Bertrand Saulquin
email: bertrand.saulquin@acri-st.fr

Ronan Fablet

Grégoire Mercier

Hervé Demarcq

Antoine Mangin

Odile Hembise Fanton D'andon

O H Fanton D' Andon

of significant time-scales into the Sea Surface Temperature anomalies relatively to ENSO periods from 1985 to 2009

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

I. INTRODUCTION

M ANY INFORMATION sources, including instrumental in situ data records and satellite observations, highlight the great variability and the nonstationarity of the earth's climate over a wide range of time-scales from months to decades. The most widely used technique to investigate the spatiotemporal variability of climate-relevant time series, such as temperature [START_REF] Chen | Modality of semiannual to multidecadal oscillations in global sea surface temperature variability[END_REF] and wind [START_REF] Blunden | State of the climate in 2010[END_REF], relies on the empirical orthogonal functions (EOFs) [START_REF] Preisendorfer | Principal Component Analysis in Meteorology and Oceanography[END_REF], also referred to as principle component analysis (PCA) in the literature. This method combines the extraction of the main deformation modes of the covariance (correlation) of a univariate or bivariate [singular value decomposition (SVD)] datasets and the analysis of the time correlation of these principal modes with potential causing factors. An introduction to univariate and multivariate EOF analysis may be found in [START_REF] Björnsson | A manual of EOF and SVD analysis of climatic data[END_REF] and a thorough review of advanced EOF-based methods along with intercomparisons is presented by Bretherton et al. [START_REF] Bretherton | An intercomparison of methods for finding coupled patterns in climate data[END_REF]. These EOF-based analyses, however, suffer from intrinsic limitations, the main one being the assumption that the considered processes are stationary. Nevertheless, geophysical dynamics widely involve nonstationary processes (e.g., emergence of extreme events including, e.g., large Niño events, time shifts of seasonal cycles, propagation phenomena, and trends), which may hardly be characterized as stationary. Environmental data also involve strong autocorrelation level [START_REF] Frankignoul | Stochastic climate models. Part II: Application to SST anomalies and thermocline variability[END_REF]. For instance, a positive anomaly in the observed wind or temperature at a given day (week) is often associated with similar conditions the following days (weeks). This natural autocorrelation is the result of short time and local events but also of large-scale signals such as, e.g., the wellknown El-Niño/La-Niña oscillation [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], [START_REF] Philander | Niño, La Niña, and the Southern Oscillation[END_REF]. Such autocorrelated level clearly affects the determination of correlation significance level used as input of the EOF [START_REF] Jackson | Robust principal component analysis and outlier detection with ecological data[END_REF]. Both nonstationarity and autocorrelation may affect the interpretation of the extracted principal modes. Nevertheless, these aspects are often overlooked by EOF-based approaches. Besides, EOF is also known to be prone to outliers [START_REF] Jackson | Robust principal component analysis and outlier detection with ecological data[END_REF] and can hardly reveal fine time-scales signatures, which typically involve greater nonstationary variabilities.

Wavelet analysis is particularly appealing to address these issues. In contrast to EOF-based approaches, wavelet analysis actually addresses the decomposition of the fluctuations exhibited by nonstationary signals. An introduction to wavelet analysis related to climate research is given by Torrence and Compo [START_REF] Torrence | A practical guide to wavelet analysis[END_REF]. Wavelet analysis has been used to investigate global climate changes in sea surface temperature (SST) [START_REF] Lau | Climate signal detection using wavelet transform: How to make a time-series sing[END_REF], [START_REF] Sonechkin | Wavelet analysis of nonstationary and chaotic time-series with an application to the climate change problem[END_REF] and interactions between physical parameters such as SST and sea surface height (SSH) [START_REF] Leeuwenburgh | The effect of ocean currents on sea surface temperature anomalies[END_REF]. While EOF-based schemes aim at extracting the main patterns of the covariance (or correlation) structure, wavelet analysis identifies and characterizes local time-scale patterns. The correlation between two processes can also be decomposed in the time-scale domain based on the wavelet coherency spectrum [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], [START_REF] Rouyer | Analysing multiple time-series and extending significance testing in wavelet analysis[END_REF].

In this paper, we further investigate wavelet analysis for geophysical time series to develop an event-based representation and analysis of a geophysical dataset. Formally, we regard a time series as a collection of significant elementary time-scale events and use an unsupervised clustering method, namely a Gaussian mixture mode (GMM) [START_REF] Flannery | Gaussian mixture models and k-means clustering[END_REF], to characterize the significant timescales of the dataset.

To illustrate our approach, we study the SST anomalies (SSTAs) observed over the globe from 1985 to 2009. First, we characterize four characteristic low-frequency patterns in the SSTA time-scale distribution and study their space and time distribution regarding the ENSO modes. We also focus onto the high-frequency (HF) SSTA and show a strong spatial signature of ENSO. Usually, only the low frequency in the SSTA (from 1.5 to 8 years) is attributed to ENSO [START_REF] Philander | Niño, La Niña, and the Southern Oscillation[END_REF], [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF] and previous works (e.g., Enfield [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF]) use an EOF decomposition of the filtered SSTA in the 1.5-to 8-year range. We underlie here that ENSO events also depict HF signatures in the SSTA. This paper does not support a full description of the ENSO phenomenon, but it uses knowledge on its interactions with the SSTA to illustrate the added value, compared to standard methods, of both the decomposition of the time series using an events-based framework and the proposed data mining approach.

