The study area is depicted in Figure 1 ([56–58]) together with some environmental variables. The selected variables demonstrate a very large spatial variability of the landscape as well as climatic conditions. The study region covers an area of approximately 18 million km² (land surface: 12 million km²). Only land pixels (see Section 2.3) are included in this study without any additional efforts to mask out inland water bodies (e.g., lakes and rivers). According to the Koeppen climate classification [59], the climate in the area ranges from polar to arid. Precipitation and temperatures show a large gradient from the fully humid to very dry Sahara desert and from polar tundra to cold/hot arid. Land cover comprises a large number of different classes (mainly cropland, forest, shrubs, grassland and bare areas), and is generally fine structured [23,60]. This highly variable environmental setting permits comparing GIMMS and MODIS NDVI time series across various eco-zones and environments. Nonetheless, the findings of this study are necessarily restricted to the selected study area.

We used the MOD13Q1 and MYD13Q1 NDVI collection 5 products of the MODIS Terra and Aqua satellites from 2000 onwards from the Land Processes Distributed Active Archive Center (LP DAAC). The data of both satellites are processed in a phased production providing a global NDVI with improved temporal frequency of eight days (Terra 16-day period starting Day 001, Aqua 16-day period starting Day 009). The gridded Level-3 product offers data in approximately 250-m spatial resolution in Sinusoidal projection. The Level-3 product is calculated from the Level-2G daily surface reflectance gridded data (MOD09 and MYD09 series) using the Constrained View angle-Maximum Value Composite (CV-MVC) compositing method [61].

For processing the data, we set-up in a first step an operational processing chain that downloads, mosaics, resamples, reprojects, and performs an image cropping to a dedicated tile system on a daily basis based on the “MODIS” R package [62]. The data are reprojected to geographic coordinates (datum WGS84) using nearest neighbor resampling. One file of the dedicated tile system covers the extent of 1 × 1°. The 448 × 448 pixels per tile have thus a spatial resolution of 0.002232°. The reprojected data are archived and further processed in two different ways: (1) an on-demand simplified filtering is applied upon user’s request via a web application [63], and (2) operational filtering procedures are applied for European areas with two processing lines: (i) an enhanced near real-time (NRT) weekly processing of new/updated NDVI data, and (ii) a processing of the entire NDVI time-series at once (launched only once a year). For this study, only the last data (ii) were considered. All procedures were implemented in MATLAB and are based on the Whittaker smoother [28,64,65]. Compared to our web application [63], the operational filtering procedures have the advantage to take the MODIS quality flag during smoothing into account, as well as the exact composite day. The Whittaker smoother was shown to perform well against a number of other filters based either on curve fitting or Fast Fourier transform (FFT) [66]. In [64], it was shown that this filter permits a significant increase in the signal-to-noise ratio (SNR) of coarse resolution NDVI time series.

Besides VI usefulness information, the smoother also takes into account land/water mask layers of the VI Quality Assessment Science Data Set [61]. Pixels having a VI usefulness value lower than three were considered to be acceptable and assigned a weight of one (very good to good quality), while a VI usefulness larger than seven was excluded from further processing with a weight of zero (not acceptable). VI usefulness values between three and seven were linearly scaled between one and zero.

For the back-processing, the smoothing parameter λ of the Whittaker filter was fixed to a constant value for the entire study region. After some trial-and-error tests, a value of 30.000 was found acceptable, balancing fidelity to the MODIS data with the roughness of the resulting curve. To further reduce the possible impact of undetected clouds and poor atmospheric conditions, three filtering iterations were performed to fit the upper envelope of the NDVI. Multiple filter runs were for example recommended by [2,12]. The second parameter of the Whittaker smoother (i.e., order difference) was set after some tests to two. Based on the order difference, the smoother calculates the roughness of the smoothed curve [65]. From the resulting daily NDVI values (combining inputs from MOD13Q1 and MYD13Q1), all images corresponding to “Mondays” were extracted and stored as a 7-daily data set. This NDVI is further referred as filtered MODIS data set. The weekly data were considered sufficient for most of the analyses, reducing the computational load of the exercise. For the analysis of timing of (phenological) events, however, the (smoothed) daily NDVI series were used allowing a better retrieval of start/maximum of season.

