Analysis of the Earth’s Radiation Budget using the CERES product

Analysis of the Earth’s Radiation Budget using the CERES product#

This notebook-tutorial provides an introduction to the use of the Cloud and Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Earth’s Radiation Budget (ERB) data record for climate studies.

The Earth's Radiation Budget (ERB) Essential Climate Variable (ECV) and the CERES EBAF product are described in the introduction. Then, a first use case provides an analysis of the time averaged global and seasonal climatological distributions of the Earth's radiation budget as well as the monthly mean climatology. The second use case presents the time series and trend analysis of ERB. Step-by-step instructions are provided on data preparation, the use cases are extensively documented and each line of code is explained.

The three figures below show some results from the use cases and illustrate the successful run of the code.

1. Introduction#

The Earth’s Radiation Budget (ERB) represents the overall balance between incoming and outgoing radiant energy at the Earth’s top-of-the-atmosphere (TOA). This Essential Climate Variable (ECV) is the primary forcing of the climate system and is therefore a fundamental quantity to be monitored to understand the Earth’s climate and its variability. The ERB comprises the quantification of the incoming radiation from the sun and the outgoing reflected shortwave and emitted longwave radiations. The Earth is in a state of dynamic radiative balance; energy arriving from the sun is balanced by outgoing radiation from the top-of-the-atmosphere. Changes in the Earth’s surface and atmosphere (including cloud amount and properties, and concentrations of greenhouse gases) will alter the radiative forcing of the Earth system and change the balance and distribution of outgoing thermal radiation and reflected solar radiation.

In the Copernicus Climate Data Store (CDS), a dataset of ERB has been “brokered” from the Clouds and Earth’s Radiant Energy System (CERES) Energy Balanced And Filled (EBAF) edition 4.2. CERES EBAF provides a state-of-the-art Climate Data Record (CDR) of monthly mean top of atmosphere (TOA) radiative fluxes. This widely used CDR is produced by the CERES team at the NASA/Langley center from the CERES instruments onboard the Terra and Aqua satellites. The CERES EBAF data is suitable for analysis of variability at the intra-seasonal, inter-annual, and longer time scales.

In this Jupyter notebook tutorial, we present examples, based on monthly mean ERB products, to illustrate the philosophy on the usage, visualisation, and analysis of the ERB dataset. Produced images and processed data can be saved to personal devices for later use.

You will find further information about the dataset as well as the data in the Climate Data Store catalogue entry Earth’s Radiation Budget, sections “Overview”, “Download data” and “Documentation”:

Earth’s radiation budget from 1979 to present derived from satellite observations

2. Search, download and view data#

Before we begin, we must prepare our environment. This includes installing the Application Programming Interface (API) of the CDS, and importing the various python libraries that we will need.

How to access the notebooks#

This tutorial is in the form of a Jupyter notebook, written in Python 3.9.4. You will not need to install any software for the training as there are a number of free cloud-based services to create, edit, run and export Jupyter notebooks such as this. Here are some suggestions (simply click on one of the links below to run the notebook):

Run the tutorial via free cloud platforms:

The cdsapi is used to download the data. This package is not included by default on most cloud platforms yet. You can use pip to install it:
!pip install cdsapi

Import libraries#

To run this notebook in your own environment, we advise you to install Anaconda, which contains most of the libraries you will need. You will also need to install the CDS API (!pip install cdsapi) for downloading data programatically from the CDS. It is also recommended to use Python 3.9.4 for the purpose of reproducibility and compatibility, with respect to the latest updates of the different libraries.

The data have been stored in files written in NetCDF format. To best handle these, we will import the library Xarray which is specifically designed for manipulating multidimensional arrays in the field of geosciences. The libraries Matplotlib and Cartopy will also be imported for plotting and visualising the analysed data. We will also import the libraries zipfile to work with zip-archives, OS to use OS-functions and pattern expansion, and urllib3 for disabling warnings for data download via CDS API.

# Libraries to work with zip-archives, OS functions and pattern expansion
import zipfile
import os

# Disable warnings for data download via API
import urllib3
urllib3.disable_warnings()

# CDS API library
import cdsapi

# Libraries for working with multidimensional arrays
import xarray as xr
import numpy as np
import pandas as pd
# Import a sublibrary method for the seasonal decomposition of the time series
from statsmodels.tsa.seasonal import seasonal_decompose

# Libraries for plotting and visualising the data
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
from cartopy.mpl.ticker import (LongitudeFormatter, LatitudeFormatter)

Download Data Using CDS API#

Set up CDS API credentials#

To set up your CDS API credentials, please login/register on the CDS, then follow the instructions here to obtain your API key.

