Rwtss - R interface to Web Time Series Service
Introduction
Recently, the concept of data cubes has emerged as a relevant paradigm for organising Earth observation data for performing analysis. In an intuitive sense, data cubes are temporal sequences of images from the same geographical area. This sequence is organised consistently to allow algorithms to explore the data in both the spatial and temporal directions[Appel2019]. Data cubes are thus an efficient way to explore satellite image archives spanning years or even decades.
Data cubes rely on the fact that Earth observation satellites revisit the same place at regular intervals. Thus measures can be calibrated so that observations of the same place in different times are comparable. These calibrated observations can be organised in regular intervals, so that each measure from sensor is mapped into a three dimensional multivariate array in space-time. Let S = {s1, s2, …, sn} be a set of remote sensing images which shows the same region at consecutive times T = {t1, t2, …, tn}. Each location of a pixel in an image (latitude, longitude, time) maps to a position in a 3D array. Each array position will be associated to a set of attributes values A = {a1, a2, …, am} which are the sensor measurements at each location in space-time (see figure below}). For optical sensors, these observations are proportional to Earth’s reflexion of the incoming solar radiation at different wavelengths of the electromagnetic spectrum.
A Normalized Difference Vegetation Index (NDVI) time series
In what follows, we use the term “coverage” in the same sense as the definition of a “data cube”, proposed from Appel and Pebesma (Appel and Pebesma 2019): A regular, dense Earth observation (EO) data cube is a four-dimensional array with dimensions x (longitude or easting), y (latitude or northing), and time, with the following properties:
- Spatial dimensions refer to a single spatial reference system (SRS)};
- Cells of a data cube have a constant spatial size (with regard to the cube’s SRS)};
- The spatial reference is defined by a simple offset and the cell size per axis, i.e., the cube axes are aligned with the SRS axes;}
- The temporal reference is a known set of non-overlapping temporal intervals; each temporal interval is defined by a simple start date/time and the temporal duration of cells;}
- All cells have the same set of attributes; each attribute can be a
scalar or a vector;}
- For every combination of dimensions, a cell has a single set of attribute values.}
This definition of EO data cubes reflects their construction. Data cubes are built of 2D images collected on a specific date constrained by satellite orbits. These images are then grouped together in arbitrary intervals. In principle, a data cube can have an image on time 1, another image at time 5, another at time 8, and so on. Since interpolation in space is different from interpolation in time, a data set composed by these images would make a valid data cube. Space needs to be compact (dense) in a data cube, but time does not need to be. Thus, a sequence of 2D + time images need not be dense. 2D images in a data cube can correspond to different instants of acquisition.
Web Services for Earth Observation Data Cubes
Web services interfaces isolate users from concrete implementations, thus increasing portability There are many ways to implement Earth observation data cubes. One of the earlier approaches is to break large images in chunks and store them in an object-relational DBMS, as done in RASDAMAN (Baumann et al. 1998). Google Earth Engine(Gorelick et al. 2017) uses a massive parallel design; image data is partitioned in hundreds or thousands of CPUs, processed separately and later aggregated using map-reduce techniques. The Open Data Cube software, after making the required geometric and radiometric transformations in the images, stores them in files, which are indexed in a PostgreSQL database (Lewis et al. 2017). Similar file-based approaches are used in the R package “gdalcubes” (Appel and Pebesma 2019). Each of these designs is associated to a different API, thus making compatibility and interoperability between them hard to achieve.
Given the different designs of Earth observation data cubes, and their inherent limitations for achieving interoperability, one natural approach is to propose Web services that would present a unified interface for accessing them. Web services interfaces isolate users from concrete implementations, thus increasing portability(Ferris and Farrell 2003). In the geospatial domain, web service standards developed by the Open Geospatial Consortium have achieved considerable impact (Percivall 2010). Since services such as WMS (Web Map Service) and WCS (Web Coverage Service) are used worldwide with success, it is natural to ask: how to design web services for big Earth observation (EO) data? The current work addresses this issue and proposes WTSS (Web Time Series Service), a new services for big EO data.
Satellite Image Time Series
Given a series of remote sensing snapshots, we can reorganise them into a set of time series. A satellite image time series is obtained by taking measurements in the same pixel location (x, y) in consecutive times t1, ..., tm, as shown in the figure below.
Events associated to a time series
Recent results in the literature show that analysis of satellite image times series enables extracting long-term trends of land change \citep(Pasquarella et al. 2016). Such information which would be harder to obtain by processing 2D images separately. These analysis are supported by algorithms such as TWDTW (Maus et al. 2016), TIMESTAT (Jonsson and Eklundh 2004) and BFAST (Verbesselt et al. 2010). These algorithms process individual time-series and combine the results for selected periods to generate classified maps.
For example, classification methods such as TWDTW (Maus et al. 2019) can then break an image time series into a set of intervals. As an example, the figure below shows four events extracted from a remote sensing time series, expressed in terms of the its intervals. From 2000 to 2001 the area was a forest that was deforested in 2002. From 2003 to 2005 the area it was used for pasture and from 2005 to 2008, it was transformed into a cropland. This kind of classification is done by algorithms such that split a time series into a set of events. Combining snapshots with time series, scientists can explore the full depth of big remote sensing data archives.
Web Time Series Service (WTSS)
Motivated by the need to retrieve satellite image time series from large 3D arrays, we have designed and implemented the Web Time Series Service (WTSS). A WTSS server takes as input a 3D array. Each array has a spatial and a temporal dimension and can be multidimensional in terms of its attributes. The WTSS service is independent of the actual data architecture used for 3D array store. It can work with solutions such as flat files, MapReduce distributed datasets, array databases or object-relational databases.
The WTSS API has three commands: (a) list_coverages that returns a list of coverages available in the server; (b) describe_coverage that returns the metadata for a given coverage; (c) time_series that returns a time series for a spatio-temporal location.