After smoothing, the MODIS data set was spatially aggregated to fit the resolution of the GIMMS data set (1/12°). This was done by averaging the smoothed MODIS data to the GIMMS grid. Pixels flagged as water were excluded from the averaging procedure. With respect to coastal pixels, a mask was applied for the subsequent analysis. It comprises all pixels that represent water in at least one time step of either of both time series. This mask was expanded by one pixel to further reduce possible artifacts. The remaining land pixels should be largely unaffected by coastal water. However, no attempts were made to exclude inland water bodies from the two series.

As the NDVI does not scale linearly there will be a certain impact compared to aggregating the reflectances and then calculating NDVI e.g., [67]. Nevertheless, we decided to aggregate NDVI rather than the reflectances. The decision was done after having analyzed the impact of the different aggregation approaches for a test dataset (2002 to 2004) covering the Iberian Peninsula. For the exercise, MOD09Q1 reflectance data were used. From the reflectances, the two spatially aggregated NDVI were calculated. It turned out that the impact of different aggregation schemes was significantly smaller than the one caused by using different sensors (not shown).

The NDVI3g data set is the latest version of the Global Inventory Modeling and Mapping Studies (GIMMS) project [44]. The data set is currently under investigation by a number of research teams. Important contributions can be found in this special issue. The original GIMMS data set was produced from the AVHRR sensor data taking into account various deleterious effects, such as calibration loss, orbital drift, volcanic eruptions, etc. [68]. The third generation GIMMS NDVI is a 15-day Maximum Value Composite derived from AVHRR sensor data from NOAA 7 to 18 satellites. It covers the period 1981–2011. The data set has an improved calibration and cloud masking compared to older versions of the GIMMS data set [44]. For the purpose of our study, the extent of the GIMMS NDVI3g data set was cut to the extent of the study area (Figure 1), while preserving the original GIMMS NDVI3g grid with a spatial resolution of 1/12°.

To allow comparability between the two time series, the GIMMS data set was smoothed in a similar way as the MODIS data. As the exact composite DOY of the GIMMS data set is not known, the 8th and 23th day of the month were assigned as DOY for the 1st and 2nd compositing period of the month, respectively (Table 2). Next, the Whittaker filter was applied to the GIMMS data set to produce daily NDVI values between 2002 and 2011 (ten years). Similar to the MODIS data, the filtered GIMMS data were saved as 7-daily values (corresponding to Mondays). For detecting the phenological indicators, we made again use of the daily GIMMS values.

Regarding a suitable filter setting for the GIMMS data, different tests were performed. The tests aimed at identifying a parameter setting providing GIMMS data similar to the MODIS data in terms of curve shape, amplitude and timing of feature of the NDVI profiles. The decision was made based on the root mean square difference (RMSD) between the data sets. The selected setting was a λ of 30.000, one iteration and a second order difference. Table 2 summarizes the main choices regarding the spatio-temporal homogenization of the two data sets.

Note that filtering the GIMMS time series ending December 2011 implies that the last observations were possibly less accurately filtered compared to observations situated in the middle of the series (e.g., temporal edge effects). This was considered overall acceptable but might influence some of the results. This problem did not occur when filtering the MODIS data because the MODIS time series extends into 2013 (and starts before 2002).

Phenological metrics were extracted for all pixels having a maximum NDVI of at least 0.3. An approach was implemented for detecting uni- and bi-modal growing seasons. In case of bi-modal growing seasons, only the metrics of the first season were extracted. The selected approach can also handle seasons spanning over different years. The extraction was done in four steps: (1)

Detecting the number of cycles by means of auto-correlation information (e.g., [69]): The number of lags was chosen to be little less than two years. Next the algorithm was searching for maxima and minima on the auto-correlation function (ACF). Two cycles were detected, if a second distinct maximum in the ACF before the end of the year appeared. The maximum was accepted, if the increase before the maximum and decrease after the maximum in the ACF was more than 0.1.

The extraction procedure used the entire filtered time series from 2002 to 2011 at daily time steps. However, the actual start and maximum were detected for the growing seasons from 2003 to 2011. This restriction was necessary as growing seasons might span different years. For example, valid starts of the growing season of 2003 can range from beginning of July 2002 (−183) to end of June 2003 (181) counted in days of year (DOY). The timing of the seasonal maximum is defined in a similar way, e.g., ranging from the beginning of November 2002 (DOY −60) to end of October 2003 (DOY 304). If values occurred outside the defined start and maximum ranges, they were considered misdetections and flagged as “no data”. A number of alternative algorithms for extracting phenological signals from remotely sensed time series have been described in the literature (for a review see [3,72]). However, it was out of scope of this study to explore more than one algorithm.