II. EVENT-BASED ANALYSIS OF GEOPHYSICAL TIMES SERIES

A. Wavelet-Based Extraction of Elementary Time-Scale Events

Wavelet analysis aims at characterizing nonstationary signals, i.e., signals whose statistical characteristics (e.g., mean and variance) may change over time. From the decomposition of a one-dimensional (1-D) signal in the time-scale domain, significant frequencies can be detected in any given time interval. Such decompositions typically achieve a better detection and description of the characteristic time-scale variabilities of the observed phenomenon [START_REF] Torrence | A practical guide to wavelet analysis[END_REF] and represent a real added value to unmix nonstationary scale-dependent processes compared to classical covariance-based analysis (e.g., EOF-based schemes [START_REF] Preisendorfer | Principal Component Analysis in Meteorology and Oceanography[END_REF] and autoregressive models [START_REF] Brockwell | Time-Series: Theory and Methods[END_REF]). Formally, the wavelet transform of a 1-D signal consists in computing the complex wavelet coefficients as the projection of the signal onto scaled and translated versions of the selected mother wavelet [START_REF] Gu | Secular changes of annual and interannual variability in the Tropics during the past century[END_REF] where s is the time-scale, t and T time instants, and stands for the conjugate complex of the mother wavelet .Sincethe wavelet transform computes the similarity between the wavelets and the signal, the choice of the mother wavelet is important. SST is often modeled using harmonics [START_REF] Levitus | A comparison of the annual cycle of two sea surface temperature climatologies of the World Ocean[END_REF] and Gu and Philander [START_REF] Gu | Secular changes of annual and interannual variability in the Tropics during the past century[END_REF] suggest that the ENSO signal may be represented by sinusoids. This supports the choice of the Morlet wavelet, stated as a time-windowed pure harmonic component. The wavelet power spectrum of the time-scale decomposition (1) is defined as Here, we propose to model the studied geophysical process as a collection of significant elementary time-scale events. Formally, this amounts to viewing the spectrum as a sum of K individual events and a red noise where is the detected event j, , a theoretical red noise Fourier power spectrum [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], whose relevance, compared to the white noise model, is acknowledged for geophysical processes (a positive anomaly in the observed t e m p e r a t u r eo nag i v e nd a yi so f t e na s s o c i a t e dw i t hs i m i l a r conditions the following days). The first-order red noise is characterized as where is the lag-1 autocorrelation, i.e., the mean correlation between samples at the current and preceding time steps. is a white noise process with zero mean and variance .If [START_REF] Björnsson | A manual of EOF and SVD analysis of climatic data[END_REF], it resorts to the white noise model. For a given time series, we use a robust estimation of the noise model parameters, i.e., autocorrelation coefficient [START_REF] Sarnaglia | Estimation of periodic autoregressive processes in the presence of additive outliers[END_REF] and variance [START_REF] Hoaglin | Understanding Robust and Exploratory Data Analysis[END_REF]. Regarding the significance level, we follow Torrence and Compo [START_REF] Torrence | A practical guide to wavelet analysis[END_REF] who showed that if the original signal'sF o u r i e r components are normally distributed, then the wavelet power spectrum P is distributed. The associated 95% confidence level is then obtained using > where is the variance of the noise model (in practice, we used a robust estimation of the variance of the time series) and is the chi-square distribution with two degrees of freedom.

is the theoretical Fourier power spectrum of the red noise Fig. 1 shows the distribution of the theoretical Fourier power spectrum [START_REF] Frankignoul | Stochastic climate models. Part II: Application to SST anomalies and thermocline variability[END_REF] for both a red ( , red curve) and a white noise ( , blue curve). Their corresponding dashed lines represent the 95% confidence level [START_REF] Bretherton | An intercomparison of methods for finding coupled patterns in climate data[END_REF] for value set to 1. As illustrated (Fig. 1), if the autocorrelation of the noise is ignored in the analysis, it typically leads to an over-detection of the low-frequency component of the signal and an under-detection of its HF component.

To match the time-scale dimension of the wavelet power spectrum

(2), the theoretical 1-D Fourier power spectrum (6) is expanded for each time step t Our implementation of the wavelet analysis involves 69 time-scales ranging from 0.2 to 8.5 years: with (2 months) and the time step (1 month) determine the smallest time-scale (2 months) and J the largest scale (8.5 years).

The determination of the elementary time-scale events from the wavelet spectrum [START_REF] Fablet | Multiscale geometric deformations along planar curves: Application to satellite tracking and ocean observation data[END_REF] (see Section III-C for an example of wavelet power spectrum) involves the extraction of local regions of interest as maximal level-sets [START_REF] David | Distinctive image features from scale-invariant keypoints[END_REF], [START_REF] Monasse | Fast computation of a contrast invariant image representation[END_REF], i.e., areas of the wavelet spectrum which depict an energy level above the significance level [START_REF] Frankignoul | Stochastic climate models. Part II: Application to SST anomalies and thermocline variability[END_REF]. In our implementation, we first detect all the significant local maxima [START_REF] Fablet | Multiscale geometric deformations along planar curves: Application to satellite tracking and ocean observation data[END_REF] in the valid part of the wavelet spectrum, i.e., out of the cone of influence [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], and then determine their associated maximal level-set. A maximal level set is the largest time-scale area in the spectrum, which contains only one maximum of energy. Finally, an ellipse is fitted onto the selected spectrum area (event).

Each ellipse is described by its time and time-scale extensions and the position of its center (local maximum of energy). Ellipse axes refer to the main axes of the time-scale covariance, which are, even if not addressed in this paper, directly linked to the frequency modulation observed during the propagation of the event [START_REF] Rouyer | Analysing multiple time-series and extending significance testing in wavelet analysis[END_REF].

B. Event-Based Mining of the Event Database

Our event-based mining strategy involves an unsupervised analysis of the time-scale distribution of the elementary events. This distribution is modeled as a mixture of Gaussian modes. By nature, when considering time-scale analysis, occurrences of HF events are greater than those at low-frequencies. This natural distribution of the scale of the events is referred in the literature as a fractal distribution [START_REF] Mandelbrot | The Fractal Geometry of Nature[END_REF]. To account for this scale-dependent sampling, the mixture model involves a scale-dependent normalization factor. Formally, the considered normalized mixture model resorts to where is the scale-related normalization accounting for the global scale-dependent sampling of the elementary events, I is the number of modes (Gaussians), the prior of t h em o d eio ft h em i x t u r e ,Nt h e normal probability density function (PDF) of the time-scale events with mean ,a n d standard deviation

An exponential distribution for is proven meaningful (see Section IV-D)

To infer the parameters of the mixture model, we first fitthe normalization factor and in a second step, mixture model parameters and are estimated using an EM (Expectation-Maximization) procedure [START_REF] Dempster | Maximum likelihood from incomplete data via the EM algorithm[END_REF], which aims at maximizing [START_REF] Jackson | Robust principal component analysis and outlier detection with ecological data[END_REF] or minimizing the log likelihood For a given initialization for model parameters, the EM procedure iterates expectation steps (E-step), which compute the posterior likelihoods given current model parameters, and maximization steps (M-step) to update the model parameters given the posteriors. The algorithm iterates until numerical convergence < . The estimation of the number of modes of the mixture model proceeds as follows: given 15 initial modes in the mixture model, only the modes with > year are kept in the model after each EM step.

III. APPLICATION TO THE SATELLITE-DERIVED SSTA OBSERVED FROM 1985 TO 2009

A. Pathfinder Dataset

Satellite-derived SST data are extracted from the global AVHRR Pathfinder SST v5.2 [START_REF] Casey | The past, present and future of the AVHRR Pathfinder SST Program[END_REF] daily gridded product (http://www.nodc.noaa.gov/SatelliteData/pathfinder4km/). To avoid diurnal effect, we used the data acquired at nighttime. A quality control was performed by selecting pixels with a quality flag level greater than 3. This quality flag is provided in the Pathfinder v5.2 product, and its level was determined using Kilpatrick studies [START_REF] Kilpatrick | Overview of the NOAA/ NASA advanced very high resolution radiometer Pathfinder algorithm for sea surface temperature and associated match-up database[END_REF]. First, the estimation of the SSTA involves the estimation of monthly mean SST fields at 36 km 6) as a function of the period for a white noise (blue curve) and a red noise (red curve), this latest being the representative of a geophysical time series. In dashed lines, the corresponding 95% confidence levels [START_REF] Bretherton | An intercomparison of methods for finding coupled patterns in climate data[END_REF].