You can add this API key to your current session by uncommenting the code below and replacing ######### with your API key.

URL = 'https://cds.climate.copernicus.eu/api'
KEY = '#####################'

Here we specify a data directory in which we will download our data and all output files that we will generate:

# Data directory for downloading the data
DATADIR = './'
# Filename for the zip file downloaded from the CDS
download_zip_file = os.path.join(DATADIR, 'ceres-erb-monthly.zip')
# Filename for the netCDF file which contain the merged contents of the monthly files.
merged_netcdf_file = os.path.join(DATADIR, 'ceres-erb-monthly.nc')

Search for data#

To search for data, visit the CDS website. Here you can search for CERES EBAF data using the search bar. The data we need for this use case is the Earth’s radiation budget from 1979 to present derived from satellite observations. This catalogue entry provides data from various sources: NASA CERES EBAF, NOAA/NCEI HIRS OLR, ESA Cloud-CCI, EUMETSAT’s CM SAF CLARA-A3, C3S CCI and C3S RMIB TSI.

After selecting the correct catalogue entry, we will specify the product family, the origin, the sensor on satellite (for CCI product family only), the type of variable, the type of climate data record, the time aggregation, the temporal and geographical coverage we are interested in. These can all be selected in the “Download data” tab. In this tab a form appears in which we will select the following parameters to download:

Product family: CERES EBAF (Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced And Filled (EBAF))
Origin: NASA (National Aeronautics and Space Administration)
Variable: all (use Select all button)
Climate data record type: Thematic Climate Data Record (TCDR)
Time aggregation: Monthly mean
Year: all (use Select all button)
Month: all (use Select all button)
Geographical area: Whole available region

If you have not already done so, you will need to accept the “terms & conditions” of the data before you can download it.

At the end of the download form, select “Show API request”. This will reveal a block of code, which you can simply copy and paste into a cell of your Jupyter Notebook (see cell below) …

Download data#

… Having copied the API request into the cell below, running this will retrieve and download the data you requested into your local directory. However, before you run the cell below, the terms and conditions of this particular dataset need to have been accepted in the CDS. The option to view and accept these conditions is given at the end of the download form, just above the “Show API request” option.

dataset = "satellite-earth-radiation-budget"
request = {
    'product_family': 'ceres_ebaf',
    'origin': 'nasa',
    'variable': ['incoming_shortwave_radiation', 
                 'outgoing_longwave_radiation', 
                 'outgoing_shortwave_radiation'
                ],
    'climate_data_record_type': 'thematic_climate_data_record',
    'time_aggregation': 'monthly_mean',
    'year': ['%04d' % (year) for year in range(2000, 2023)],
    'month': ['%02d' % (month) for month in range(0, 13)]
}

client = cdsapi.Client(url=URL,key=KEY)
client.retrieve(dataset, request, download_zip_file)

Plot data#

We can visualize one time step to figure out what the data look like. Xarray offers built-in matplotlib functions that allow you to plot a DataArray. With the function plot(), you can easily plot e.g. the first time step of the loaded array.

da_toa_erb[0, :, :].plot()

<matplotlib.collections.QuadMesh at 0x1687351c0>

../_images/063dfe9b6fdfc76ed6ecc61b12ad975c9acd708a3673b7cf1cda95e58fd743f0.png

Figure 1 shows the Top of the Atmosphere Net Earth’s Radiative Flux for March 2000.

An alternative to the built-in Xarray plotting functions is to make use of a combination of the plotting libraries matplotlib and Cartopy. One of Cartopy’s key features is its ability to transform array data into different geographic projections. In combination with matplotlib, it is a very powerful way to create high-quality visualisations and animations. In later plots, we will make use of these libraries to produce more customised visualisations.

4. Time series and trend analysis of the Earth’s Radiation Budget#

After looking at the time averaged global distribution of the Earth's radiation budget, we further investigate the dataset. The CERES-EBAF product spans over 20 years of satellite observations, and another useful way of analysing and visualizing the temporal evolution of total column water vapour is using the time series. We will calculate global time series, plot it, and discuss most important features.

We first create a temporal subset for the time period January 2001 to December 2021.

