Sixty-plus cumulative years of different data sets were acquired over the 21-year period [1993–2013]. They include measurements from 10 different altimeters: ERS-1 (repeat 35-day and geodetic 168-day period orbits), ERS-2, EN (repeat track and geodetic orbits), TP (historical repeat orbit and new interleaved orbit, i.e., on the midway of its historical ground tracks), J1 (repeat track orbit, interleaved and geodetic end of life orbit), J2, GFO, C2, AL and HY-2A. The different periods covered by the different altimeters are summarized in Fig. 1. The main differences from DT2010 are the introduction of the year 2011 for C2 and the first cycles of the J1 geodetic orbit (cycle 500 to 505, May to mid-June 2012).

The detection of invalid measurements involves various algorithms, from the simplest, such as threshold selection for the different parameters, to more complex (e.g., SLA selection with splines). It was based on the same approach developed for DT2010, detailed in Dibarboure et al. (2011). Details of threshold editing can be found in the handbook of each altimeter mission (e.g., Aviso/SALP, 2013, 2015b) as well as Cal/Val reports and publications (e.g., Aviso/SALP, 2015a; Ablain et al., 2010).

For the DT2014 processing, a specific procedure was established specifically for non-repeat track and new repeat track orbit missions, inducing a more restrictive data selection. As these new missions are able to sample the ocean surface in areas never reached before by older altimeters, their data are usually contaminated by the reduced quality of the mean sea surface (MSS) in these specific areas. Such anomalies were observed in the DT2010 along-track SLA fields, and were responsible for the introduction of anomalies into the gridded fields, especially in coastal and high-latitude areas. In order to avoid this problem in the DT2014 products, the criteria used for the detection of erroneous measurements along non-repeat tracks and the new repeat tracks were strongly restricted in coastal areas. Indeed, the measurements along the ERS-1 (during the geodetic phase), EN geodetic, J1 geodetic, C2, and HY-2A orbits are systematically rejected when closer than 20 km to the coast. In the same way, the poor quality of the MSS in the Laptev Sea leads to systematic rejection of the measurements along non-repeat track orbits in this area. The use of a MSS to generate SLA along non-repeat track orbits is discussed in Sect. 2.2.4.

The first homogenization step consists of acquiring altimeter and ancillary data from the different altimeters that are a priori as homogeneous as possible. The data should include the most recent standards recommended for altimeter products by the different agencies and expert groups such as OSTST, ESA Quality Working groups or the ESA SL_cci project. The up-to-date standards used for DT2014 are described and discussed in Sect. 2.1.

Although the raw input L2 GDR data sets are properly homogenized and edited (see Sect. 2.2.2), they are not always coherent due to various sources of geographically correlated errors (instrumental, processing, orbit residual errors). Consequently, the multi-mission cross-calibration algorithm aims to reduce these errors in order to generate a global, consistent and accurate data set for all altimeter constellations.

The second homogenization step, crucial for climate signals, consists of ensuring mean sea level continuity between the three altimeter reference missions. The DUACS DT system uses, first, TP from 1993 to April 2002, then J1 until October 2008 and, finally, J2 that covers the end of the period. This processing step consists of reducing the global and regional biases for each transition (TP-J1 and J1-J2), using the tandem phase of the J1 and J2 altimeters where the altimeters follow the same orbit with a few minutes' phase offset. The methodology is described in ESA SL_cci (2015). After removing the mean global bias observed, the regional biases are estimated in two steps. First a polynomial along-track adjustment allows reduction of the latitude-dependent biases between the two successive reference missions. A second adjustment consists of reducing regional long-wavelength residual biases. As illustrated in Fig. 2, this adjustment permits removal of large spatial pattern (basin-scale) errors on the order of 1–2 cm.

Next, a cross-calibration process consists of reducing orbit errors through a global minimization of the crossover differences observed for the reference mission, and between the reference and other missions also identified as complementary and opportunity missions (i.e., TP after April 2002, J1 after October 2008, ERS-1, ERS-2, EN, GFO, AL, C2 and HY-2A). The methodology, used also for DT2010 data set, is described by Le Traon and Ogor (1998).