Connecting to a WTSS server
The first step towards using the service is connecting to a server that supports the WTSS protocol. Currently, Brazil’s National Institute for Space Research (INPE) runs such a service. In the package, the connection is enabled by using the URL of the service. So, the first procedure is to find the URL of a WTSS service.
Listing coverages available at the WTSS server
This operation allows clients to retrieve the capabilities provided by any server that implements WTSS. It returns a list of coverage names available in a server instance.
## [1] "MOD13Q1-6" "MYD13Q1-6"Describing a coverage from the WTSS server
This operation returns the metadata for a given coverage identified by its name. It includes its range in the spatial and temporal dimensions.
# Connect to the WTSS server at INPE Brazil
desc <- Rwtss::describe_coverage(wtss_inpe, name = "MOD13Q1-6")## ---------------------------------------------------------------------## WTSS server URL = https://brazildatacube.dpi.inpe.br/wtss## Cube (coverage) = MOD13Q1-6## Timeline - 508 time steps## start_date: 2000-02-18 end_date: 2022-03-22## ---------------------------------------------------------------------The coverage description is also saved as a tibble in the wtss object, to be used whenever required.
Obtaining a time series
This operation requests the time series of values of a coverage
attribute at a given location. Its parameters are: (a)
wtss.obj: either a WTSS object (created by the operation
wtss::WTSS as shown above) or a valid WTSS server URL; (b)
name: Cube (coverage) name; (c) attributes: vector of
band names (optional). If omitted, all bands are retrieved; (d)
longitude: longitude in WGS84 coordinate system;
(e)latitude: Latitude in WGS84 coordinate system;
(f)start_date (optional): Start date in the format yyyy-mm-dd
or yyyy-mm depending on the coverage. If omitted, the first date on the
timeline is used; (g) end_date(optional): End date in the
format yyyy-mm-dd or yyyy-mm depending on the coverage. If omitted, the
last date of the timeline is used; (h) To access the BDC time series it
is necessary to provide a token, provide the token through the
token parameter. To create a new BDC token, please see this
tutorial.
# Request a time series from the "MOD13Q1" coverage
ndvi_ts <- Rwtss::time_series(
URL = wtss_inpe,
name = "MOD13Q1",
attributes = c("NDVI","EVI"),
longitude = -45.00,
latitude = -12.00,
start_date = "2000-02-18",
end_date = "2016-12-18",
token = "YOUR-BDC-TOKEN"
)## longitude latitude start_date end_date label cube
## 1 -45 -12 2000-02-18 2016-12-18 NoClass MOD13Q1-6
## time_series
## 1 11005.0000, 11021.0000, 11037.0000, 11053.0000, 11069.0000, 11085.0000, 11101.0000, 11117.0000, 11133.0000, 11149.0000, 11165.0000, 11181.0000, 11197.0000, 11213.0000, 11229.0000, 11245.0000, 11261.0000, 11277.0000, 11293.0000, 11309.0000, 11323.0000, 11339.0000, 11355.0000, 11371.0000, 11387.0000, 11403.0000, 11419.0000, 11435.0000, 11451.0000, 11467.0000, 11483.0000, 11499.0000, 11515.0000, 11531.0000, 11547.0000, 11563.0000, 11579.0000, 11595.0000, 11611.0000, 11627.0000, 11643.0000, 11659.0000, 11675.0000, 11688.0000, 11704.0000, 11720.0000, 11736.0000, 11752.0000, 11768.0000, 11784.0000, 11800.0000, 11816.0000, 11832.0000, 11848.0000, 11864.0000, 11880.0000, 11896.0000, 11912.0000, 11928.0000, 11944.0000, 11960.0000, 11976.0000, 11992.0000, 12008.0000, 12024.0000, 12040.0000, 12053.0000, 12069.0000, 12085.0000, 12101.0000, 12117.0000, 12133.0000, 12149.0000, 12165.0000, 12181.0000, 12197.0000, 12213.0000, 12229.0000, 12245.0000, 12261.0000, 12277.0000, 12293.0000, 12309.0000, 12325.0000, 12341.0000, 12357.0000, 12373.0000, 12389.0000, 12405.0000, 12418.0000, 12434.0000, 12450.0000, 12466.0000, 12482.0000, 12498.0000, 12514.0000, 12530.0000, 