resolution. A minimum of 30 observations per grid cell is used to estimate the average. The seasonal signal (climatology) must be then removed from the SST to obtain the SSTA. The harmonicbased estimation of a climatology of is more accurate than the simple average estimation [START_REF] Narapusetty | Optimal estimation of the climatological mean[END_REF]. Hence, for each time series, a local climatology composed of four harmonics and a linear trend [START_REF] Saulquin | Detection of linear trends in multisensor time-series in the presence of autocorrelated noise: Application to the chlorophyll-a SeaWiFS and MERIS data sets and extrapolation to the incoming sentinel 3-OLCI mission[END_REF] is estimated and subtracted from the SST to remove 12, 6, 4, and 3 months periodicities Finally, SSTA monthly fields were spatially averaged on a grid. The resulting studied SSTA dataset is a matrix. We removed land cells and obtained 32 047 continuous time series of 300 months (no missing data) with a view to characterizing the spatiotemporal variability of the SSTA at global scale from 1985 to 2009. Fig. 2 shows the standard deviation of the monthly SSTA for the 1985-2009 period. It highlights three types of regions of low-frequency variability: the equatorial pacificu pt o (and in a less pronounced way the equatorial Atlantic), the temperate regions, mostly of the northern hemisphere, with a maximum amplitude in the north Pacific gyre and the north-western Atlantic gyre, and the equatorial borders of the major upwelling areas.

Multivariate Enso Index

The Niño/La Niña events have been thoroughly addressed in the literature and the reader may refer to ñhttp://elNiño.noaa.gov/ as an interesting entry point to understand the ENSO and its regional impacts. The low-frequency variability in the SSTA can be associated with low-frequency atmospheric climatic variations. As a peculiar example, El-Niño-La-Niña events relate to oceanic-atmospheric oscillations of the equatorial Pacific [START_REF] Philander | Niño, La Niña, and the Southern Oscillation[END_REF]. Among the numerous ENSO-related indexes, we consider the Multivariate ENSO Index (MEI, http://www.esrl.noaa.gov/psd/ enso/mei/), which is based on six observed variables over the tropical Pacific: sea-level pressure, zonal and meridional components of the surface wind, SST, surface air temperature, and total cloudiness fraction of the sky. As suggested by the NOAA (http://www.esrl.noaa.gov/psd/enso/mei/rank.html), Niño regimes were defined as the periods for which the MEI index value exceeded the percentile 30 of the positive values and conversely, La Niña regimes as significantly negative periods (below percentile 30 of the negative values).

C. Event Detection Examples in SSTA Time Series D. Characteristic Time-Scales of SSTA Elementary Events

From the 32 047 SSTA time series, we extracted 486 144 significant elementary events with estimated mean scales from 0.2 to 8 years. Fig. 4(a) shows the time-scale distribution of these events. The exponential distribution [red curve, Fig. 4(a)] is the normalization factor used to account for the scaledependent sampling [START_REF] Sonechkin | Wavelet analysis of nonstationary and chaotic time-series with an application to the climate change problem[END_REF]. Fig. 4(b) shows the normalized time-scale distribution. We divided our dataset of events in two main categories 1) Events with mean time-scale lower than 0.4 year showed a uniform normalized-scale distribution and were gathered in a single category, referred to the HF category. Fig. 3. Illustration of the event-based analysis of SSTA time series. Top: SSTA time series observed at and , i.e., in the eastern equatorial Pacific known to be strongly affected by ENSO processes. Bottom: the corresponding wavelet power spectrum and the detected significant elementary events delimited by ellipses with the corresponding maximum of energy indicated by a cross. See Section II-A and [START_REF] David | Distinctive image features from scale-invariant keypoints[END_REF], [START_REF] Monasse | Fast computation of a contrast invariant image representation[END_REF] for details on the detection of the elementary events as local significant spectrum areas with respect to the theoretical energy depicted by a red noise with the same correlation and variance statistics than the considered series.

2) Events with scale greater than 0.4 year showed significant Gaussians modes in the normalized-scale-distribution. We fitted a Gaussian mixture model ( 9) to this dataset. The parameter estimation needed 400 EM iterations, using as convergence criterion a log likelihood threshold value of . The estimated model involved seven Gaussian modes [Fig. 4 We will see later that the spatial distribution of the 1.54-year scale events also relates to ENSO region of influence. For this reason, we consider this scale as an additional characteristic ENSO time-scale. Table I summarized the characteristics (mean and standard deviation) of the Gaussian distributions for the four low-frequency reference time-scales of the SSTA. Standard deviations for reference scales greater than 1.54 are relatively low ensuring a narrow distribution and a very good confidence in these three classes.

E. Spatial Distribution of the SSTA Characteristic Scales

We investigate the spatial distribution of both the HF and the low-frequency characteristic time-scales. From the inferred Gaussian mixture model, we can evaluate the posterior membership probability of the th event with a mean time-scale to be assigned to the category The spatial distribution of the given event category is estimated for each pixel (time series) using the mean number of events for where K is the number of detected events in the time series. Fig. 5 shows the estimated for both the HF category [ < year, Fig. 5(a)] and the characteristic time-scales at 1.54, 3.36, and 5.03 years [Fig. 5(b)-(d)].

The HF events [Fig. 5(a)] contributed for 61% of the total number of the detected events. Overall, the mean number of detected HF events is of 10.1 over the globe for the considered 25-year period. Local maxima of 18 detections are observed on the Peruvian shores, in the South-Eastern part of the Niño3 reference area, the western Mediterranean Sea, the Arabian Sea and the Okhotsk Sea. The Arabian Sea is strongly affected by monsoon winds reversal, whose effect on SST variability from climatology is already known [START_REF] Krishnamurthy | Relation between Indian monsoon variability and SST[END_REF], whereas the high-latitudinal areas are commonly affected by winter storms that increase the SST variability, probably enhanced by the presence of the continents. No similar pattern is observed in the high latitudes of the southern hemisphere, probably because of the low interference of continental masses and the regularity of the circumpolar winds. A minimum of three events are observed in the equatorial part of the Eastern Pacific from 160 to , where the variance in the SSTA is mostly driven by the low frequency at 1.54 and 3.36-year scale [Fig. 5

TABLE I MEAN AND STANDARD DEVIATION OF THE GAUSSIAN DISTRIBUTIONS FOR THE FOUR LOW-FREQUENCY REFERENCE TIME-SCALES OF THE SSTA FROM 1985 TO 2009

Events at 1.54-year scale [Fig. 5(b)] represent 11% of the total number of events and show a mean number of two detected events over the globe for the 1985-2009 period. Local maxima were observed in the eastern part of the Niño3 area underlying the signature of ENSO at this scale onto the SSTA. Local patches clearly appear at this scale in the Gulf of Mexico, the North Atlantic, the Namibian shores, the western Mediterranean Sea, and the Okhotsk Sea. Eastern boundary systems (Humboldt and Benguela coastal upwelling regions) specially show a higher number of events, probably caused by a high interannual variability.