The last step consists of applying the long-wavelength error reduction algorithm. This process reduces geographically correlated errors between neighboring tracks from different sensors. This optimal interpolation-based empirical correction (Appendix B) also contributes to reduction of the residual high-frequency signal that is not fully corrected by the different corrections that are applied (mainly the Dynamic Atmospheric Correction and Ocean tides). This empirical processing requires an accurate description of the variability of the error signal associated with the different altimeter missions. The variance of the correlated long-wavelength errors used in the DT2014 processing is described in Sect. 2.2.6.

In order to take advantage of the repeat characteristics of some altimeter missions, and to facilitate use of altimeter products by the users, the measurements are co-located onto theoretical positions, allowing us to estimate a precise mean sea surface (MSS) along these tracks, also referred to as the mean profile (MP). The MPs are time averages of the co-located sea surface height (SSH) measured by the altimeters with repeating orbits. The DT2014 reprocessing includes the reprocessing of these MPs along the TP/J1/J2, TP-interleaved/J1-interleaved, ERS-1/ERS-2/EN/AL and GFO tracks. The MPs need to be consistent with the altimeter standards (see Sect. 2.1) and the MSS that is used for the non-repeat track orbit missions. MP reprocessing includes specific attempts to improve accuracy and extend the estimates into the high-latitude areas. One of the main changes included in the new MP reprocessing is the use of a new 20-year [1993–2012] altimeter reference period, as more fully explained in Sect. 2.3. Additionally, the precision of the different MPs was improved by combining altimeter data that are on the same orbit. In this way, TP, J1 and J2 measurements are all used to define the corresponding MP; TP-interleaved and J1-interleaved or ERS-2 and EN are also merged. ERS-1 measurements were not used in the MP computation. We indeed considered that the temporal period covered by ERS-2 and EN was long enough and allows us to discard the reduced-quality ERS-1 35-day repetitive measurements over year 1993. This processing leads to an improved definition of the MPs with, in particular, a gain of defined positions near the coast. The number of points defined within 0–15 km from the coast in the new MPs is twice (3 times) the number observed in the previous MP version along respective TP and TP-interleaved theoretical tracks. In the same way, an additional 15 to 20 % points are defined near the coasts along the GFO and EN theoretical tracks in the new MPs. The MP along EN theoretical tracks is also more accurately defined in the high-latitude areas, taking advantage of increased ice melt since 2007 (Fig. 3).

In the case of the non-repeating missions (i.e., ERS-1 during the geodetic phase; EN after the orbit change; J1 in the geodetic phase; C2) or recent missions following the newest theoretical track (i.e., HY-2A), the estimation of a precise MP is not possible. In this case, the SLA is estimated along the real altimeter tracks, using a gridded MSS as a reference. The latter is the MSS_CNES_CLS_11 described by Schaeffer et al. (2012) and corrected in order to be representative of the 20-year [1993–2012] period (see also Sect. 2.3).

The SLA, obtained by subtracting the MP or MSS from the SSH measured by the altimeter, is affected by measurement noise. A Lanczos low-pass along-track filtering allows us to reduce this noise. Two different filtering parameterizations are used, according to the application. For the generation of the L3 along-track SLA, the cut-off wavelength was revisited in the DT2014 in order to reduce random measurement noise as much as possible whilst retaining the dynamic signal. More details are given in the following section. For the generation of the L4 gridded SLA, the filtering is also intended to reduce small-scale dynamical signals that cannot be accurately retrieved. Details are given in Sect. 2.2.6.

The gridded product processing parameters are a trade-off between the altimeter constellation sampling capability and the signal to be retrieved. For DT2010 the processing and, in particular, the along-track noise filtering were set up in accordance with this objective. Consequently, the global DT2010 along-track SLA products were low-pass filtered with a Lanczos cut-off filter with wavelengths depending on latitude (250 km near the Equator, down to 60 km at high latitudes). This technical choice was mostly linked to the ability of the TP altimeter mission to capture ocean dynamic mesoscale structures (Le Traon and Dibarboure, 1999). However, it strongly reduced the along-track resolution that can be useful and beneficial for modeling and forecasting systems. For this reason a dedicated along-track product that preserves the along-track 1 Hz short-wavelength signals has been developed in the framework of the DT2014 reprocessing. The main inputs come from the study by Dufau et al. (2016).