12546.0000, 12562.0000, 12578.0000, 12594.0000, 12610.0000, 12626.0000, 12642.0000, 12658.0000, 12674.0000, 12690.0000, 12706.0000, 12722.0000, 12738.0000, 12754.0000, 12770.0000, 12784.0000, 12800.0000, 12816.0000, 12832.0000, 12848.0000, 12864.0000, 12880.0000, 12896.0000, 12912.0000, 12928.0000, 12944.0000, 12960.0000, 12976.0000, 12992.0000, 13008.0000, 13024.0000, 13040.0000, 13056.0000, 13072.0000, 13088.0000, 13104.0000, 13120.0000, 13136.0000, 13149.0000, 13165.0000, 13181.0000, 13197.0000, 13213.0000, 13229.0000, 13245.0000, 13261.0000, 13277.0000, 13293.0000, 13309.0000, 13325.0000, 13341.0000, 13357.0000, 13373.0000, 13389.0000, 13405.0000, 13421.0000, 13437.0000, 13453.0000, 13469.0000, 13485.0000, 13501.0000, 13514.0000, 13530.0000, 13546.0000, 13562.0000, 13578.0000, 13594.0000, 13610.0000, 13626.0000, 13642.0000, 13658.0000, 13674.0000, 13690.0000, 13706.0000, 13722.0000, 13738.0000, 13754.0000, 13770.0000, 13786.0000, 13802.0000, 13818.0000, 13834.0000, 13850.0000, 13866.0000, 13879.0000, 13895.0000, 13911.0000, 13927.0000, 13943.0000, 13959.0000, 13975.0000, 13991.0000, 14007.0000, 14023.0000, 14039.0000, 14055.0000, 14071.0000, 14087.0000, 14103.0000, 14119.0000, 14135.0000, 14151.0000, 14167.0000, 14183.0000, 14199.0000, 14215.0000, 14231.0000, 14245.0000, 14261.0000, 14277.0000, 14293.0000, 14309.0000, 14325.0000, 14341.0000, 14357.0000, 14373.0000, 14389.0000, 14405.0000, 14421.0000, 14437.0000, 14453.0000, 14469.0000, 14485.0000, 14501.0000, 14517.0000, 14533.0000, 14549.0000, 14565.0000, 14581.0000, 14597.0000, 14610.0000, 14626.0000, 14642.0000, 14658.0000, 14674.0000, 14690.0000, 14706.0000, 14722.0000, 14738.0000, 14754.0000, 14770.0000, 14786.0000, 14802.0000, 14818.0000, 14834.0000, 14850.0000, 14866.0000, 14882.0000, 14898.0000, 14914.0000, 14930.0000, 14946.0000, 14962.0000, 14975.0000, 14991.0000, 15007.0000, 15023.0000, 15039.0000, 15055.0000, 15071.0000, 15087.0000, 15103.0000, 15119.0000, 15135.0000, 15151.0000, 15167.0000, 15183.0000, 15199.0000, 15215.0000, 15231.0000, 15247.0000, 15263.0000, 15279.0000, 15295.0000, 15311.0000, 15327.0000, 15340.0000, 15356.0000, 15372.0000, 15388.0000, 15404.0000, 15420.0000, 15436.0000, 15452.0000, 15468.0000, 15484.0000, 15500.0000, 15516.0000, 15532.0000, 15548.0000, 15564.0000, 15580.0000, 15596.0000, 15612.0000, 15628.0000, 15644.0000, 15660.0000, 15676.0000, 15692.0000, 15706.0000, 15722.0000, 15738.0000, 15754.0000, 15770.0000, 15786.0000, 15802.0000, 15818.0000, 15834.0000, 15850.0000, 15866.0000, 15882.0000, 15898.0000, 15914.0000, 15930.0000, 15946.0000, 15962.0000, 15978.0000, 15994.0000, 16010.0000, 16026.0000, 16042.0000, 16058.0000, 16071.0000, 16087.0000, 16103.0000, 16119.0000, 16135.0000, 16151.0000, 16167.0000, 16183.0000, 16199.0000, 16215.0000, 16231.0000, 16247.0000, 16263.0000, 16279.0000, 16295.0000, 16311.0000, 16327.0000, 16343.0000, 16359.0000, 16375.0000, 16391.0000, 16407.0000, 16423.0000, 16436.0000, 16452.0000, 16468.0000, 16484.0000, 16500.0000, 16516.0000, 16532.0000, 16548.0000, 16564.0000, 16580.0000, 16596.0000, 16612.0000, 16628.0000, 16644.0000, 16660.0000, 16676.0000, 16692.0000, 16708.0000, 16724.0000, 16740.0000, 16756.0000, 16772.0000, 16788.0000, 16801.0000, 16817.0000, 16833.0000, 16849.0000, 16865.0000, 16881.0000, 16897.0000, 16913.0000, 16929.0000, 16945.0000, 16961.0000, 16977.0000, 16993.0000, 17009.0000, 17025.0000, 17041.0000, 17057.0000, 17073.0000, 17089.0000, 17105.0000, 17121.0000, 17137.0000, 17153.0000, 0.3743, 0.8203, 0.8022, 0.8090, 0.7489, 0.7273, 0.6985, 0.6543, 0.6081, 0.5833, 0.5618, 0.5048, 0.5157, 0.5618, 0.5589, 0.5193, 0.1141, 0.8076, 0.7851, 0.8418, 0.7880, 0.7904, 0.8284, 0.6521, 0.7711, 0.7907, 0.7810, 0.7566, 0.7047, 0.6328, 0.5894, 0.5315, 0.5260, 0.5038, 0.4550, 0.4465, 0.4392, 0.4577, 