interest. We can hypothesize, given the RCP 8.5 trajectory, that future conditions will more regularly resemble the 2012-2016 drought, which could lead to the same vegetation reduction response documented here and that more frequent drought events could lead to development of plant communities that are better adapted to low precipitation, high temperature conditions.

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