The 3.36-year event category [Fig. 5(c)] accounts for 4% of all elementary events with a mean number of 0.8 event over the globe from 1985 to 2009. Its spatial distribution highlights regions known to be strongly affected by ENSO: the central equatorial Pacific, the central Humboldt system, and the northern Indian Ocean [START_REF] Preisendorfer | Principal Component Analysis in Meteorology and Oceanography[END_REF], [START_REF] Philander | Niño, La Niña, and the Southern Oscillation[END_REF], [START_REF] Krishnamurthy | Relation between Indian monsoon variability and SST[END_REF]- [START_REF] Wang | Interdecadal changes in the major modes of Asian-Australian monsoon variability: Strengthening relationship with ENSO since the late 1970 s[END_REF]. In the Indian Ocean, we observe that the low-frequency signature of ENSO onto the SSTA is also observed at this time-scale. This influence of ENSO on the monsoon in this region has been largely documented [START_REF] Krishnamurthy | Relation between Indian monsoon variability and SST[END_REF]- [START_REF] Wang | Interdecadal changes in the major modes of Asian-Australian monsoon variability: Strengthening relationship with ENSO since the late 1970 s[END_REF] but often without time-scale analysis [START_REF] Wang | Interdecadal changes in the major modes of Asian-Australian monsoon variability: Strengthening relationship with ENSO since the late 1970 s[END_REF] or at multidecadal time-scale [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF].

The 5.03-year event category [Fig. 5(d)] represents 1.5% of the elementary events with a mean number of 0.3 event over the globe. The highlighted areas are the Western part of the Pacific Ocean, the central Humboldt and southern Argentinian shores, as well as, in general, the boundaries of the regions detected at 3.36-year scales.

ENSO signal is known to propagate [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF] and, e.g., ENSO signal generally occurs 4 months after it starts in the West of Peru [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF] and until 9 months in the Philippines [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF]. Fig. 5(b)-(d) suggests that the propagation of the ENSO signal includes time-scale shifts as already envisaged by Torrence and Webster [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF]. As a peculiar example, in the Eastern intertropical Pacific [Fig. 5(c)], the detected events at 5.03-year scale [Fig. 5(d)] geographically surround the detected 3.36-year scale events suggesting the shift between frequencies during the ENSO propagation. We note that the proposed methodology (compare Section II-B) suits well to address such hypothesis compared to EOF method that does not involve such an explicit scale-related analysis [START_REF] Enfield | Multiscale variabilities in global sea surface temperature and their relationships with tropospheric climate patterns[END_REF].

F. Density of HF and 1.54-Year Events With Respect to ENSO Modes

To address possible HF signatures of ENSO from the analysis of the space-time distribution of HF and 1.54-years event categories, we analyze the distribution of both HF and 1.54-year event categories conditionally to the three ENSO conditions. We use the estimation of the starting and ending times of the events of category C to analyze their density D relatively to the ENSO regime for normal, Niño, and Niña periods (compare Section II-B for the ENSO mode definition) where is the number of months spent in events of class during period and the number of months of period . The density is a time and energy normalized representation of the energy observed for each and ENSO mode. It aims at estimating the number of months where the energy is significant at this time-scale compared to the local conditions.

During normal periods, i.e., out of ENSO periods, the HF [Fig. 6(a)] and the 1.54-year frequency events [Fig. 6

Pacific shows similarly high values ( >

), but on a relatively moderate extent. The Okhotsk and Mediterranean Sea show a high density of event at the 1.54-year scale, whose origin is probably linked to their specific regional climate and proximity to anticyclonic areas of St. Helen and Libya [START_REF] Pedgley | Long-Range Insect Migration in Relation to Climate and Weather: Africa and Europe. Insect Migration: Tracking Resources Through Space and Time[END_REF].

To highlight the ENSO impact onto the time-scale distribution of the SSTA, event density anomaly maps are computed for both scales during Niño [Fig. 6(c During Niño periods [Fig. 6(c) and (d)], the intensity of the easterlies decreases, and the warm pool of SST, usually observed in the middle of the intertropical Pacific, moves Eastward. We observe globally an increase by 11% and 6% of the HF and 1.54-year frequency events with respect to the density outside ENSO events. A large positive anomaly in the HF density of is observed over the East equatorial Pacific from to [Fig. 6(c)], in the South Atlantic, the Agulhas current [START_REF] Rouault | Coastal oceanic climate change and variability from 1982 to 2009 around South Africa[END_REF], and in New Zealand. The last three patterns correspond to the border of the southern ocean anticyclonic regions, except for the eastern pacific, where the ENSO effects dominate. A large positive anomaly of , i.e., an increase by 80% compared to the normal HF conditions, is observed in the North East Atlantic. This is in agreement with a known influence of El Niño in the North Atlantic [START_REF] Hastenrath | The Southern Oscillation in the Atlantic sector[END_REF], [START_REF] Wang | Teleconnected influence of North Atlantic sea surface temperature on the El Nino onset[END_REF]. Negative anomalies in the HF density [Fig. 6(c)] are observed in an extended area of the Chile-Peruvian upwelling system, suggesting that the decrease in the easterlies intensity, and the resulting decrease in the upwelling intensity, tends to reduce the number of observed HF events in this area.

Niña periods [Fig. 6(e) and (f)] are characterized, in average, by a moderate positive anomaly of 8% for HF events and an increase by 6% for the 1.54-year scale, with nevertheless specific spatial patterns. In contrast to Niño phases, the easterlies strength increases during Niña periods [Fig. 6(e) and (f)] and the intertropical Pacific surface warm waters move westward. The signature of the southern Humboldt upwelling is clearly visible at the 1.54-year scale, with a positive anomaly of but off the stronger Peruvian upwelling. In the Guinea gulf and Benguela upwelling ( ), Niña periods are characterized by a large negative anomaly in the SSTA events at 1.54-year scale. In this region, the SSTA is mostly dependent on the upwelling intensity, suggesting a specific stabilization of its variability during Niña periods compared to normal periods [Fig. 6(b)]. Off South Africa, we observe a clear opposite influence onto the SSTA between the West and the East shores for both Niño and Niña periods and both scales, a difference already highlighted by Rouault et al. [START_REF] Rouault | Coastal oceanic climate change and variability from 1982 to 2009 around South Africa[END_REF].

It is obvious that we cannot interpret all the local differences observed in the time-scale distributions of the SSTA anomalies. ENSO phenomena are particularly complex and involve both atmospheric and oceanic processes, the SSTA being the resulting interaction between these two factors. Other large scale processes such as the Pacific Decadal Oscillation (PDO) [START_REF] Alexander | Forecasting Pacific SSTs: Linear inverse model predictions of the PDO[END_REF], [START_REF] Mantua | A Pacific interdecadal climate oscillation with impacts on salmon production[END_REF] and the Atlantic Multidecadal Oscillation (AMO) [START_REF] Knight | Climate impacts of the Atlantic multidecadal oscillation[END_REF] also affect the SSTA. It appears nevertheless that significant differences are found in the observed distributions of the HF and 1.54-year events time-scales SSTA between, on the one hand, the ENSO/ normal periods, and the other hand, the Niño and Niña phases. This observation emphasizes the interest of dedicated time-scale decomposition methods to improve our understanding of processes at various spatiotemporal scales, the reference scales exhibited from the GMM [Fig. 4(b)] being used to choose the time-scales to be studied and discretize the dataset in an optimal way (compared to the standard wavelet analysis).