0.5749, 0.7814, 0.8166, 0.7905, 0.7398, 0.7802, 0.7710, 0.8170, 0.8004, 0.7928, 0.7433, 0.7041, 0.6949, 0.5966, 0.6204, 0.6764, 0.7012, 0.6390, 0.5743, 0.5156, 0.5338, 0.4695, 0.5439, 0.4904, 0.7132, 0.7387, 0.6747, 0.7353, 0.7677, 0.7782, 0.8321, 0.8129, 0.8307, 0.8782, 0.8052, 0.7884, 0.7703, 0.7066, 0.6268, 0.5536, 0.5278, 0.4927, 0.4545, 0.4165, 0.4496, 0.5100, 0.6041, 0.7517, 0.8122, 0.8101, 0.8101, 0.7669, 0.3635, 0.7951, 0.7921, 0.8408, 0.8223, 0.8179, 0.8142, 0.7707, 0.7403, 0.6816, 0.6171, 0.5896, 0.4975, 0.4763, 0.4829, 0.4526, 0.4872, 0.5218, 0.5892, 0.5764, 0.7673, 0.8600, 0.8600, 0.8548, 0.7882, 0.8124, 0.8460, 0.8134, 0.8334, 0.8010, 0.8114, 0.7732, 0.6514, 0.6285, 0.5630, 0.5037, 0.5037, 0.4547, 0.4293, 0.5223, 0.4566, 0.5799, 0.7038, 0.8055, 0.8174, 0.8054, 0.8006, 0.8352, 0.8258, 0.8057, 0.8036, 0.8215, 0.8001, 0.7840, 0.7746, 0.7567, 0.6755, 0.5973, 0.5086, 0.4697, 0.4503, 0.4833, 0.4809, 0.5258, 0.8063, 0.8044, 0.8033, 0.8721, 0.8721, 0.8038, 0.8068, 0.8216, 0.8263, 0.7981, 0.7672, 0.7210, 0.6784, 0.5762, 0.5337, 0.5425, 0.5102, 0.4628, 0.4284, 0.4522, 0.4253, 0.4006, 0.4252, 0.4032, 0.4340, 0.6707, 0.7723, 0.7223, 0.7664, 0.7847, 0.8400, 0.8066, 0.6652, 0.8111, 0.7948, 0.8045, 0.7915, 0.7155, 0.7151, 0.6551, 0.5809, 0.5138, 0.4620, 0.4503, 0.4452, 0.4066, 0.4768, 0.5212, 0.7434, 0.8283, 0.8283, 0.8401, 0.8485, 0.8066, 0.8164, 0.8032, 0.8067, 0.8270, 0.7943, 0.7787, 0.7171, 0.5890, 0.5877, 0.5120, 0.4341, 0.4625, 0.4670, 0.4636, 0.5865, 0.7974, 0.8157, 0.8201, 0.8143, 0.8413, 0.8065, 0.8180, 0.8350, 0.8255, 0.7837, 0.7897, 0.7520, 0.6818, 0.6522, 0.5606, 0.4737, 0.4973, 0.4715, 0.4092, 0.4048, 0.3698, 0.4586, 0.4307, 0.6527, 0.7836, 0.8010, 0.8171, 0.8171, 0.8452, 0.8296, 0.8188, 0.7933, 0.8145, 0.6663, 0.7856, 0.7339, 0.7003, 0.5550, 0.4901, 0.5176, 0.4694, 0.4574, 0.4197, 0.4313, 0.4250, 0.6415, 0.7684, 0.8285, 0.8546, 0.8128, 0.8588, 0.8222, 0.7122, 0.7846, 0.8015, 0.7755, 0.7533, 0.6605, 0.5719, 0.5170, 0.4538, 0.4486, 0.4398, 0.4267, 0.4500, 0.4554, 0.3682, 0.4556, 0.3998, 0.3895, 0.5960, 0.6449, 0.7909, 0.7748, 0.7985, 0.8537, 0.8449, 0.7817, 0.8286, 0.8020, 0.7916, 0.6812, 0.6337, 0.5962, 0.5574, 0.4469, 0.4641, 0.3935, 0.4312, 0.4432, 0.4001, 0.4504, 0.6269, 0.6949, 0.7995, 0.8611, 0.8384, 0.8008, 0.7723, 0.3673, 0.8062, 0.8195, 0.7777, 0.7632, 0.7672, 0.7103, 0.5514, 0.4847, 0.4626, 0.4078, 0.3827, 0.4059, 0.4077, 0.4114, 0.4349, 0.4633, 0.6795, 0.7416, 0.8137, 0.8418, 0.7812, 0.7912, 0.8443, 0.8184, 0.8361, 0.7954, 0.8086, 0.7851, 0.6880, 0.6377, 0.5712, 0.4961, 0.4792, 0.4510, 0.4136, 0.4169, 0.4494, 0.3980, 0.4247, 0.6314, 0.7986, 0.7325, 0.7325, 0.7876, 0.8533, 0.8084, 0.8209, 0.8291, 0.7709, 0.7238, 0.6865, 0.6302, 0.6000, 0.5504, 0.5306, 0.4658, 0.4154, 0.4281, 0.4314, 0.4926, 0.7028, 0.6441, 0.8110, 0.7986, 0.8041, 0.3019, 0.4967, 0.4808, 0.4319, 0.4091, 0.3940, 0.3741, 0.3247, 0.3097, 0.2911, 0.2767, 0.2669, 0.2730, 0.3215, 0.3612, 0.2920, 0.1279, 0.5582, 0.4937, 0.5111, 0.5427, 0.4616, 0.5372, 0.4711, 0.4777, 0.4912, 0.4467, 0.4268, 0.4160, 0.3271, 0.2898, 0.2884, 0.2712, 0.2602, 0.2639, 0.2539, 0.2577, 0.2706, 0.3727, 0.5507, 0.8241, 0.5492, 0.4255, 0.4896, 0.5190, 0.5845, 0.5056, 0.5014, 0.4604, 0.4006, 0.3689, 0.2856, 0.3087, 0.3646, 0.3802, 0.3673, 0.3052, 0.3100, 0.3249, 0.2598, 0.3129, 0.2636, 0.5047, 0.4777, 0.3773, 0.4377, 0.5551, 0.6040, 0.5381, 0.6274, 0.5803, 0.5028, 0.4758, 0.4689, 0.3680, 0.4043, 0.3271, 0.2954, 0.3084, 0.2786, 0.2750, 0.2306, 0.2860, 0.2570, 0.4245, 0.4743, 0.5588, 0.5483, 0.4651, 0.6099, 0.3657, 0.6109, 0.6187, 0.4761, 0.5708, 0.5328, 0.4700, 0.4154, 0.4008, 0.3791, 0.3152, 0.2930, 0.2650, 0.2637, 0.2617, 0.2730, 0.3137, 0.3454, 0.3443, 0.3062, 0.5623, 0.5404, 0.5404, 0.5483, 0.5580, 0.6531, 0.6346, 0.4623, 0.5352, 0.4507, 0.4584, 0.4488, 0.3662, 0.3424, 0.3050, 