# Time domain indicators and operations

## Contents

## Compositing

### Monthly composites (S30)

The monthly composites of MCYFS are always derived from the 10-daily composites, during the post-processing. Contrary to the compositing in the pre-processing, another program for compositing is used (i.e. the GLIMPSE module COMPOSIT), which basically works in the same way. The compositing inspects several input images, registered at different times/dates within a given period (one month in this case). These “inputs” must all be expressed in the same geo-referencing system and cover parts or the totality of a given target region. The procedure then creates a single output image (the composite or synthesis), by inspection of each pixel in the target area, scanning of the corresponding input-measurements and selection of the “best available measurement” according to a specified “compositing criterion”. In practice, the compositing is mostly performed with grouped input images. This means that each “input” relates to several image layers (spectral bands, NDVI, angles, ancillary info) – all with the same registration time and extension.

The compositing criterion used in MCYFS is either a conditioned NDVI-MVC (Maximum Value Compositing) or maximum fAPAR criterion. This gives preference to the values of the registration with the highest NDVI (NOAA- and METOP-AVHRR-S10) or fAPAR (VGT-S10 and MODIS-S10), as far as this is labelled as cloud free and falls within the accepted range of scan angles (or view angles). Once, this “best registration” is defined, all its values (bands, NDVI, angles, ancillary data,…) are copied to as many layers in (separate ENVI-images) the composite. DMP is treated separately with a mean filter.

### Quality of the compositing

The different compositing steps (Segments→S1→S10 →S30) can be evaluated by means of the following two ancillary images, which are also created by the involved programs:

- IMG with Ngood: This gives per pixel the number of unflagged measurements available for the compositing. The higher Ngood for a certain pixel, the better the choice.
- IMG with Segment_ID: This is the ID of the raw segment whose values were selected by the compositer for the concerned pixel. Via this ID, also the other characteristics of the segment can be traced back (registration data/time, cloud cover, RMSE,...). The quicklooks with the registration date are derived in this way.

## Long term statistics

For the most relevant vegetation parameters (NDVI, fAPAR, DMP, Ts) the long term statistics is computed, also called Historical Year (HY). This is interesting as such, but it also forms the reference for the computation of Difference images. GLIMPSE-program HISTORY scans all images available over the years, for a selected variable and period in the year (e.g. all DMP-images of the 10th dekad in the year). It then creates 14 new images, which parameterize the historical distribution of each pixel: 11 deciles (Min,…, Median,… Max), the mean µ, the standard deviation σ, and the number of “good” measurements (Ngood) available to compute these statistics (no snow/cloud/error). The deciles (except Min/Max) are optional, and in practice they are only needed for the computation of the VPI (Sannier et al., 1998), or in general HPVI (see Difference to long term average).

The 14 parameters are stored in separate images |
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The 14 parameters are stored in separate images and labelled via the years yy=50-63: • yy=50-60: Deciles of variable in steps of 10% (50=Min, 55=Median or 50% decile, 60=Max) • yy=61: Number of “good” measurements available to compute statistics (no snow/cloud/error) • yy=62: Mean value of the parameter (sensu strictu, this is the Long Term Average LTA) • yy=63: Standard deviation around the mean |

For each variable (NDVI, fAPAR,...) the HY thus comprises 168 or 60 S30-images (12 months x 14/5) and 504 or 180 S10-scenes (36 dekads x 14/5). The Ngood-images are always BYTE, but the others have the same scaling (VALUES) and datatype as the input images (all BYTE, except Short INTEGER for DMP). However, they only have one flag (255, -32768 for DMP) which groups all cases with missing values (cloud/snow/error/nodata). More on data formats can be found in the section Images.

Information on the filenames of the historical year is provided in the section Filename conventions.

The historical year is regularly updated to include the most recent years. The timing and periodicity of the update depends on the sensor (in general every 2 years).

## Difference images

Difference images are computed for all relevant variables (NDVI, fAPAR, DMP, Ts) and both periodicities (S10, S30). As shown in the table below, there is choice between various operators, and both the previous year and the historical year can be used as a reference.

_{Difference Operators}

*X( _{y,p}) = Value of variable X in period p (dekad/month) of year y*

*MIN( _{p}), MAX(_{p}), µ(_{p}), σ(_{p})= minimum, maximum, mean and standard deviation of the “Historical Year” for given variable X and period p*

All requested difference images can be computed with GLIMPSE-programs INDEX (to previous year) and HISTORvi (to historical year). When applied on NDVI, the HPVI (Historical Probability Vegetation Index) or HCVI (Classified Historical Probability Index) to Sannier's VPI (Vegetation Productivity Index). This index requires the presence of the deciles in the historical year (see Long term statistics).

The different operators are discussed below in more detail.

### Difference to previous year

Two different operators are used to express the difference between the current and the previous year, i.e. the absolute and the relative difference. The following table expresses for which sensors and indicators these two differences are computed.

_{Difference products delivered for the different sensors and indicators in MCYFS. I: image format, Q: quicklook, D: database. circle with +: smoothed time series, + : non-smoothed time series.}

### Difference to historical year

The difference images for the MCYFS are based on a “fixed” historical year (see Long term statistics), which is only recomputed at fixed time intervals, to include at once all the data of the previous year. However, in this approach new observations can indeed fall beyond the historical Min/Max. For HPVI (VPI), the program HISTORVI (GLIMPSE) clearly labels this kind of outliersIn the alternative approach, at every dekad the historical year is first updated to include the new image before the differences are computed. This eliminated the chance that the HPVI runs beyond its natural limits (0% - 100%).

The difference operators used in MCYFS are listed in the table above. The tabulated difference operators are extremely correlated, so it suffices to select only one or two. Compared to the absolute and relative difference, the other differences use the distribution of the concerned indicator, making them more suitable to interpret the spatial patterns of the magnitude or severity of the change.

When applied on the NDVI, the HPVI is the Vegetation Productivity Index of Sannier et al. (1998). More information on how to interpret the HPVI can be found in the box below.

Interpretation of the HPVI

The figure above shows an example for the case of NDVI. The green line represents the cumulative histogram, which is derived from the historical values available for the considered period. The red line, which connects the selected set of percentiles, forms an approximation of the true histogram. These percentiles are derived and stored by program HISTORY. But while the figure only shows 6 of these (P0, P20, …, P100), we work with 11 deciles (P0, P10, …, P100). New observations are referenced to this (approximative) histogram, which allows deriving their historical probability. The example (blue point) has a relatively high NDVI and hence a high probability (89%). Thus, 89% of the past observations were equal or less than the current value and 11% of the past observations is higher. A probability of 50% means that in 50% of the past observations, the value was equal or less than the current value, and that in 50% of the past observations the value is higher than the current value. Therefore, the current value corresponds to the median value. Sannier et al. (1998) immediately classified the probabilities in 5 groups (HCVI: 0-20%, …, 80-100%). We however keep the orig¬inal probabilities (BYTE: in steps of 0.5%). The classification is only performed at the level of the QuickLooks.

The following table lists which differences relative to the historical year are computed for MCYFS.

**Difference products delivered for the different sensors and indicators in MCYFS.**

**I: image format, Q: quicklook, D: database. circle with + : smoothed time series, + : non-smoothed time series.**