A SLA power spectrum density analysis was used in order to determine the wavelength where signal and error are on the same order of magnitude. It represents the minimum wavelength associated with the dynamical structures that altimetry would statistically be able to observe with a signal-to-noise ratio greater than 1. This wavelength has been found to be variable in space and time (Dufau et al., 2016). The mean value was found to be nearly 65 km. It was defined with a single year of Jason-2 measurements, over the global ocean, excluding latitudes between 20∘ S and 20∘ N (due, in part, to the limit of the underlying surface quasi-geostrophic turbulence in these areas). In the end the cut-off length of 65 km in the DT2014 along-track low-pass filtering processing was retained. It is considered as the minimal low-pass cut-off length that can be applied to along-track SLA in order to reduce noise effects and preserve as much as possible the physical signal. This however cannot be defined as a perfect noise removal operation since, in practice, a signal-to-noise ratio of 2 to 10 (cut-off with a wavelength of 100–150 km or more) would be required to obtain a noise-free topography.

The filtered along-track products are subsampled before delivery in order to retain every second point along the tracks, leading to a nearly 14 km distance between successive points. Because some applications need the full resolution data, the non-filtered and non-sub-sampled products are also distributed in DT mode.

Before the multi-mission merging into a gridded product, the along-track measurements are also low-pass filtered in view of the mapping process. In this case, the aim of the filtering is also to reduce the signature of the short-scale signals that cannot be properly retrieved mainly due to limitations of the altimetry spatial and temporal sampling. Indeed, the altimeter inter-track diamond distances and the revisit time period limit the observation of mesoscale structures. Previous studies (Le Traon and Dibarboure, 1999; Pascual et al., 2006) underscore the necessity of a minimum of a two-satellite constellation for the retrieval of mesoscale signals. Thus, in view of the mapping process, the along-track SLA are low-pass filtered by applying a cut-off wavelength that varies with latitude in order to attenuate SLA variability with wavelengths shorter than nearly 200 km near the Equator, and nearly 65 km for latitudes higher than 40∘. Finally, a latitude-dependent sub-sampling is applied in order to be commensurate with the filtering.

The objective of the mapping procedure is to construct a SLA field on a regular grid by combining measurements from different altimeters. The DUACS mapping processing mainly focuses on mesoscale signal reconstruction. It uses an optimal interpolation (OI) processing as described in Appendix B. This methodology requires a description of the observation errors and of the characteristics of the physical signal that we want to map. The parameters used for the mapping procedure are a compromise between the characteristics of the physical field we focus on and the sampling capabilities associated with the altimeter constellation. The parameters used in the DT2014 OI processing were optimized. An important improvement implemented in DT2014 is the use of more accurately defined correlation scales for the signal we want to map, and a more precise estimation of the error budgets associated with the different altimeter measurements. These two parameters indeed have a direct impact on mapping improvements as underscored by previous studies (Fieguth et al., 1998; Ducet et al., 2000; Leben et al., 2002; Griffin and Cahill, 2012, among others). The spatial variability of the spatial and temporal scales of the signal (see Dibarboure et al., 2011) is better accounted for. Both the spatial and temporal scales are defined as functions of latitude and longitude. The spatial correlation scales however stay mainly dependent on latitude. Evolution of the zonal and temporal correlation scales with latitude is given in Fig. 4. The zonal (meridional) correlation scales range between 80 (80) km and slightly more than ∼ 400 (300) km. The larger values are observed in the low-latitude band (±15∘ N) where they are mainly representative of the equatorial wave signature. A global reduction of the correlation scales is observed in the poleward direction. At mid-latitudes (between 20 and 40∘), the typical values observed range between 100 (100) km and 200 (150) km for zonal (meriodional) scales. Poleward of 60∘, local increases of up to 200 km of the correlation can be observed. Temporal scales are more dependent on both longitude and latitude position. Shorter temporal scales are fixed at 10 days. The longer scales are observed at mid-latitudes (20 to 60∘) where maximum observed values range between 30 and 45 days. Propagation speeds are also taken into account. They are mainly westward oriented with extreme values ranging from nearly 30 cm s-1 for latitudes around 5∘ to a few centimeters at high latitudes. Eastward propagations of a few centimeters are also observed close to the Equator and in the circumpolar jet.