Generally, GIMMS and MODIS NDVI data sets show a reasonable agreement regarding their spatial distribution and temporal behavior. Exemplary annual profiles (averaged over the 2002–2011 time period) of the two time series are reported in Figure 2. Likewise, the two cumulated distribution functions derived from the entire time series display only little divergences (Figure 3). This also holds for the multi-annual mean and standard deviation (Figure 4). Together these findings demonstrate a generally relative good correspondence between the GIMMS and MODIS derived vegetation densities. It also demonstrates the success of the applied pre-processing and smoothing, yielding identical spatial and temporal resolutions of the originally very different data sets.

However, despite the general agreement, some persistent differences can be observed. In particular, in winter time, significant differences in the averaged NDVI of the two time series are visible in Northern and Eastern Europe (e.g., Sweden, Finland) (Figure 5). On the contrary, the agreement between the two data sets is better for these areas during summer months (June, July, and August) and (to a lesser extent) in spring and autumn. The same can be observed in Figure 2 where some of the displayed profiles reveal a stronger disagreement during winter time. However, particularly in Spain, France and Italy, one can observe higher differences in the summer and spring months than in winter.

The differences between the two time series become more evident, when plotting (pixel-by-pixel) the NDVI values against each other (Figure 6). The results indicate relatively large scatter around the 1-to-1 line with sometimes extremely large differences between individual observations. In addition, a small bias between GIMMS and MODIS is observed. The GIMMS data reveal on average a somewhat higher NDVI compared to MODIS. However, most of the observations fall well within a range of ± 0.1 NDVI units (Figure 6, right). Calculated over all pixels and all time steps (i.e., all weekly observations between 2002 and 2011), we find a correlation between GIMMS and MODIS time series of about (R²) 0.88 (Figure 6). This correlation shows a clear seasonal component (Figure 7, left). The intra-annual coefficient of determination (R²) varies between 0.78 (winter) and 0.92 (summer).

A value of R² ≥ 0.9 is found between week 13 (end of March) and 37 (mid-September). The root mean square difference (RMSD) exceeds >0.05 throughout the year (blue line), with values approaching or exceeding 0.10 between week 40 (Beginning of October) and 13 (End of March). This confirms again that the largest differences regarding the observed vegetation densities occur during winter time. The inter-annual agreement/disagreement between the two data sets is depicted in Figure 7 (right). Results show only little variability from year to year, except for the last year in the time series (2011). Indeed, this year is the last year in the original GIMMS time series. Hence, the filtering/smoothing might be affected by the temporal edge effects mentioned before (2.5). This will in particular affect the November/December observations of GIMMS (see also weeks 49 to 52 in Figure 7 left). We tested the effect of excluding the weeks 49–52 of 2011 on the calculations of Figure 7. The biggest absolute differences for the intra-annual variation of RMSD and R² appear in week 52 with 0.006 and 0.02, respectively. The absolute differences for the inter-annual variation of RMSD and R² calculated for 2011 are slightly lower. As the described differences in these particular weeks are irrelevant for calculating SOS and MOS, we kept all data in our analysis.

The spatial pattern of the pixel-wise correlation between the two time series across all weekly observations is shown in Figure 8 (left). The map reveals a clear spatial pattern with high correlations (>0.8) over much of the central and eastern part of Europe as well as the northern parts of the Maghreb countries (Algeria and Morocco). Correlations are markedly lower in the coastal parts of Spain, Italy, and Greece/Turkey and to a lesser extent in France, Ireland and the UK. Particularly in Portugal, Galicia, and to a lesser extent in Brittany, very low correlations are accompanied with almost continuously high NDVI levels and a low variability (see Figures 4 and 5). In these areas, clear differences between the NDVI profiles occur (not shown). Very low correlations between the time series are also found over the arid parts of North Africa. In these areas, however, the low correlations are a direct result of the constantly low vegetation density (Figure 5). To further explore the impact of intra-annual vegetation dynamics on the derived (pixel-wise) agreement/disagreement between the two time series, Figure 8 (right) shows the RMSD between the two data sets.

The RMSD pattern displays a relatively high disagreement over Scandinavia and Eastern Europe, but also in the alpine region and Spain. The best agreement is observed over the constantly dry parts of North Africa (e.g., Sahara) and the non-coastal areas of the UK and Ireland. Some larger reddish spots (RMSD > 0.2) in Sweden and Estonia/Russia are due to inland lakes not masked out for this study.

