Investigating the Relationship between X-Band SAR Data from COSMO-SkyMed Satellite and NDVI for LAI Detection

Monitoring spatial and temporal variability of vegetation is important to manage land and water resources, with significant impact on the sustainability of modern agriculture. Cloud cover noticeably reduces the temporal resolution of retrievals based on optical data. COSMO-SkyMed (the new Italian Synthetic Aperture RADAR-SAR) opened new opportunities to develop agro-hydrological applications. Indeed, it represents a valuable source of data for operational use, due to the high spatial and temporal resolutions. Although X-band is not the most suitable to model agricultural and hydrological processes, an assessment of vegetation development can be achieved combing optical vegetation indices (VIs) and SAR backscattering data. In this paper, a correlation analysis has been performed between the crossed horizontal-vertical (HV) backscattering (°HV) and optical VIs (VIopt) on several plots. The correlation analysis was based on incidence angle, spatial resolution and polarization mode. Results have shown that temporal changes of °HV (Δ°HV) acquired with high angles (off nadir angle; θ > 40°) best correlates with variations of VIopt (ΔVI). The correlation between ΔVI and Δ°HV has been shown to be temporally robust. Based on this experimental evidence, a model to infer a VI from ° (VISAR) at the time, ti + 1, once known, the VIopt at a reference time, ti, and Δ°HV between times, ti + 1 and ti, was implemented and verified. This approach has led to the development and validation of an algorithm for coupling a VIopt derived from DEIMOS-1 images and °HV. The study was carried out over the Sele plain (Campania, Italy), which is mainly characterized by herbaceous crops. In situ measurements included leaf area index OPEN ACCESS Remote Sens. 2013, 5 1390 (LAI), which were collected weekly between August and September 2011 in 25 sites, simultaneously to COSMO-SkyMed (CSK) and DEIMOS-1 imaging. Results confirm that VISAR obtained using the combined model is able to increase the feasibility of operational satellite-based products for supporting agricultural practices. This study is carried out in the framework of the COSMOLAND project (Use of COSMO-SkyMed SAR data for LAND cover classification and surface parameters retrieval over agricultural sites) funded by the Italian Space Agency (ASI).


Introduction
Earth observation (EO) is more and more used to manage land and water resources for agricultural applications, such as leaf water potential [1,2], soil water content [3][4][5][6][7], irrigation water management [8][9][10] and flood prediction [11][12][13].Diversely from optical imaging, the temporal resolution of observations from active sensors, such as SAR, is not limited by sky cloudiness; if carefully validated, it may be used in combination with thermal and optical imageries to provide a more continuous monitoring of land surfaces.Several new SAR missions have been launched or planned: ALOS-PALSAR (Japan); COSMO-SkyMed 1 and 2 (Italy); TerraSAR-X and TerraSAR-X2 (Germany); SeoSAR PAZ 1 and 2 (Spain); Sentinel 1 (European Space Agency); Radarsat RCM (Canada); Kompsat 5 (Korea).These new SAR missions (acquiring at X-, C-and L-bands) are characterized by dual polarization capability, a short revisit time (from 12 h to ~10 days) and high spatial resolution (<20 m), which could provide suitable data for operative crop monitoring [14,15].
Mapping vegetation using X-band data has limitations [23], because radiation at X-band penetrates only the upper part of the canopy; thus, radar backscattering is only related to the top layer and the crown.
Although X-band is not the most suitable for agro-hydrological applications, vegetation can be monitored combing optical and SAR backscattering data.
Recently, some research efforts have been carried out in addressing biomass or vegetation water content [24] using X-band images.However, the use of SAR data to reproduce 'optical' vegetation indices, such as the normalized difference vegetation index (NDVI) and leaf area index (LAI), is an important task, because these are key-input data in both mass and energy exchange models of soil-vegetation-atmosphere systems (e.g., SWAP and SEBAL, et similia).
COSMO-SkyMed, given its high temporal and spatial resolution, opened new opportunities for an operative monitoring in this framework.This paper explores the possibility of coupling SAR and optical images for assessing a new type of VI, as resulting from the project "Use of COSMO-SkyMed data for LANDcover classification and surface parameters retrieval over agricultural sites" (COSMOLAND), funded by the Italian Space Agency (ASI) [25].
The specific objectives of the COSMOLAND project were: (i) improving, tailoring and validating methods and algorithms for land-cover classification and surface parameter retrieval (including LAI) at the regional scale, using COSMO-SkyMed X-band SAR (CSK) data, as well as observations with optical passive sensors; and (ii) integrating the output of these algorithms into existing hydrological/crop growth models.This research was carried out in the framework of the first objective.