# Select time period for the incoming shortwave radiation data array
ceres_solar = da_solar.sel(time=slice('2001-01-01', '2021-12-31'))

# Select time period for the outgoing shortwave radiation data array
ceres_toa_sw = da_toa_sw.sel(time=slice('2001-01-01', '2021-12-31'))

# Select time period for the outgoing longwave radiation data array
ceres_toa_lw = da_toa_lw.sel(time=slice('2001-01-01', '2021-12-31'))

# Compute the net radiative flux for the selected time period
ceres_toa_erb = ceres_solar - ceres_toa_sw - ceres_toa_lw

Spatial aggregation#

We would like to visualise these data, not in maps but as one dimensional time series of global average values. To do this, we will first need to aggregate the data spatially to create a single global average at each time step. In order to aggregate over the latitudinal dimension, we need to take into account the variation in area as a function of latitude. We will do this by using the cosine of the latitude as a proxy:

# Define weights as the cosine of latitudes
weights = np.cos(np.deg2rad(ceres_solar.lat))
weights.name = "weights"

# Spatial aggregation of CERES-EBAF incident solar flux
ceres_solar_weighted = ceres_solar.weighted(weights)

# Spatial aggregation of CERES-EBAF reflected solar flux
ceres_toa_sw_weighted = ceres_toa_sw.weighted(weights)

# Spatial aggregation of CERES-EBAF Earth emitted longwave flux
ceres_toa_lw_weighted = ceres_toa_lw.weighted(weights)

# Spatial agregation of CERES-EBAF net radiative flux
ceres_toa_erb_weighted = ceres_toa_erb.weighted(weights)

The next step is to compute the mean across the latitude and longitude dimensions of the weighted data array with the mean() method.

# Weighted mean of CERES-EBAF incident solar flux
ceres_solar_wmean = ceres_solar_weighted.mean(dim=("lat", "lon"))

# Weighted mean of CERES-EBAF reflected solar flux
ceres_toa_sw_wmean = ceres_toa_sw_weighted.mean(dim=("lat", "lon"))

# Weighted mean of CERES-EBAF Earth emitted longwave flux
ceres_toa_lw_wmean = ceres_toa_lw_weighted.mean(dim=("lat", "lon"))

# Weighted mean of CERES net radiative flux
ceres_toa_erb_wmean = ceres_toa_erb_weighted.mean(dim=("lat", "lon"))

4.1. Time series and trend analysis of the top-of-atmosphere incoming solar radiation#

Global time series of TIS#

Now we can plot the time series of globally averaged TIS data over time using the plot() method.

# Define the figure and specify size
fig15, ax15 = plt.subplots(1, 1, figsize=(16, 8))

# Configure the axes and figure title
ax15.set_xlabel('Year')
ax15.set_ylabel('W.m$^{-2}$')
ax15.grid(linewidth=1, color='gray', alpha=0.5, linestyle='--')
ax15.set_title('$\\bf{Global\ time\ series\ of\ TIS\ from\ CERES\ EBAF}$', fontsize=20, pad=20)

# Plot the data
ax15.plot(ceres_solar_wmean.time, ceres_solar_wmean)

# Save the figure
fig15.savefig(f'{DATADIR}ceres_isf_global_timeseries.png')

../_images/9b40826b336f4b167c7f522f2e905dd450f7d7da96998463afa4aec099e6d9ed.png

Figure 15 shows the time series of the incoming solar flux at the top of the atmosphere.

From the time series, we can infer a clear seasonal cycle with an amplitude of over 20 W/m$^{2}$ in the global space and time averaged TSI, associated to the Earth's orbit around the sun. Another very slight long-term seasonal trend is also noticeable, that corresponds to the sunspot cycle. The Earth and solar seasonal cycles will now be studied in more details by the seasonal decomposition of the incoming solar flux.

Trend analysis and seasonal cycle of TIS#

The time series can be further analysed by extracting the trend, or the running annual mean, and the seasonal cycle.

To this end, we will convert the Xarray Data Array into a time series with the pandas library before decomposing it into the trend, the seasonal cycle and the residuals by using the seasonal_decompose() method and visualizing the results.