G. Investigating Frequency Shifts in the SSTA and the Intertropical Pacific During the ENSO 1997-2000 Event

Time-scale changes during Niño-Niña periods are suspected to occur [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF], [START_REF] Kestin | Time-frequency variability of ENSO and stochastic simulations[END_REF], [START_REF] Compo | Changes of subseasonal variability associated with Niño[END_REF]- [START_REF] Kirtman | Decadal variability in ENSO predictability and prediction[END_REF] and Compo et al. [START_REF] Compo | Changes of subseasonal variability associated with Niño[END_REF] underlined that ENSO time-scale variability at decadal scales may differ substantially from one ENSO event to another. An and Wang [START_REF] An | Interdecadal change of the structure of the ENSO mode and its impact on the ENSO frequency[END_REF] also showed a significant relationship between the observed ENSO frequency and observed SSTA structures, underlying the influence of these frequency shifts. To investigate the time-scale variability of ENSO, we focus on the 1997-2000 ENSO major event in the intertropical Pacific, the strongest ever recorded. We clearly see in Fig. 5(c), the strong signature of this ENSO event in the intertropical Pacific at 3.36-year scale. Fig. 7(a) shows the distribution of the observed mean time (center of the events) at 3.36-year scale. The maximum in the distribution is observed in August 1999, i.e., approximately in the middle of the Niño period. To investigate frequency shifts during we estimate the distribution of the variables and where T3.36, T1.54, and THF are, respectively, the position (time) of the event centers (maximum of energy) at 3.36-years, 1.54-years, and HF, collocated in the same spectrum. Fig. 7(b) shows the probability density functions of both and , estimated using, respectively, 1302 and 1474 pairs of events.

In Fig. 7(b), we observe a clear increase in the number of 1.54to 3.36-year pair of events, with a maximum observed 2 months later than the maximum at 3.36-years. Conversely, we observe a decrease in the number of HF to 3.36-year pair of events in the intertropical Pacific during the maximum of the ENSO 1997-2000 event with a minimum observed 2 months before the maximum at 3.36 years. This underlies the time-scale shifts from high to low frequencies during this ENSO. This observation motivates the determination of both the reference scales and their relative distribution to characterize ENSO compared to a classical sum of the spectrum energy between the 1.5-and 7-year scales [START_REF] Philander | Niño, La Niña, and the Southern Oscillation[END_REF]: even if the 1.5-7 year sum of energy is constant in time, the shift between scales provides a significant signature of ENSO 1997-2000.

IV. CONCLUSION AND FUTURE WORK

We propose in this paper an event-based mining of geophysical time series. We regard a time series as a collection of significant elementary time-scale events complemented by a red noise process. Our approach resorts to a normalized representation in variance of a time series through the detection of significant time-scale events. This is of key interest for SST anomalies that show a high spatial and temporal variability of the variance. The estimation of the threshold in energy to detect a significant event accounts for the autocorrelation and noise level of the local time series. This is also a key issue for geophysical time series, which depict naturally large autocorrelation noise levels (typically from 0.3 to 0.7 in the monthly SSTA dataset studied here).

The method is applied to the global SSTA observed from 1985 to 2009. We use a mixture of Gaussian to identify four reference time-scales at 1.54, 3.36, 5.03, and 7.11 years. The spatial distribution of these low-frequency reference scales highlights the intertropical Pacific, the West of Peru, the Indian Ocean, and the South of the Atlantic, regions known as being strongly influenced by ENSO. In addition, we reveal that ENSO modes are also characterized by significant space-time differences in the distribution of HF events (typically, with characteristic timescale below 4 months). We show that the HF event density of the SSTA increases by in mean 11% over the globe during Niño events, with a maximum of 80% in the North East of Europe and 6% during Niña periods. Even if all this HF variability may not be attributed to ENSO, this large increase is a significant signature of the Niño periods and is minimized by the EOF approach, which tends to exhibit by construction the low-frequency correlation modes. Our method also allows identifying times-scale shifts in the energy spectrum in the intertropical Pacific during the major 1997-2000 ENSO event with a maximum shift from the HF toward the reference (3.36-year scale) observed 2 months before the maximum of energy at the 3.36-year scale.

Compared to EOF-based time series analysis, the key contribution of the proposed event-based approach is to account for signal nonstationarity and noise autocorrelation in the timescale decomposition of geophysical processes variability. While EOF-based schemes mainly reveal low-frequency patterns, our wavelet-based approach can identify both low-frequency and HF signatures and investigate their respective space-time distribution.

Compared to classical wavelet approach, our main methodological contribution lies in the characterization of significant times-scales in the SSTA taking into account the spatially varying variance and the autocorrelation of each time series. The classical wavelet approaches [START_REF] Torrence | A practical guide to wavelet analysis[END_REF], [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF] usually consider a time-scale sum of the energy between 1.5 and 7 years to depict the ENSO signatures in the SSTA [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF]. Nevertheless, even if the 1.5-to 7-year sum of energy may be constant in time, the shift between scales is also a significant signature of ENSO 1997-2000 [Fig. 7(b)]. Compo [START_REF] Torrence | Interdecadal changes in the ENSOmonsoon system[END_REF] already pointed out that ENSOinduced changes in extratropical 500-mb height variability are time-scale dependent and An and Wang [START_REF] An | Interdecadal change of the structure of the ENSO mode and its impact on the ENSO frequency[END_REF] showed also a relationship between ENSO frequency changes and observed structure in the SSTA, raising the crucial question of the choice of discrete frequency bands. The present methodology addresses this question providing a quantitative mean to unmix the processes and study their time-scale relationships [Fig. 7(b)]. These time-scale dependencies may evolve in time, which make them particularly difficult to deal with from an extension of the crosswavelet spectrum [START_REF] Torrence | A practical guide to wavelet analysis[END_REF].

Our event-based methodology opens new perspectives for the analysis of multivariate time series such as wind and SST, light, and chlorophyll-a. While we consider here the interaction between elementary events at different characteristic scales of the same geophysical variable, this methodology could be applied to two or more variables. Besides, the event-based detection could also be considered to address long-term trend estimation [START_REF] Saulquin | Detection of linear trends in multisensor time-series in the presence of autocorrelated noise: Application to the chlorophyll-a SeaWiFS and MERIS data sets and extrapolation to the incoming sentinel 3-OLCI mission[END_REF] and correlation analysis while being robust to the presence of lowfrequency nonstationary signals such as ENSO.

Fig. 1 .

 1 Fig. 1. Theoretical Fourier spectrum (6) as a function of the period for a white noise (blue curve) and a red noise (red curve), this latest being the representative of a geophysical time series. In dashed lines, the corresponding 95% confidence levels[START_REF] Bretherton | An intercomparison of methods for finding coupled patterns in climate data[END_REF].