The start of the season (SOS) was determined for each pixel and each year in the time series (2003–2011) using the relative threshold approach described in Section 2.6. The algorithm yields up to nine SOS estimates per pixel. The cumulated distribution functions of SOS derived from the two time series are shown in Figure 9. Both data sets reveal a similar shape of the SOS distribution. However, GIMMS (in red) depicts SOS frequently more than one week earlier, compared to MODIS (in blue). A similar trend is already visible in Figure 2 where the NDVI profiles of the GIMMS data start rising earlier than MODIS.

The inter-annual variability (“range”: difference (in days) between maximum and minimum) of SOS exhibits a relative similar spatial distribution in both data sets (Figure 10). However, the SOS extracted from the MODIS time series shows a larger inter-annual variability compared to GIMMS in many coastal areas of the North Sea (Belgium, Netherlands, Germany, Poland, and Sweden). The opposite can be observed over the north part of Spain.

A more detailed analysis at pixel level shows that the SOS extracted from the two series often reveal high differences. Figure 11 (left) presents the frequency distribution of the SOS differences (SOS_GIMMS–SOS_MODIS) over the entire time series (2003–2011). It can be seen that many observations fall outside the range of ±30 days. Only 32% of the observations have (acceptable) differences ≤1 week. Generally, GIMMS depicts the SOS earlier than MODIS confirming earlier findings (Figures 2 and 9). This can be consistently observed for individual years and is exemplarily shown in Figure 11 (right) for the year 2007. In this example, MODIS data evidences a SOS on average 14 days later than GIMMS. The differences between the two time series can also be clearly seen when mapping the spatial distribution of the SOS for a particular year. For example, Figure 12 (right) displays the SOS for 2007 estimated by GIMMS (top) and MODIS (bottom). The median SOS across all years (Figure 12, left) confirms again the large differences between the two data sets regarding the SOS.

The disagreement between the two time series is further sustained when plotting the SOS of both time series against each other (Figure 13). The regression analysis between the two SOS data sets reveals only a R² of ∼0.66, if data from all years are pooled together. A larger number of strong outliers can also be detected. They mostly correspond to cases where the detection algorithm (see Section 2.6) depicts different parts of the growth cycles of an individual pixel. This often happens if the profiles show multiple—but not well distinguished—peaks in one but not the other data set (not shown).

Analyzed separately for each individual year, some inter-annual variability in the correlation between SOS from GIMMS and MODIS are found (Figure 14). Somehow higher (spatial) correlations can be observed in 2005, 2006, and 2009, which also correspond to years with delayed onset of vegetation growth (negative North Atlantic Oscillation index) and more homogeneous growth patterns. Despite the R² occasionally exceeding 0.7, the RMSD between the two series of SOS always remains in the range 30–40 days (blue).

At the pixel level, we find both high and low rank correlation (Spearman’s Rho) between SOS from GIMMS and MODIS (Figure 15). P-values were computed for testing the hypothesis of no correlation against correlation is greater than zero (Figure 15, upper right). In most cases, the strong positive correlations (>0.6) were significant at the 0.05 level. Low/negative correlations are often present in areas with reduced inter-annual variability of SOS and where extracting SOS is influenced by snow cover (Figure 10).

Similar to the SOS, the maximum of the season (MOS) was determined within the growing season for each pixel and each year in the time series (2003–2011), yielding up to nine MOS estimates per pixel. The cumulated frequency distributions of the MOS extracted from GIMMS and MODIS are shown in Figure 16 (top) demonstrating a good correspondence between the two data sets. Likewise, the co-distribution shown in the scatterplot of Figure 16 (bottom) reveals, that the majority of the pixels (in green-yellow-red) well distribute around the 1-to-1 line.

The spatial pattern in MOS is similar for the two data sets when averaged over all years (Figure 17, top). The same holds to a lesser extent for the observed inter-annual range of MOS (bottom); compared to the MODIS extracted MOS, the inter-annual variability derived from GIMMS data is often much higher. In some areas, the range between the earliest and the latest MOS exceeds 100 days where MODIS yields an inter-annual range of MOS of about 30 days (e.g., southern part of Sweden). Secondary maxima in the GIMMS data, not present in MODIS, are the main reason (not shown).

The correlation between the two MOS products at pixel level is displayed in Figure 18 (left) along with the median of differences (right). In most regions, the GIMMS and MODIS MOS values had a Spearman’s Rho exceeding 0.4. Regions with low rank correlation (left) and high p-value (center) often correspond to regions with low SOS correlation (Figure 15, top left).