# Convert the Xarray data array ceres_solar_wmean into a time series
ceres_solar_wmean_series = pd.Series(ceres_solar_wmean)
# Define the time dimension of ceres_solar_weighted_mean as the index of the time series
ceres_solar_wmean_series.index = ceres_solar_wmean.time.to_dataframe().index

# Decomposition of the time series into the trend, the seasonal cycle and the residuals
ceres_solar_seasonal_decomposition = seasonal_decompose(ceres_solar_wmean_series,
                                                        model='additive',
                                                        period=12)

# Plot the resulting seasonal decomposition
ceres_solar_seasonal_decomposition.plot()
plt.xlabel("Time")
plt.savefig(f'{DATADIR}ceres_solar_timeseries_climatology.png')

../_images/5b5cfb7dcbe19cb0d79fc8c9cb5b8a87cb5ac5777b4f7d3108bede7ca512d68f.png

Figure 16 shows the decomposition of the TIS time series into the trend corresponding to the sunspot cycle (2nd panel), and the seasonal cycle with the confirmed amplitude of 20 W/m$^{2}$ (3rd panel), from which are derived the anomalies or de-trended and de-seasonalised time series that have the characteristics of an uncorrelated noise pattern (4th panel).

4.2. Time series and trend analysis of the top-of-atmosphere reflected solar flux#

Global time series of TOA RSF#

We will now plot the time series of globally averaged TOA RSF data over time using the plot() method.

# Define the figure and specify size
fig17, ax17 = plt.subplots(1, 1, figsize=(16, 8))

# Configure the axes and figure title
ax17.set_xlabel('Year')
ax17.set_ylabel('W.m$^{-2}$')
ax17.grid(linewidth=1, color='gray', alpha=0.5, linestyle='--')
ax17.set_title('$\\bf{Global\ time\ series\ of\ TOA\ RSF\ from\ CERES\ EBAF}$', fontsize=20, pad=20)

# Plot the data
ax17.plot(ceres_toa_sw_wmean.time, ceres_toa_sw_wmean)

# Save the figure
fig17.savefig(f'{DATADIR}ceres_toa_sw_global_timeseries.png')

../_images/033563727c171f5c251c1fc9537214e8cb69d38782b54fec9014e494f4add73a.png

Figure 17 shows the time series of the reflected solar flux at the top of the atmosphere.

From the time series of the global space and time averaged RSF, we can infer a clear seasonal cycle associated to the Earth’s orbit around the sun and a long-term seasonal cycle corresponding to the sunspot cycle together with a negative trend. They will now be further examined through the seasonal decomposition of the incoming solar flux.

Trend analysis and seasonal cycle of TOA RSF#

The time series can be further analysed by extracting the trend, or the running annual mean, and the seasonal cycle.

To this end, we will convert the Xarray Data Array into a time series with the pandas library before decomposing it into the trend, the seasonal cycle and the residuals by using the seasonal_decompose() method and visualizing the results.

# Convert the Xarray data array ceres_toa_sw_wmean into a time series
ceres_toa_sw_wmean_series = pd.Series(ceres_toa_sw_wmean)
# Define the time dimension of ceres_toa_sw_wmean as the index of the time series
ceres_toa_sw_wmean_series.index = ceres_toa_sw_wmean.time.to_dataframe().index

# Decomposition of the time series into the trend, the seasonal cycle and the residuals
ceres_toa_sw_seasonal_decomposition = seasonal_decompose(ceres_toa_sw_wmean_series,
                                                         model='additive',
                                                         period=12)

# Plot the resulting seasonal decomposition
ceres_toa_sw_seasonal_decomposition.plot()
plt.xlabel("Time")
plt.savefig(f'{DATADIR}ceres_toa_sw_timeseries_climatology.png')

../_images/82a73a0c36d030d2be08a0c0b03c602651526f580e38d54ba73ed22ee363a846.png

Figure 18 shows the decomposition of the TOA RSF time series into a negative trend of ~-0.1 W/m$^{2}$/year (2nd panel) and a seasonal cycle with an amplitude of ~15 W/m$^{2}$ (3rd panel), from which are derived the anomalies that have the characteristics of an uncorrelated noise pattern (4th panel).

As explained earlier (see the climatologcal distribution of the TOA RSF), the minimum values of the reflected solar flux are found over cloud free ocean areas and the maximum values over high albedo surfaces, such as snow or deserts. The negative trend can thus be due to a loss of snow and ice, especially in the Arctic and Antarctic regions.

4.3. Time series and trend analysis of the top-of-atmosphere outgoing longwave radiation#

Global time series of TOA OLR#

We will now plot the time series of globally averaged outgoing longwave radiation data over time using the plot() method.