0.2713, 0.2731, 0.2728, 0.2919, 0.3232, 0.3093, 0.4048, 0.4129, 0.5045, 0.5129, 0.5390, 0.3883, 0.5290, 0.5143, 0.5109, 0.5585, 0.4954, 0.5282, 0.4492, 0.4173, 0.4206, 0.3481, 0.2993, 0.2661, 0.2634, 0.2807, 0.2717, 0.2631, 0.3417, 0.5467, 0.5331, 0.5333, 0.4925, 0.4925, 0.5231, 0.4761, 0.6133, 0.5139, 0.5054, 0.4358, 0.4055, 0.3668, 0.2945, 0.2600, 0.2753, 0.2619, 0.2467, 0.2551, 0.2541, 0.2572, 0.2635, 0.2739, 0.2356, 0.2698, 0.3849, 0.4660, 0.4671, 0.6031, 0.6089, 0.5333, 0.4999, 0.2908, 0.5071, 0.4860, 0.4646, 0.4405, 0.4015, 0.3892, 0.3513, 0.3094, 0.2718, 0.2878, 0.2447, 0.2414, 0.2857, 0.2541, 0.2731, 0.5586, 0.5426, 0.5426, 0.4812, 0.5079, 0.6184, 0.5138, 0.5457, 0.5616, 0.4661, 0.5004, 0.4793, 0.3691, 0.2864, 0.3019, 0.2721, 0.2427, 0.2571, 0.2617, 0.2862, 0.4052, 0.5136, 0.5750, 0.5470, 0.5671, 0.5635, 0.5687, 0.4959, 0.4799, 0.4922, 0.5101, 0.5140, 0.4244, 0.3543, 0.3506, 0.2771, 0.2417, 0.2667, 0.2603, 0.2333, 0.2311, 0.2429, 0.2870, 0.2462, 0.4090, 0.5220, 0.6086, 0.5739, 0.5739, 0.5469, 0.6630, 0.6069, 0.5870, 0.5054, 0.4483, 0.4709, 0.3864, 0.3660, 0.2736, 0.2446, 0.2626, 0.2477, 0.2702, 0.2346, 0.2465, 0.2877, 0.3460, 0.6101, 0.5753, 0.5437, 0.6374, 0.5105, 0.5698, 0.5851, 0.4243, 0.4841, 0.4827, 0.4222, 0.3302, 0.3303, 0.2501, 0.2216, 0.2210, 0.2141, 0.2353, 0.2432, 0.2512, 0.2406, 0.2747, 0.2459, 0.2209, 0.4143, 0.3409, 0.4600, 0.4602, 0.6631, 0.5555, 0.5472, 0.5683, 0.5014, 0.4182, 0.4660, 0.3747, 0.3156, 0.2850, 0.2612, 0.2346, 0.2457, 0.2261, 0.2381, 0.2707, 0.2415, 0.2492, 0.3507, 0.4481, 0.5279, 0.5067, 0.5618, 0.6464, 0.5944, 0.3125, 0.5791, 0.4298, 0.4812, 0.4580, 0.4324, 0.3777, 0.2895, 0.2457, 0.2562, 0.2647, 0.2479, 0.2629, 0.2582, 0.2440, 0.2537, 0.2349, 0.3932, 0.5701, 0.5893, 0.5835, 0.5745, 0.6538, 0.5329, 0.6309, 0.5189, 0.5096, 0.4231, 0.4516, 0.3389, 0.3282, 0.2812, 0.2488, 0.2513, 0.2461, 0.2332, 0.2476, 0.2787, 0.2551, 0.2491, 0.3713, 0.5316, 0.5575, 0.5575, 0.6100, 0.5970, 0.6144, 0.5070, 0.4795, 0.4555, 0.4000, 0.3826, 0.3480, 0.3045, 0.2811, 0.2796, 0.2442, 0.2347, 0.2489, 0.2707, 0.2894, 0.4694, 0.4262, 0.5431, 0.5786, 0.5459The result of the operation is a tibble, which is a
generalization of a data.frame, the usual way in R
to organise data in tables. Tibbles are part of the
tidyverse, a collection of R packages designed to work
together in data manipulation (Wickham and
Grolemund 2017). The tibble contains data and metadata. The first
six columns contain the metadata: satellite, sensor, spatial and
temporal information, and the coverage from where the data has been
extracted. The spatial location is given in longitude and latitude
coordinates for the “WGS84” ellipsoid. The time_series
column contains the time series data for each spatiotemporal location.
This data is also organized as a tibble, with a column with the dates
and the other columns with the values for each spectral band.
## Index NDVI EVI
## 1 2000-02-18 0.3743 0.3019
## 2 2000-03-05 0.8203 0.4967
## 3 2000-03-21 0.8022 0.4808
## 4 2000-04-06 0.8090 0.4319
## 5 2000-04-22 0.7489 0.4091
## 6 2000-05-08 0.7273 0.3940
## 7 2000-05-24 0.6985 0.3741
## 8 2000-06-09 0.6543 0.3247
## 9 2000-06-25 0.6081 0.3097
## 10 2000-07-11 0.5833 0.2911
## 11 2000-07-27 0.5618 0.2767
## 12 2000-08-12 0.5048 0.2669
## 13 2000-08-28 0.5157 0.2730
## 14 2000-09-13 0.5618 0.3215
## 15 2000-09-29 0.5589 0.3612
## 16 2000-10-15 0.5193 0.2920
## 17 2000-10-31 0.1141 0.1279
## 18 2000-11-16 0.8076 0.5582
## 19 2000-12-02 0.7851 0.4937
## 20 2000-12-18 0.8418 0.5111
## 21 2001-01-01 0.7880 0.5427
## 22 2001-01-17 0.7904 0.4616
## 23 2001-02-02 0.8284 0.5372
## 24 2001-02-18 0.6521 0.4711
## 25 2001-03-06 0.7711 0.4777
## 26 2001-03-22 0.7907 0.4912
## 27 2001-04-07 0.7810 0.4467
## 28 2001-04-23 0.7566 0.4268
## 29 2001-05-09 0.7047 0.4160
## 30 2001-05-25 