Fig. 2 .

 2 Fig. 2. The standard deviation of the monthly SSTA for the period 1985-2009 (source: Pathfinder v5.2).

  (b)]. Modes 3 and 4 showed mean scale of 0.70 and 1.54 years, respectively. They both refer to the interannual variability, the seasonal component (mainly the energy at a 1-year scale), being removed in the SSTA. Modes 5-7 at scales 3.36, 5.03, and 7.11 years, respectively, contain the very low-frequency changes in the SSTA caused by large space-time climatic signals such as ENSO and are therefore considered as the three characteristic low-frequency time-scales of ENSO influences onto the SSTA.

  (b) and (c)].

Fig. 4 .

 4 Fig. 4. Time-scale distribution and characteristic time-scales of the elementary events extracted from the SSTA dataset. (a) The initial distribution across scales of all of the extracted elementary events and the fitted exponential decay (11) corresponding to the natural fractal distribution of the event time-scales [25]. (b) The observed normalized distribution (9) with the seven Gaussian modes [(10), blue] found in the SSTA time-scale distribution. In red, the mixture model (9) fitted onto the distribution.

  (b)] show, respectively, a global mean density values of 0.19 and . Local maximum values of HF density are observed in the West of Peru, in an extended area of the Peruvian-Chile upwelling cell, i.e., for most of the Humboldt upwelling system [43], in the Arabian Sea and the Okhotsk Sea. The lowest density value ( ) is reached in the eastern part of the Pacific Ocean. At the 1.54-year scale [Fig. 6(b)], the West African Benguela region ( ; ) [37], characterized by a strong upwelling, displays a high density of , whereas the East equatorial

Fig. 5 .

 5 Fig. 5. Spatial distribution of the estimated SSTA characteristic time-scales. Mean number of events by time-scale categories from 1985 to 2009. (a) For the HF event category ( < ); (b)-(d) for characteristic time-scales of, respectively, 1.54, 3.36, and 5.03 years.

  ) and (d)] and Niña periods [Fig. 6(e) and (f)]. Fig. 6(a) and (b) being taken as the reference state.

Fig. 6 .

 6 Fig. 6. Observed spatial distributions of HF and 1.54-year scale event density for normal conditions [(a) and (b)], Niño [(c) and (d)], and Niña conditions [(e) and (f)].

Fig. 7 .

 7 Fig. 7. (top) Temporal distribution of the maximum of energy (event centers) observed in the intertropical Pacific at 3.36-year scale [known as being a reference time-scale for ENSO, compare Fig. 5(b) and [7]]. Highlighted in pink are the Niño periods and light blue are the Niña periods. (bottom) Distribution of the observed time shifts between the maximum of energy of the events at 3.36 and 1.54 years (blue) and 3.36 and HF (red).

ACKNOWLEDGMENT

This work has benefitted MCGS (Marine Collaborative Ground Segment; http://www.mcgs.fr). MCGS is a project aimed at making the most of ESA Sentinels satellites' potential for users driven services based on high-level products. MCGS addresses the need of the European Space Agency to build up data processing centers in conjunction with the Copernicus Program for the provision of services to local and national, public and private European institutions or entities involved in marine activities.


Pierre Louis Frison

Grégoire Mercier

G Faye

Éric Mougin

Pierre Louis Hiernaux

Cédric Lardeux

J P Rudant

Analysis of L and C-bands SAR images time series over a Sahelian area

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Analysis of L-and C-Band SAR Image

Time Series Over a Sahelian Area P.-L. Frison, G. Mercier, G. Faye, E. Mougin, P. Hiernaux, C. Lardeux, and J.-P. Rudant

Abstract-This letter presents an analysis of two synthetic aperture radar (SAR) images time series over a Sahelian area, which is located in the Gourma region, Mali. The first one is acquired at the C-band by the Environment Satellite-Advanced SAR sensor in wide swath (WS) mode and the second one at the L-band by the ALOS-Phased Array-type L-band SAR in fine, dual, and WS modes. A change detection method based on random projection and the hue-saturation-value transform appears to be very well appropriated to detect the temporal changes appearing on both data sets. The results illustrate the higher penetration depth of the L-band over such sandy soils. The C-band time series is found to be very sensitive to surface changes (soil moisture and vegetation growth). By contrast, the L-band time series appear to be very stable over the sandy soils, i.e., the only temporal changes occurring over temporary or permanent ponds.

Index Terms-ALOS/Phased

Array-type L-band SAR (PALSAR), ENVISAT/Advanced Synthetic Aperture Radar (ASAR), Mali, radar, Sahel, semiarid regions, synthetic aperture radar (SAR), time series analysis.

I. INTRODUCTION

S INCE the launch of the European Remote Sensing 1 (ERS-1) synthetic aperture radar (SAR) in 1991, land surfaces have been continuously observed by numerous spaceborne SAR sensors in different configurations and frequencies, i.e., at X-, C-, and L-bands. C-band radar data have shown their potential for the monitoring of semiarid areas, allowing the estimation of vegetation biomass and/or soil moisture content. Past studies have shown that over semiarid Sahelian areas characterized by rather low vegetation cover (< 30%) and biomass (< 1.5 ton dry matter per hectare), C-band radar data are both sensitive to vegetation and soil parameters (roughness and soil moisture), [START_REF] Jarlan | Analysis of ERS wind scatterometer time series over Sahel (Mali)[END_REF], [START_REF] Ulaby | Microwave Remote Sensing Active and Passive[END_REF]. On the other hand, the L-band larger wavelength should significantly reduce the vegetation contribution in the radar signal that should be largely dominated by the soil contribution. G. Mercier is with Télécom Bretagne, Sciences et Techniques de l'Information, de la Communication, et de la Connaissance/Connaissance, Information, Décision Laboratory, Unité Mixte de Recherche 6285, Technopole Brest-Iroise, 29238 Brest, France (e-mail: gregoire.mercier@telecombretagne.eu).

E. Mougin and P. Hiernaux are with the Geosciences Environnement Toulouse Laboratory, UMR Centre National de la Recherche Scientifique 5563, 31400 Toulouse, France (e-mail: eric.mougin@get.ops-mip.fr).

In order to make a deeper comparison between the differences observed at the C-and L-bands over Sahelian areas, two time series acquired by ENVISAT-Advanced SAR (ASAR) and ALOS-Phased Array-type L-band SAR (PALSAR) sensors over the Gourma region, Mali, are analyzed. A particular attention is put on the temporal changes that are observed over the two time series, allowing the analysis of the sensitivity of both frequencies to the seasonal variation of surface features.

The first section presents the study site and the data used in the study. The change detection method is detailed in the second section. The results are then discussed.