# Define the figure and specify size
fig19, ax19 = plt.subplots(1, 1, figsize=(16, 8))

# Configure the axes and figure title
ax19.set_xlabel('Year')
ax19.set_ylabel('W.m$^{-2}$')
ax19.grid(linewidth=1, color='gray', alpha=0.5, linestyle='--')
ax19.set_title('$\\bf{Global\ time\ series\ of\ OLR\ from\ CERES\ EBAF}$', fontsize=20, pad=20)

# Plot the data
ax19.plot(ceres_toa_lw_wmean.time, ceres_toa_lw_wmean)

# Save the figure
fig19.savefig(f'{DATADIR}ceres_toa_lw_global_timeseries.png')

../_images/467af4f709f8d5b953965f3a01889747f45ae9016e6be06e6150b9da8d9c8ad1.png

Figure 19 shows the time series of the outgoing longwave radiation at the top of the atmosphere. From the time series, we can infer a seasonal pattern along with a trend in the global space and time averaged TOA OLR.

We will now procede to the seasonal decomposition of the Earth-emitted longwave radiation at the top of the atmosphere and analyse more specifically the trend and seasonal cycle of CERES-EBAF OLR.

Trend analysis and seasonal cycle of TOA OLR#

The time series can be further analysed by extracting the trend, or the running annual mean, and the seasonal cycle.

To this end, we will convert the Xarray Data Array into a time series with the pandas library before decomposing it into the trend, the seasonal cycle and the residuals by using the seasonal_decompose() method and visualizing the results.

# Convert the Xarray data array ceres_toa_lw_wmean into a time series
ceres_toa_lw_wmean_series = pd.Series(ceres_toa_lw_wmean)
# Define the time dimension of ceres_toa_lw_wmean as the index of the time series
ceres_toa_lw_wmean_series.index = ceres_toa_lw_wmean.time.to_dataframe().index

# Decomposition of the time series into the trend, the seasonal cycle and the residuals
ceres_toa_lw_seasonal_decomposition = seasonal_decompose(ceres_toa_lw_wmean_series,
                                                         model='additive',
                                                         period=12)

# Plot the resulting seasonal decomposition
ceres_toa_lw_seasonal_decomposition.plot()
plt.xlabel("Time")
plt.savefig(f'{DATADIR}ceres_toa_lw_timeseries_climatology.png')

../_images/b91aa4d856b1f7a95b61fe9c7e29b43eff1dd134b0b42cdba14e63a80fbc5b1e.png

Figure 20 shows the decomposition of the outgoing lonwave radiation time series into a positive trend of ~0.05 W/m$^{2}$/year (2nd panel), and a seasonal cycle with an amplitude of ~8 W/m$^{2}$ (3rd panel), from which are derived the anomalies that have the characteristics of uncorrelated noise pattern (4th panel).

The observed inter-annual variations in the 2nd panel of Figure 20 suggest an influence of the “El Niño” or “La Niña” Southern Oscillation on the TOA OLR. The increase in this Earth-emitted longwave radiation is clearly related to the increase of surface temperatures.

4.4. Time series and trend analysis of the top-of-atmosphere net Earth’s radiation budget#

Global time series of TOA net ERB#

We will now plot the time series of the globally averaged TOA net Earth’s radiative flux over time using the plot() method.

# Define the figure and specify size
fig21, ax21 = plt.subplots(1, 1, figsize=(16, 8))

# Configure the axes and figure title
ax21.set_xlabel('Year')
ax21.set_ylabel('W.m$^{-2}$')
ax21.grid(linewidth=1, color='gray', alpha=0.5, linestyle='--')
ax21.set_title('$\\bf{Global\ time\ series\ of\ TOA\ net\ ERB\ from\ CERES\ EBAF}$', fontsize=20, pad=20)

# Plot the data
ax21.plot(ceres_toa_erb_wmean.time, ceres_toa_erb_wmean)

# Save the figure
fig21.savefig(f'{DATADIR}ceres_toa_erb_global_timeseries.png')

../_images/50f2cd29c968846396f5c22aafd6d3a1d5bc5e461c193f6cca27ef90a45e98b0.png

Figure 21 shows the time series of the net Earth’s radiation budget at the top of the atmosphere. From the time series, we can infer a seasonal pattern together with a slightly increasing trend in the global space and time averaged TOA net ERB.

Since CERES EBAF is a stable and robust product which has been validated with other data, this trend can be assumed to be a real climatological variability in the net Earth's radiation flux at the top of the atmosphere.