0.6328 0.3271
## 31 2001-06-10 0.5894 0.2898
## 32 2001-06-26 0.5315 0.2884
## 33 2001-07-12 0.5260 0.2712
## 34 2001-07-28 0.5038 0.2602
## 35 2001-08-13 0.4550 0.2639
## 36 2001-08-29 0.4465 0.2539
## 37 2001-09-14 0.4392 0.2577
## 38 2001-09-30 0.4577 0.2706
## 39 2001-10-16 0.5749 0.3727
## 40 2001-11-01 0.7814 0.5507
## 41 2001-11-17 0.8166 0.8241
## 42 2001-12-03 0.7905 0.5492
## 43 2001-12-19 0.7398 0.4255
## 44 2002-01-01 0.7802 0.4896
## 45 2002-01-17 0.7710 0.5190
## 46 2002-02-02 0.8170 0.5845
## 47 2002-02-18 0.8004 0.5056
## 48 2002-03-06 0.7928 0.5014
## 49 2002-03-22 0.7433 0.4604
## 50 2002-04-07 0.7041 0.4006
## 51 2002-04-23 0.6949 0.3689
## 52 2002-05-09 0.5966 0.2856
## 53 2002-05-25 0.6204 0.3087
## 54 2002-06-10 0.6764 0.3646
## 55 2002-06-26 0.7012 0.3802
## 56 2002-07-12 0.6390 0.3673
## 57 2002-07-28 0.5743 0.3052
## 58 2002-08-13 0.5156 0.3100
## 59 2002-08-29 0.5338 0.3249
## 60 2002-09-14 0.4695 0.2598
## 61 2002-09-30 0.5439 0.3129
## 62 2002-10-16 0.4904 0.2636
## 63 2002-11-01 0.7132 0.5047
## 64 2002-11-17 0.7387 0.4777
## 65 2002-12-03 0.6747 0.3773
## 66 2002-12-19 0.7353 0.4377
## 67 2003-01-01 0.7677 0.5551
## 68 2003-01-17 0.7782 0.6040
## 69 2003-02-02 0.8321 0.5381
## 70 2003-02-18 0.8129 0.6274
## 71 2003-03-06 0.8307 0.5803
## 72 2003-03-22 0.8782 0.5028
## 73 2003-04-07 0.8052 0.4758
## 74 2003-04-23 0.7884 0.4689
## 75 2003-05-09 0.7703 0.3680
## 76 2003-05-25 0.7066 0.4043
## 77 2003-06-10 0.6268 0.3271
## 78 2003-06-26 0.5536 0.2954
## 79 2003-07-12 0.5278 0.3084
## 80 2003-07-28 0.4927 0.2786
## 81 2003-08-13 0.4545 0.2750
## 82 2003-08-29 0.4165 0.2306
## 83 2003-09-14 0.4496 0.2860
## 84 2003-09-30 0.5100 0.2570
## 85 2003-10-16 0.6041 0.4245
## 86 2003-11-01 0.7517 0.4743
## 87 2003-11-17 0.8122 0.5588
## 88 2003-12-03 0.8101 0.5483
## 89 2003-12-19 0.8101 0.4651
## 90 2004-01-01 0.7669 0.6099
## 91 2004-01-17 0.3635 0.3657
## 92 2004-02-02 0.7951 0.6109
## 93 2004-02-18 0.7921 0.6187
## 94 2004-03-05 0.8408 0.4761
## 95 2004-03-21 0.8223 0.5708
## 96 2004-04-06 0.8179 0.5328
## 97 2004-04-22 0.8142 0.4700
## 98 2004-05-08 0.7707 0.4154
## 99 2004-05-24 0.7403 0.4008
## 100 2004-06-09 0.6816 0.3791
## 101 2004-06-25 0.6171 0.3152
## 102 2004-07-11 0.5896 0.2930
## 103 2004-07-27 0.4975 0.2650
## 104 2004-08-12 0.4763 0.2637
## 105 2004-08-28 0.4829 0.2617
## 106 2004-09-13 0.4526 0.2730
## 107 2004-09-29 0.4872 0.3137
## 108 2004-10-15 0.5218 0.3454
## 109 2004-10-31 0.5892 0.3443
## 110 2004-11-16 0.5764 0.3062
## 111 2004-12-02 0.7673 0.5623
## 112 2004-12-18 0.8600 0.5404
## 113 2005-01-01 0.8600 0.5404
## 114 2005-01-17 0.8548 0.5483
## 115 2005-02-02 0.7882 0.5580
## 116 2005-02-18 0.8124 0.6531
## 117 2005-03-06 0.8460 0.6346
## 118 2005-03-22 0.8134 0.4623
## 119 2005-04-07 0.8334 0.5352
## 120 2005-04-23 0.8010 0.4507
## 121 2005-05-09 0.8114 0.4584
## 122 2005-05-25 0.7732 0.4488
## 123 2005-06-10 0.6514 0.3662
## 124 2005-06-26 0.6285 0.3424
## 125 2005-07-12 0.5630 0.3050
## 126 2005-07-28 0.5037 0.2713
## 127 2005-08-13 0.5037 0.2731
## 128 2005-08-29 0.4547 0.2728
## 129 2005-09-14 0.4293 0.2919
## 130 2005-09-30 0.5223 0.3232
## 131 2005-10-16 0.4566 0.3093
## 132 2005-11-01 0.5799 0.4048
## 133 2005-11-17 0.7038 0.4129
## 134 2005-12-03 0.8055 0.5045
## 135 2005-12-19 0.8174 0.5129
## 136 2006-01-01 0.8054 0.5390
## 137 2006-01-17 0.8006 0.3883
## 138 2006-02-02 0.8352 0.5290
## 139 2006-02-18 0.8258 0.5143
## 140 2006-03-06 0.8057 0.5109
## 141 2006-03-22 0.8036 0.5585
## 142 2006-04-07 0.8215 0.4954
## 143 2006-04-23 0.8001 0.5282
## 144 2006-05-09 0.7840 0.4492
## 145 2006-05-25 0.7746 0.4173
## 146 2006-06-10 0.7567 0.4206
## 147 2006-06-26 0.6755 0.3481
## 148 2006-07-12 0.5973 0.2993
## 149 2006-07-28 0.5086 0.2661
## 150 2006-08-13 0.4697 0.2634
## 151 2006-08-29 