II. STUDY SITE AND DATA

A. Study Site

The study site (1 • W-2 • W, 14.5 • N-17.5 • N) is located within the Sahelian zone, in the Gourma region, which stretches from the loop of the Niger River southward down to the state border with Burkina-Faso [START_REF] Mougin | The AMMA Gourma observatory site in Mali: Relating climatic variations to changes in vegetation, surface hydrology, fluxes and natural resources[END_REF].The region experiences a single rainy season with most precipitation falling between late June and mid-September with mean annual rainfall ranging from about 150 to 600 mm along this north-south transect. The rainy season is followed by a long dry season of eight months in the south increasing to ten months in the north. The vegetation consists in a herbaceous layer almost exclusively composed of annual plants and a sparse woody plant population (mean cover below 5%).The phenology of vegetation is mainly determined by rainfall. Grass development starts after the first rains in June or July, and senescence approximately coincides with the end of the rainy season. There is no green vegetation during the dry season, a part from a few shrubs foliage.

The underlying geology of the Gourma region includes precambrian sandstone and schist eroded into a peneplain surface with occasional plateaus of hard sandstones that have resisted erosion. The Gourma peneplain is at between 250-and 330m altitude with the highest isolated sandstone buttes reaching 900-1100 m. The eroded and exposed peneplain surfaces are locally capped by an iron pan formed during the humid period of the Tertiary, but larger areas of the region are covered by deep and stabilized sand dunes deposited during arid periods of the Quaternary. In addition to these two major landforms and also inherited from the humid periods of the Quaternary, remnants of alluvial systems and lacustrine depressions can be observed. At mesoscale, soil types can be gathered into three main categories: sandy soils extending over 58% of the area, shallow soils on rock and hard pan outcrops extending on 23.3%, and fine textured soils in low lands on 18.7%. The land units are presented in Fig. 1(a). They correspond to the dominant category (> 66%) and are labeled "mosaic" otherwise.

III. CHANGE DETECTION METHOD

Change detection in remote sensing image series may be difficult due to artifacts, such as scalloping, that where present on some of the studied images. Moreover, the high dynamic range of the gray tone values and the presence of speckle (even after filtering process) in radar images make inefficient traditional methods based on the analysis of the relative differences or ratio. The extension proposed in [START_REF] Inglada | A new statistical similarity measure for change detection in multitemporal SAR images and its extension to multiscale change analysis[END_REF] that is based on a Kullback-Leibler divergence of the local statistics cannot be used here because the change detection process is applied on a time series and not on the comparison between two dates.

The change detection technique has to balance between the detection of highest variability between seasonal land cover and the mitigation of false detection due to the differences in the observation conditions. In order to reduce artifacts due to speckle, a multilooking process is made by applying a boxcar filter uniformly to the images. The size of the local window is 10 × 10 on fine beam mode images and 4 × 4p i x e l so nW S mode images.

One of the usual change detection methods from a long time series is based on the principal component (PC) analysis because it is often considered that the axis hooded by the second highest eigenvalue is related to changes [START_REF] Celik | Unsupervised change detection in satellite images using principal component analysis and k-means clustering[END_REF], under the hypothesis that the change areas are much less representative (statistically) than the no change areas. In such a representation, the pixels of image time series are considered to be vector-pixels in a feature space whose dimension is equal to the number of acquisitions. When no change occurs, the vector pixels have components that are distributed along the mean axis (hooded by the eigenvector associated to the highest eigenvalue), which corresponds to a normal evolution in the time series. On the contrary, when a change occurs at a specific date and a specific location, the components of the related pixel are becoming different from the "normal" components so that the vector pixel is moving away from the mean axis. Unfortunately, the use of the second eigenvector for characterizing changes is not relevant for the considered SAR image series. In fact, the variability induced by the scene and the SAR sensor make changes through isotropic directions away from the mean axis, so that the second PC holds only partial information of the changes. As a consequence, the distance to the mean axis appears to be a valuable alternative. Hence, if we consider change detection from a set of three images, the second and third PCs should be required to define the distance of the mean axis. In a 3-D space, this distance to the main axis appears to be similar to the saturation measure from the hue-saturation-value (HSV) color transform. In this case, the involved distance is similar (but not equivalent) to the Euclidean distance, and for which details may be found in [START_REF] Kruse | A technique for enhancing digital color images by contrast stretching in Munsell color space[END_REF]. However, in N -D feature space (N>3), it is difficult to choose the good PC axes or the appropriated subspace to highlight changes. Then, this approach should be implemented in a reduced dimension feature space to cope with reasonable memory requirement and computation space. In [START_REF] Inglada | Land-cover maps from partially cloudy multitemporal image series: Optimal temporal sampling and cloud removal[END_REF], it has been stressed that an appropriated time series image classification could be restricted to a very limited number of images if those images correspond to the key period of temporal change. In the present application, no aprioricriterion has been found to select the most appropriated images. Thus, a random projection technique has been applied. This strategy remains valuable only if the number of images in the time series is important, if not, a simple exhaustive search has to be used.

From the N images in the time series, three acquisitions are chosen randomly. They are considered as components of a red-green-blue (RGB) false color representation. This color space is transformed in the HSV representation [START_REF] Kruse | A technique for enhancing digital color images by contrast stretching in Munsell color space[END_REF]. Then, the saturation channel is considered to be representative of changes in-between the three selected images. The process is iterated K times, and the mean of the saturation channels serves the change measure of the time series. For N ≤ 6, the combination may be performed through an exhaustive selection of triplets yielding C N 3 combinations (C N 3 ≤ 20). When N>6,thethree channels are randomly chosen and the process is repeated K times (with K arbitrary chosen to 50 in the present case). It is worth noting that the radiometric-based change detection procedure is sensitive to the differences in radiometry so that a special care has to be brought to the image intercalibration.

IV. RESULTS AND DISCUSSION

Fig. 1(b) and (c) shows the study site acquired by the ASAR and PALSAR sensors on December 16, 2005 and January 1, 2008, respectively, both in WS mode. On the whole, the two images are similar. The Niger River is the bright line crossing the top of the image. The sandy soils correspond to darker zones. The bright patterns correspond either to relief (buttes and rock or hard pan outcrops, as for the center of the red square) or to lowlands [as for the bottom right of the red square in Fig. 1(c)], which are characterized by very rough and surfaces concentrating the trees that can be encountered over the study site. Bright linear structures correspond also to the remnants of alluvial systems, which are clearly visible on both images. However, they are better discriminated at the L-band due to the higher penetration depth in sandy soils for lower frequencies. In particular, the sand dunes, up to 10 m thick, oriented from west to east, appear with the C-band [see Fig. 1(b)] in alternate dark and lighter rectilinear structures in the upper third of the image, whereas they are not visible with the L-band [see Fig. 1(c)].