We will now procede to the seasonal decomposition of the net Earth's radiation budget and analyse more specifically the trend and seasonal cycle of the TOA net ERB.

Trend analysis and seasonal cycle of TOA net ERB#

The time series can be further analysed by extracting the trend, or the running annual mean, and the seasonal cycle.

# Convert the Xarray data array ceres_toa_erb_wmean into a time series
ceres_toa_erb_wmean_series = pd.Series(ceres_toa_erb_wmean)
# Define the time dimension of ceres_toa_sw_wmean as the index of the time series
ceres_toa_erb_wmean_series.index = ceres_toa_erb_wmean.time.to_dataframe().index

# Decomposition of the time series into the trend, the seasonal cycle and the residuals
ceres_toa_erb_seasonal_decomposition = seasonal_decompose(ceres_toa_erb_wmean_series,
                                                          model='additive',
                                                          period=12)

# Plot the resulting seasonal decomposition
ceres_toa_erb_seasonal_decomposition.plot()
plt.xlabel("Time")
plt.savefig(f'{DATADIR}ceres_toa_erb_timeseries_climatology.png')

../_images/c91d57f251d5f381de1ca3a348deaafde164f379b3dd627b98fe77a2976f00b0.png

Figure 22 shows the decomposition of the CERES-EBAF TOA net ERB time series into a positive trend of ~0.05 W/m$^{2}$/year (2nd panel), and a seasonal cycle with an amplitude of ~20 W/m$^{2}$ (3rd panel), from which are derived the anomalies that have the characteristics of uncorrelated noise pattern (4th panel).

The trend analysis presents an oscilation around the year 2010 that can be related to a moderate “El Niño” event in this time period. The positive trend of the net Earth's radiative flux confirms global warming.

5. Conclusion#

In this notebook we have provided use cases, based on the Cloud and Earth’s Radiant Energy System (CERES) Energy Balanced And Filled (EBAF) Earth's radiation budget (ERB) data record, to illustrate the way this dataset can be used to study, analyse and visualise this essential climate variable. The current dataset indicates a clear increase of the net Earth's radiative flux between January 2001 and December 2021. Comparisons with other independent datasets can be made to further investigate the trends that can be attributed to global warming, El-Niño events and external solar cycle forcing.

Analysis of the Earth’s Radiation Budget using the CERES product

Contents

Analysis of the Earth’s Radiation Budget using the CERES product#

1. Introduction#

2. Search, download and view data#

How to access the notebooks#

Import libraries#

Download Data Using CDS API#

Set up CDS API credentials#

Search for data#

Download data#

Inspect data#

Plot data#

3. Climatology of the Earth’s Radiation Budget#

3.1. Climatology of the top-of-atmosphere incoming solar radiation#

Time averaged global climatological distribution of TIS#

Time averaged seasonal climatological distribution of TIS#

Zonally averaged monthly mean climatology of TIS#

3.2. Climatology of the top-of-atmosphere reflected solar flux#

Time averaged global climatological distribution of TOA RSF#

Time averaged seasonal climatological distribution of TOA RSF#

Zonally averaged montly mean climatology of TOA RSF#

3.3. Climatology of the top-of-atmosphere outgoing longwave radiation#

Time averaged global climatological distribution of TOA OLR#

Time averaged seasonal climatological distribution of TOA OLR#

Inter-annual variability of TOA OLR#

Zonally averaged montly mean climatology of TOA OLR#

3.4. Climatology of the top-of-atmosphere net Earth’s radiation budget#

Time averaged global climatological distribution of TOA net ERB#

Time averaged seasonal climatological distribution of TOA ERB#

Zonally averaged montly mean climatology of TOA net ERB#

4. Time series and trend analysis of the Earth’s Radiation Budget#

Spatial aggregation#

4.1. Time series and trend analysis of the top-of-atmosphere incoming solar radiation#

Global time series of TIS#

Trend analysis and seasonal cycle of TIS#

4.2. Time series and trend analysis of the top-of-atmosphere reflected solar flux#

Global time series of TOA RSF#

Trend analysis and seasonal cycle of TOA RSF#

4.3. Time series and trend analysis of the top-of-atmosphere outgoing longwave radiation#

Global time series of TOA OLR#

Trend analysis and seasonal cycle of TOA OLR#

4.4. Time series and trend analysis of the top-of-atmosphere net Earth’s radiation budget#

Global time series of TOA net ERB#

Trend analysis and seasonal cycle of TOA net ERB#

5. Conclusion#