Observation errors are defined with an uncorrelated component and an along-track long-wavelength correlated component (see Appendix B). The variance of the uncorrelated errors is defined assuming a 1 Hz initial measurement noise of nearly 3 cm for TP, J1, J2 and AL. Nearly 4 cm is used for the other altimeters. The effect of the filtering and sub-sampling that are applied to the measurement is taken into account and modulates the initial noise estimation. In addition to this noise effect, nearly 15 % of the signal variance is used to take account of small-scale variability, which cannot be retrieved (see the discussion in Le Traon et al., 2001). Additional errors induced by the geodetic characteristics of some orbits (and also the use of a gridded MSS, rather than a more precise MP, as explained in Sect. 2.2.4) are taken into account. In the same way, additional variance is included in the altimeter error budget for which the absence of dual-frequency and/or radiometer measurements leads to the necessity for a model solution for the ionospheric and wet-troposphere signal corrections. The variance associated with along-track long-wavelength correlated errors corresponds to the residual orbit errors, as well as tidal and dynamic atmospheric signal correction errors. In the DT2014 products, the long-wavelength residual ionosphere signal, which can be observed when this correction is obtained from a model (typically for missions with mono-frequency measurements), is taken into account for ERS-2, C2 and HY-2A. In the same way, geodetic missions, for which no precise mean profile is available (see Sect. 2.2.4), present additional long-wavelength errors induced by the use of a global gridded MSS for the SLA computation. These additional MSS errors are taken into account in the reprocessed products for C2, J1 geodetic phase, EN on it geodetic orbit and HY-2A. In the end, the variance of long-wavelength errors represents between 1 and 2 % of the signal variance in high-variability areas (e.g., the Gulf Stream, Kuroshio) and up to 40 % in low-variability areas and in high ionospheric signal areas for missions without dual-frequency measurement.

Other important changes in the mapping process consist of computing the maps with a daily sampling (i.e., a map is computed for each day of the week, while only maps centered on Wednesdays were computed for DT2010). The reader should, however, note that the timescales of the variability that is resolved in the DT2014 data set are not substantially different from DT2010; these timescales are imposed by the temporal correlation function used in the OI mapping procedure. A second important change is the definition of the grid points with a global Cartesian 1/4∘ × 1/4∘ resolution. This choice was mainly driven by user requests since Cartesian grid manipulation is simpler than working on a Mercator projection. The effects of this change are discussed in Appendix C. Note however that the grid resolution does not correspond to the spatial scales of the features that are resolved by the DT2014 SLA field. These spatial scales are about the same (perhaps slightly smaller) than in the DT2010 fields; they are imposed by the spatial correlation function used in the OI mapping procedure. In addition to the grid standard change, the area defined by the global product was extended towards the poles in order to take into account the high-latitude sampling offered by the more recent altimeters such as C2 (i.e., up to ±88∘ N).

As previously stated, two gridded SLA products are computed, using two different altimeter constellations. The all-sat-merged products take advantage of all the altimeter measurements available. This allows an improved signal sampling when more than two altimeters are available (Fig. 1). The mesoscale signal is indeed more accurately reconstructed during these periods (Pascual et al., 2006), when omission errors are reduced by the altimeter sampling. In the same way, high-latitude areas can be better sampled by at least one of the available altimeters. These products are however not homogeneous in time, leading to interannual variability of the signal that is directly linked to the evolution of the altimeter sampling. Pascual et al. (2006) indeed observed SLA root-mean-square (rms) differences between 5 and 10 cm when comparing the two- and four-altimeter configurations in high-variability areas. In order to avoid this phenomenon, two-sat merged products are also made available. These are a merging of data from two altimeters following the TP and ERS-2 tracks (e.g., TP, then J1, then J2 merged with ERS-1, then ERS-2, then EN, then AL; or C2 when neither EN nor AL is available) in order to preserve, as much as possible, the temporal homogeneity of the products. Except for the differences in altimeter constellations, the mapping parameters are the same for the all-sat-merged and two-sat-merged products.

Derived products are also disseminated to the users. These consist of the absolute dynamic topography (ADT) (maps and along-track) and maps of geostrophic currents (absolute and anomalies).

The ADT products are obtained by adding a mean dynamic topography (MDT) to the SLA field. The MDT used in the DT2014 reprocessing is the MDT CNES/CLS 2013 (Mulet et al., 2013), corrected to be consistent with the 20-year reference period used for the SLA.