0.4503 0.2807
## 152 2006-09-14 0.4833 0.2717
## 153 2006-09-30 0.4809 0.2631
## 154 2006-10-16 0.5258 0.3417
## 155 2006-11-01 0.8063 0.5467
## 156 2006-11-17 0.8044 0.5331
## 157 2006-12-03 0.8033 0.5333
## 158 2006-12-19 0.8721 0.4925
## 159 2007-01-01 0.8721 0.4925
## 160 2007-01-17 0.8038 0.5231
## 161 2007-02-02 0.8068 0.4761
## 162 2007-02-18 0.8216 0.6133
## 163 2007-03-06 0.8263 0.5139
## 164 2007-03-22 0.7981 0.5054
## 165 2007-04-07 0.7672 0.4358
## 166 2007-04-23 0.7210 0.4055
## 167 2007-05-09 0.6784 0.3668
## 168 2007-05-25 0.5762 0.2945
## 169 2007-06-10 0.5337 0.2600
## 170 2007-06-26 0.5425 0.2753
## 171 2007-07-12 0.5102 0.2619
## 172 2007-07-28 0.4628 0.2467
## 173 2007-08-13 0.4284 0.2551
## 174 2007-08-29 0.4522 0.2541
## 175 2007-09-14 0.4253 0.2572
## 176 2007-09-30 0.4006 0.2635
## 177 2007-10-16 0.4252 0.2739
## 178 2007-11-01 0.4032 0.2356
## 179 2007-11-17 0.4340 0.2698
## 180 2007-12-03 0.6707 0.3849
## 181 2007-12-19 0.7723 0.4660
## 182 2008-01-01 0.7223 0.4671
## 183 2008-01-17 0.7664 0.6031
## 184 2008-02-02 0.7847 0.6089
## 185 2008-02-18 0.8400 0.5333
## 186 2008-03-05 0.8066 0.4999
## 187 2008-03-21 0.6652 0.2908
## 188 2008-04-06 0.8111 0.5071
## 189 2008-04-22 0.7948 0.4860
## 190 2008-05-08 0.8045 0.4646
## 191 2008-05-24 0.7915 0.4405
## 192 2008-06-09 0.7155 0.4015
## 193 2008-06-25 0.7151 0.3892
## 194 2008-07-11 0.6551 0.3513
## 195 2008-07-27 0.5809 0.3094
## 196 2008-08-12 0.5138 0.2718
## 197 2008-08-28 0.4620 0.2878
## 198 2008-09-13 0.4503 0.2447
## 199 2008-09-29 0.4452 0.2414
## 200 2008-10-15 0.4066 0.2857
## 201 2008-10-31 0.4768 0.2541
## 202 2008-11-16 0.5212 0.2731
## 203 2008-12-02 0.7434 0.5586
## 204 2008-12-18 0.8283 0.5426
## 205 2009-01-01 0.8283 0.5426
## 206 2009-01-17 0.8401 0.4812
## 207 2009-02-02 0.8485 0.5079
## 208 2009-02-18 0.8066 0.6184
## 209 2009-03-06 0.8164 0.5138
## 210 2009-03-22 0.8032 0.5457
## 211 2009-04-07 0.8067 0.5616
## 212 2009-04-23 0.8270 0.4661
## 213 2009-05-09 0.7943 0.5004
## 214 2009-05-25 0.7787 0.4793
## 215 2009-06-10 0.7171 0.3691
## 216 2009-06-26 0.5890 0.2864
## 217 2009-07-12 0.5877 0.3019
## 218 2009-07-28 0.5120 0.2721
## 219 2009-08-13 0.4341 0.2427
## 220 2009-08-29 0.4625 0.2571
## 221 2009-09-14 0.4670 0.2617
## 222 2009-09-30 0.4636 0.2862
## 223 2009-10-16 0.5865 0.4052
## 224 2009-11-01 0.7974 0.5136
## 225 2009-11-17 0.8157 0.5750
## 226 2009-12-03 0.8201 0.5470
## 227 2009-12-19 0.8143 0.5671
## 228 2010-01-01 0.8413 0.5635
## 229 2010-01-17 0.8065 0.5687
## 230 2010-02-02 0.8180 0.4959
## 231 2010-02-18 0.8350 0.4799
## 232 2010-03-06 0.8255 0.4922
## 233 2010-03-22 0.7837 0.5101
## 234 2010-04-07 0.7897 0.5140
## 235 2010-04-23 0.7520 0.4244
## 236 2010-05-09 0.6818 0.3543
## 237 2010-05-25 0.6522 0.3506
## 238 2010-06-10 0.5606 0.2771
## 239 2010-06-26 0.4737 0.2417
## 240 2010-07-12 0.4973 0.2667
## 241 2010-07-28 0.4715 0.2603
## 242 2010-08-13 0.4092 0.2333
## 243 2010-08-29 0.4048 0.2311
## 244 2010-09-14 0.3698 0.2429
## 245 2010-09-30 0.4586 0.2870
## 246 2010-10-16 0.4307 0.2462
## 247 2010-11-01 0.6527 0.4090
## 248 2010-11-17 0.7836 0.5220
## 249 2010-12-03 0.8010 0.6086
## 250 2010-12-19 0.8171 0.5739
## 251 2011-01-01 0.8171 0.5739
## 252 2011-01-17 0.8452 0.5469
## 253 2011-02-02 0.8296 0.6630
## 254 2011-02-18 0.8188 0.6069
## 255 2011-03-06 0.7933 0.5870
## 256 2011-03-22 0.8145 0.5054
## 257 2011-04-07 0.6663 0.4483
## 258 2011-04-23 0.7856 0.4709
## 259 2011-05-09 0.7339 0.3864
## 260 2011-05-25 0.7003 0.3660
## 261 2011-06-10 0.5550 0.2736
## 262 2011-06-26 0.4901 0.2446
## 263 2011-07-12 0.5176 0.2626
## 264 2011-07-28 0.4694 0.2477
## 265 2011-08-13 0.4574 0.2702
## 266 2011-08-29 0.4197 0.2346
## 267 2011-09-14 0.4313 0.2465
## 268 2011-09-30 0.4250 0.2877
## 269 2011-10-16 0.6415 0.3460
## 270 