The sensitivity of L-and C-bands to seasonal changes have been analyzed by applying the change detection algorithm presented in Section III to different time series. First, a special analysis has been made on the PALSAR data acquired at fine beam mode at HH polarization, as these 12 acquisitions form the most consistent time series of the whole PALSAR data set. Temporal color composite image acquisitions made at three different dates at HH polarization is given in Fig. 2(a). The corresponding acquisition area is the red square shown in Fig. 1(c). The change detection result is presented in Fig. 2(b). The efficiency of the algorithm is worth noticing, enabling to account for the stable temporal behavior of the main relief structures or lowlands, which appear in black, independently of the high values observed on the intensity images. The rock and hard pan outcrops on the upper right corner also show a stable behavior, whereas the brighter color of the remnant alluvial system indicates that it is still temporary active with rainwater runoff. The brightest features correspond to millet fields (surrounded in orange) and to water ponds (surrounded in blue), indicating the high temporal change observed with respect to their extent and surface state (roughness and aquatic vegetation). Finally, the sandy soils (central part of the scene for example) exhibit low temporal changes, indicating the low sensitivity of the L-band to surface roughness and moisture as well to the herbaceous layer development over such semiarid areas.

For comparison with the C-band, a temporal color composite image is presented over the same subscene extracted from the ASAR WS acquisitions [see Fig. 3(a)]. The result of the temporal change algorithm obtained from the five WS acquisitions is shown in Fig. 3(b). Similarly to the L-band, the main relief, lowlands, and rock or hard pan outcrops appear in dark tones in Fig. 3(b), traducing a stable temporal behavior. The most striking difference with the L-band concerns the sandy soils, which appear as bright as water ponds and millet fields. It illustrates the high sensitivity of the C-band to surface state (surface roughness, soil moisture, and vegetation development) over such semiarid regions [START_REF] Jarlan | Analysis of ERS wind scatterometer time series over Sahel (Mali)[END_REF]. The wide extent of these areas induce confusion with millet fields and water ponds, which exhibit also significant temporal changes, leading the interpretation of this image less obvious than for the L-band.

As an illustration, Fig. 4 shows the temporal change detection obtained over a wider region with PALSAR acquisitions in wide beam mode (red rectangle corresponds to the area in Fig. 1). Fig. 4(a) shows the change detection applied to the five wide beam acquisitions, whereas Fig. 4(b) shows the change for the three acquisitions realized during the dry season. The main water ponds are easily discriminated on both images, i.e., the permanent ponds corresponding to those detected during the dry season [see Fig. 4(b)] and the temporary ponds corresponding to those detected during both dry and wet season [see Fig. 4(a)]. Water ponds detection is of prime interest: First, they consist in the main water resource in the Sahel for both livestock and people. In addition, they are a marker of hydrological processes change [START_REF] Gardelle | Less rain, more water in ponds: A remote sensing study of the dynamics of surface waters from 1950 to present in pastoral Sahel (Gourma region, Mali)[END_REF].

To analyze the influence of polarization, the same change detection method has been applied to the five dual HH/HV PALSAR acquisitions. In that case, HH acquisition has been affected to both R and G channels, and the HV acquisition has been affected to the B channel, before performing the RGB-to-HSV transform. Fig. 5 presents the mean changes observed between HH and HV polarizations, i.e., corresponding to average of the five saturation obtained. Sandy soils appear in dark tones, traducing the small differences observed between HH and HV polarizations at the L-band over such surfaces. By contrast, bright patterns correspond to either water ponds or rock and hard pan outcrops (top of the image), resulting to a larger difference between HH and HV over these surfaces than for sandy or shallow soils. These signatures occur over areas characterized by predominant surface scattering mechanisms. On the other hand, structures with a high radar response (i.e., appearing in white in the RGB space in Fig. 2(a)], such as main relief features, lowlands, or the remnant alluvial system, appear in dark tones in Fig. 5. Indeed, such white colored features in both polarizations are associated to very low saturation values.

V. C ONCLUSION

A change detection method based on random projection and the HSV representation appears well adapted to highlight changes over different SAR image sets. This algorithm, which is easy to use and of limited complexity, allowed the analysis of temporal change detection between L-and C-band SAR time series over a Sahel region. The results show that temporal changes at the L-band are observed over water ponds and millet fields, whereas sandy soils observe a rather temporal stable behavior. They indicate the low sensitivity of the L-band to roughness state and moisture of the surface as well to the herbaceous layer development over such semiarid areas. The comparison of radar intensity images between L-and C-bands illustrates the higher penetration depth of the L-band for the sandy soils, allowing a better discrimination of remnant alluvial systems than at the C-band. With respect to the C-band, in addition to water ponds and millet fields, sandy soils show also significant temporal changes due to the high sensitivity of the C-band to both vegetation and soil moisture and roughness over such areas. This analysis shows that L-band radar data is well suited for the detection of temporal or permanent ponds in the Sahelian region.

  P.-L. Frison, G. Faye, C. Lardeux, and J.-P. Rudant are with the Université Paris-Est, ESYCOM laboratory (EA 2552), UPEMLV, ESIEE-Paris, CNAM, F-77454 Marne-la-Vallée, France (e-mail: frison@univ-mlv.fr).

Fig. 1 .

 1 Fig. 1. (a) Soil-type map of the study site in Gourma, Mali. (b) Radar image acquired in WS mode at the C-band by ASAR on December 16, 2005. (c) Radar image acquired at the L-band by PALSAR on January 1, 2008.The red square corresponds to the acquisition area of PALSAR images in fine beam mode. B. SAR Data Two data sets are analyzed; they have been acquired at the C-(λ =5.6 cm) and L-bands (λ =23.6 cm) by the ASAR and PALSAR sensors, respectively. Five ASAR acquisitions have been realized between September 29 and December 16, 2005, at 35-day intervals. They have been acquired at HH polarization in wide swath (WS) mode with 150 m of spatial resolution. For these acquisitions, the study site is located at an incidence angle of about 40 • . 17 PALSAR acquisitions have been made between July 2007 and May 2009: 12 in Fine beam mode (seven in Single HH and five in Dual HH/HV polarization) with 15 m of spatial resolution, and five in Wide beam mode (i.e. 100 m of spatial resolution) at HH polarization. The study site corresponds to incidence angles of about 40 • and 35 • for fine beam and WS modes, respectively.

Fig. 2 .

 2 Fig. 2. (a) Temporal color composite image of PALSAR fine beam acquisitions (HH polarization) (R: January 17, 2007, G: October 20, 2007, B: January 22, 2009). (b) Change detection images obtained for the 12 fine beam PALSAR images time series (HH polarization). Water ponds and millet fields are surrounded in blue and orange, respectively.

Fig. 3 .

 3 Fig. 3. (a) Temporal color composite image of ASAR WS acquisitions (HH polarization) (R: July 29, G: October 7, B: November 11, 2005). (b) Change detection images obtained for the five ASAR image time series (HH polarization). Water ponds and millet fields are surrounded in blue and orange, respectively.

Fig. 4 .

 4 Fig. 4. a) Change detection obtained for the five PALSAR wide beam acquisitions (HH polarization). (b) Change detection images obtained for the three PALSAR wide beam images acquired during the dry season (HH polarization).

Fig. 5 .

 5 Fig. 5. Change detection observed between HH and HV polarizations for the five PALSAR dual-mode acquisitions.

ACKNOWLEDGMENT

The authors thank ESA for providing ASAR and PALSAR data (CAT-1 Project ID 4229).