The geostrophic current products disseminated to users are computed using a nine-point stencil width methodology (Arbic et al., 2012) for latitudes outside the ±5∘ N band. Compared with the historical centered difference methodology, the stencil width methodology allows us to correct the anisotropy inherent to the Cartesian projection. It also leads to slightly higher current intensities. In the equatorial band, the Lagerloef methodology (Lagerloef et al., 1999) introducing the β plane approximation is used, with various improvements compared to the previous DT2010 version. Indeed, the meridional velocities are introduced into the β component. Moreover, filtering of the β component is reduced, leading to more intense currents and improving the continuity of the currents within the latitudes ±5∘ N. The reader should however note that this paper is focused on a quality description of the SLA products. With this objective, the geostrophic currents used for different diagnostics presented within this paper are obtained using the same methodology (centered differences) for DT2014 and DT2010 data sets.

The DT2014 SLA products and derived products are distributed in NetCDF-3CF format convention with a new nomenclature for file and directory naming. Details are given in the user handbook (Aviso/DUACS, 2014).

In order to be compared with DT2014, the DT2010 products were first processed in order to ensure consistency in resolution and physical content. In this way,

the DT2010 products considered correspond to the 1/4∘ × 1/4∘ Cartesian resolution products previously identified as “QD” products. These products were obtained from the native DT2010 grid layout (1/3∘ × 1/3∘ Mercator grid; see Sect. 2.2.6) using bilinear interpolation.

The mapping process optimization (see Sect. 2.2.6) directly affects the SLA physical content observed within the gridded products. The differences between DT2014 and DT2010 temporal variability of the signal for the period [1993–2012] are shown in Fig. 7. The figure shows additional variability in the DT2014 products. The global mean SLA variance is now increased by nearly +3.5 cm2 within the latitude band ±60∘ N. This represents 5.1 % of the variance of the DT2010 “QD” products. This increase is mainly due to the mapping parameters including two main changes in the DT2014 products. The first one, which explains +3.6 % of the variance increase, is the change in the native grid resolution. DT2014 was computed directly on the 1/4∘ × 1/4∘ Cartesian grid resolution (see Sect. 2.2.6), while the DT2010 “QD” product was interpolated linearly from the native 1/3∘ × 1/3∘ Mercator resolution product (see Sect. 3.2.1). This interpolation process slightly smoothes the signal and directly contributes to reduction of the variance of the signal observed in DT2010. The second change implemented in the DT2014 products is the use of improved correlation scales associated with the change in the along-track low-pass filtering presented in Sect. 2.2.6). This change contributes to an increase in the SLA variance of +1.5 %. Finally, additional measurements (e.g., C2 in 2011) that were not included in the DT2010 products also contribute to improvements in the signal sampling, and thus increase the variance of the gridded signal.

The additional signal observed in the DT2014 products is not uniformly distributed, as shown in Fig. 7. Indeed, the main part of the variance increase (from +50 to more than +100 cm2) is observed in the higher variability areas and coastal areas. It is an expression of the more accurate reconstruction of the mesoscale signal in the DT2014 products, as discussed below. In some parts of the ocean we however observe a decrease in the SLA variance. The improved standards used (see Sect. 2.1) indeed contribute to local reductions of the SLA error variance. The main reduction is observed in the Indonesian area, with amplitudes ranging from 2 to 3 cm2. The SLA error variance is also reduced in the Antarctic area (latitudes < 60∘) with the higher local amplitudes. The improved DAC correction using ERA-Interim reanalysis fields over the first decade of the altimeter period is a significant contributor to the variance reduction (Carrere et al., 2015).

Analysis of the spectral content of the gridded products over the Gulf Stream area (Fig. 8) shows that all of the DT2014 products are impacted at small scales, i.e., wavelengths lower than 250–200 km. For “all-sat-merged” as well as “two-sat-merged” products the energy observed in DT2014 for wavelengths around 100 km is twice as high as that observed in the DT2010 gridded SLA products, both in the zonal and meridional directions. The maximum additional signal is observed for wavelengths ranging between 80 and 100 km. For these wavelengths, the DT2014 products have 2 to 4 times more energy than the DT2010 versions. Nevertheless, the energy associated with these wavelengths falls drastically for both DT2014 and DT2010 SLA products, meaning that DT2014 still misses a large part of the dynamic signal at these wavelengths, as discussed in Sect. 4.