2011-11-01 0.7684 0.6101
## 271 2011-11-17 0.8285 0.5753
## 272 2011-12-03 0.8546 0.5437
## 273 2011-12-19 0.8128 0.6374
## 274 2012-01-01 0.8588 0.5105
## 275 2012-01-17 0.8222 0.5698
## 276 2012-02-02 0.7122 0.5851
## 277 2012-02-18 0.7846 0.4243
## 278 2012-03-05 0.8015 0.4841
## 279 2012-03-21 0.7755 0.4827
## 280 2012-04-06 0.7533 0.4222
## 281 2012-04-22 0.6605 0.3302
## 282 2012-05-08 0.5719 0.3303
## 283 2012-05-24 0.5170 0.2501
## 284 2012-06-09 0.4538 0.2216
## 285 2012-06-25 0.4486 0.2210
## 286 2012-07-11 0.4398 0.2141
## 287 2012-07-27 0.4267 0.2353
## 288 2012-08-12 0.4500 0.2432
## 289 2012-08-28 0.4554 0.2512
## 290 2012-09-13 0.3682 0.2406
## 291 2012-09-29 0.4556 0.2747
## 292 2012-10-15 0.3998 0.2459
## 293 2012-10-31 0.3895 0.2209
## 294 2012-11-16 0.5960 0.4143
## 295 2012-12-02 0.6449 0.3409
## 296 2012-12-18 0.7909 0.4600
## 297 2013-01-01 0.7748 0.4602
## 298 2013-01-17 0.7985 0.6631
## 299 2013-02-02 0.8537 0.5555
## 300 2013-02-18 0.8449 0.5472
## 301 2013-03-06 0.7817 0.5683
## 302 2013-03-22 0.8286 0.5014
## 303 2013-04-07 0.8020 0.4182
## 304 2013-04-23 0.7916 0.4660
## 305 2013-05-09 0.6812 0.3747
## 306 2013-05-25 0.6337 0.3156
## 307 2013-06-10 0.5962 0.2850
## 308 2013-06-26 0.5574 0.2612
## 309 2013-07-12 0.4469 0.2346
## 310 2013-07-28 0.4641 0.2457
## 311 2013-08-13 0.3935 0.2261
## 312 2013-08-29 0.4312 0.2381
## 313 2013-09-14 0.4432 0.2707
## 314 2013-09-30 0.4001 0.2415
## 315 2013-10-16 0.4504 0.2492
## 316 2013-11-01 0.6269 0.3507
## 317 2013-11-17 0.6949 0.4481
## 318 2013-12-03 0.7995 0.5279
## 319 2013-12-19 0.8611 0.5067
## 320 2014-01-01 0.8384 0.5618
## 321 2014-01-17 0.8008 0.6464
## 322 2014-02-02 0.7723 0.5944
## 323 2014-02-18 0.3673 0.3125
## 324 2014-03-06 0.8062 0.5791
## 325 2014-03-22 0.8195 0.4298
## 326 2014-04-07 0.7777 0.4812
## 327 2014-04-23 0.7632 0.4580
## 328 2014-05-09 0.7672 0.4324
## 329 2014-05-25 0.7103 0.3777
## 330 2014-06-10 0.5514 0.2895
## 331 2014-06-26 0.4847 0.2457
## 332 2014-07-12 0.4626 0.2562
## 333 2014-07-28 0.4078 0.2647
## 334 2014-08-13 0.3827 0.2479
## 335 2014-08-29 0.4059 0.2629
## 336 2014-09-14 0.4077 0.2582
## 337 2014-09-30 0.4114 0.2440
## 338 2014-10-16 0.4349 0.2537
## 339 2014-11-01 0.4633 0.2349
## 340 2014-11-17 0.6795 0.3932
## 341 2014-12-03 0.7416 0.5701
## 342 2014-12-19 0.8137 0.5893
## 343 2015-01-01 0.8418 0.5835
## 344 2015-01-17 0.7812 0.5745
## 345 2015-02-02 0.7912 0.6538
## 346 2015-02-18 0.8443 0.5329
## 347 2015-03-06 0.8184 0.6309
## 348 2015-03-22 0.8361 0.5189
## 349 2015-04-07 0.7954 0.5096
## 350 2015-04-23 0.8086 0.4231
## 351 2015-05-09 0.7851 0.4516
## 352 2015-05-25 0.6880 0.3389
## 353 2015-06-10 0.6377 0.3282
## 354 2015-06-26 0.5712 0.2812
## 355 2015-07-12 0.4961 0.2488
## 356 2015-07-28 0.4792 0.2513
## 357 2015-08-13 0.4510 0.2461
## 358 2015-08-29 0.4136 0.2332
## 359 2015-09-14 0.4169 0.2476
## 360 2015-09-30 0.4494 0.2787
## 361 2015-10-16 0.3980 0.2551
## 362 2015-11-01 0.4247 0.2491
## 363 2015-11-17 0.6314 0.3713
## 364 2015-12-03 0.7986 0.5316
## 365 2015-12-19 0.7325 0.5575
## 366 2016-01-01 0.7325 0.5575
## 367 2016-01-17 0.7876 0.6100
## 368 2016-02-02 0.8533 0.5970
## 369 2016-02-18 0.8084 0.6144
## 370 2016-03-05 0.8209 0.5070
## 371 2016-03-21 0.8291 0.4795
## 372 2016-04-06 0.7709 0.4555
## 373 2016-04-22 0.7238 0.4000
## 374 2016-05-08 0.6865 0.3826
## 375 2016-05-24 0.6302 0.3480
## 376 2016-06-09 0.6000 0.3045
## 377 2016-06-25 0.5504 0.2811
## 378 2016-07-11 0.5306 0.2796
## 379 2016-07-27 0.4658 0.2442
## 380 2016-08-12 0.4154 0.2347
## 381 2016-08-28 0.4281 0.2489
## 382 2016-09-13 0.4314 0.2707
## 383 2016-09-29 0.4926 0.2894
## 384 2016-10-15 0.7028 0.4694
## 385 2016-10-31 0.6441 0.4262
## 386 2016-11-16 0.8110 0.5431
## 387 2016-12-02 0.7986 0.5786
## 388 2016-12-18 0.8041 0.5459