Compared to the DT2010 products, the new DT2014 version has more intense geostrophic currents. This has a direct signature on the eddy kinetic energy (EKE) that can be estimated from the two different versions of the product. Figure 9 shows the spatial differences of the mean EKE computed from the DT2014 and DT2010 products. As previously observed with the SLA variance, the EKE is higher in the DT2014 products. An additional 400 cm2 s-2 in levels of EKE are observed in the DT2014 products in high-variability areas. This represents a 20 % EKE increase compared to DT2010. Proportionally, the EKE increase observed in the DT2014 products is quite large in low-variability areas and eastern boundary coastal currents, where it reaches up to 80 % of the DT2010 EKE signal, as underscored by Capet et al. (2014). The global mean EKE increase, excluding the equatorial band and high-latitude areas (> ±60∘ N), represents nearly 15 % of the EKE observed in the DT2010 products. As previously observed with the SLA variance, the change in the native grid resolution and the change in the correlation scales and along-track filtering explain, respectively, +10 and +6 % of the EKE increase. The change in the altimeter standards rather contributes to slightly reducing the EKE in the DT2014.

Figure 10 shows the temporal evolution of the mean EKE over the global ocean for both DT2014 and DT2010. We first note the nearly 15 % additional mean EKE in the DT2014 product as previously discussed. We also note a significant difference in the EKE trend between DT2014 and DT2010, where the latter is in the 7-year altimeter reference period (Sect. 2.3). Indeed, the mean EKE trend is nearly -0.027 (-0.445) cm2 s-2 yr-1 when DT2010_ref7y (DT2014) products are considered. On the other hand, when DT2010 is referenced to the 20-year period, the EKE trend (-0.369 cm2 s-2 yr-1) is comparable to the DT2014. This result clearly emphasizes the sensitivity of the EKE trend estimation to the altimeter reference period. Indeed, the use of the 20-year reference period leads to a minimized signature of the SLA signal over this period. Conversely, the SLA gradients are artificially higher after 1999 when the historical [1993–1999] reference period is used. As a consequence, after 1999, the EKE from the DT2010 products (in the 7-year reference period) is higher than the EKE from the DT2014 products (we do not consider here the global mean EKE bias observed between the two products).

The accuracy of the gridded SLA field is estimated by comparing SLA maps with independent along-track measurements. Maps produced by merging of only two altimeters (i.e., “two-sat-merged” products; see Sect. 2.2.6) are compared with SLA measured along the tracks from other missions. In this way, TP interleaved is compared with a DT2014 gridded product that merges J1 and EN over the years 2003–2004. The variance of the SLA differences is analyzed for the wavelengths ranging between 65 and 500 km, characteristics of medium and large mesoscale signals. The same comparison is done using the previous DT2010 version of the products in order to estimate the improved accuracy of the new DT2014 gridded SLA fields. The results of the comparison between gridded and along-track products are shown in Fig. 11 and summarized in Table 2.

The gridded product errors for mesoscale wavelengths usually range between 4.9 (low-variability areas) and 32.5 cm2 (high-variability areas) when excluding coastal and high-latitude areas. They can, however, be lower, especially over very low-variability areas such as the South Atlantic subtropical gyre (hereafter “reference area”) where the observed errors are nearly 1.4 cm2. It is important to note that these results are representative of the quality of the “two-sat-merged” gridded products. These can be considered to be degraded products for mesoscale mapping since they use minimal altimeter sampling. On the other hand the “all-sat-merged” products, during the periods when three or four altimeters were available, benefit from improved surface sampling. The errors in these products should thus be lower than those observed in the products that merge only two altimeters.

Compared to the previous version of the products, the gridded SLA errors are reduced. Far from the coast, and for ocean variances lower than 200 cm2, the processing/parameter changes included in the DT2014 version lead to a reduction of 2.1 % of the variance of the differences between gridded products and along-track measurements observed with DT2010. The reduction is higher when considering high-variability areas (> 200 cm2), where the impact of the new DT2014 processing is maximum. In this case, it reaches 9.9 %. On the other hand, some slight degradation is observed in tropical areas, especially in the Indian Ocean. In that region, up to 1 cm2 increased variance of the differences between grids and along-track estimates is observed. This can be directly linked to the change in the processing in these latitudes, especially the reduction of the short-wavelength filtering applied before the mapping process, as explained in Sect. 2.2.6.