Test Site
The Sele plain covers an area of ≈500 km 2 and is located in the Campania region (Southern Italy) (Figure 1).The main crops are maize, forages, potatoes, vegetables, peaches, apricot and pear, which are irrigated from April to October.
The experimental farm "Improsta" is located in the Sele plain, approximately at 14°58′E, 40°33′N (see rectangle in Figure 1), and is managed by the Regional Administration of Campania.Within it, herbaceous crops, such as maize and alfalfa, are continuously monitored in several plots for research purposes and agricultural extension services.

Dataset
The dataset includes CSK and optical images (in the visible and near infrared ranges) and in situ LAI.

Satellite Images
Active microwave (SAR).The CSK mission, developed in cooperation between ASI and the Italian Defense Ministry, is planned as a constellation of four satellites, carrying X-band SAR with right and left looking imaging capabilities, an incidence angle ranging between 20° and 60° and a revisit time of 12 h in the worst case.
The antenna was designed to implement three different operation modes: (i) spotlight, for metric spatial resolution over an area footprint of 100 km 2 , in single polarization; (ii) stripmap, for decametric resolution covering areas from 900 to 1,600 km 2 , with dual polarization capability (the so-called PingPong configuration); (iii) scanSAR, for tens to hundreds meter resolution over areas ranging from 10,000 to 40,000 km 2 .
The DEIMOS-1 Mission, fully owned and operated by DEIMOS Imaging S.L., offers a new source of geospatial imagery at medium spatial resolution (22 m) covering large areas with a swath of approximately 600 km.DEIMOS-1 satellite provides a revisit time of 2-3 days, with a competitive cost per unit km 2 , thus making it particularly suitable for operational applications (e.g., precision farming).
Five DEIMOS-1 optical images have been collected between 3 August and 7 September in the framework of the project IRRISAT [26]. Figure 2 shows a CIR DEIMOS-1 color composite subset of the Improsta farm.Preliminary processing included: atmospheric correction based on MODTRAN and library reference spectra of vegetation and NDVI retrieval.

In situ LAI
LAI (m 2 • m −2 ) has been collected weekly between 1 August and 12 September with a LICOR LAI-2000 Plant Canopy Analyzer [27]; the dataset was acquired within 25 plots of corn and alfalfa.In particular, the average LAI is retrieved at sunrise from three measurement repetitions of eight below-canopy readings each.Moreover, an opaque cover (view cap) with an open wedge of 180° was used to avoid the influence of neighboring obstacles (e.g., the operator).This measurement protocol allowed to determine statistically meaningful LAI values characterized by a low ratio between SEL (standard error of the LAI) and LAI (SEL/LAI ranged between ≈0.02 and ≈0.1); thus, the actual LAI should be within ±10% of the LAI sample mean.
Measured LAI ranged between 0.36 and 5.35 m 2 • m −2 with an average value of 2.39 m 2 • m −2 .In situ LAI have been used for producing LAI maps from DEIMOS images by applying an exponential relationship with NDVI, i.e., 0.172e 3.64NDVI [28].The calibration of the NDVI vs. LAI relationship resulted in a determination coefficient, r 2 = 0.91, with a standard error (S.E.) of 0.50 m 2 • m −2 .Hereinafter, we refer to LAI as the estimated values from DEIMOS images.

Methods
Pre-processing of CSK images included: (a) backscattering calibration and (b) speckle reduction.Speckle reduction has been achieved by applying a multi-temporal filter operator [29] with a 7 × 7 kernel.The appropriate spatial resolution has been evaluated through a geo-statistical analysis based on the Moran's index [30] and the eight directions "Queen case" approach.
The multi-temporal filtering has been chosen to fully exploit both space and time dimensions to achieve the required equivalent number of looks (ENL), thus obtaining a satisfactory speckle reduction [31,32].
The resulting speckle index was on average 0.12 compared to 0.20 in the original images.Moreover, the chosen filter preserves the spatial resolution of the input data that is still suitable for crop monitoring and similar to the spatial resolution of the optical images.
Hereinafter,  CSK is used to indicate °H V , °H H , °V V , as well as the depolarization difference, dpr = °H V − °H H (dB).This latter is sensitive either to bare soil roughness or to crop height; indeed, variations of these surface characteristics determine a higher increase of °H V compared to that of °H H [33,34].
The comparison between  CSK and VIs was made following two different approaches: (1) image segmentation and comparison of average values for each class; (2) temporal variation within small homogeneous areas.
The relationship between  CSK and VIs is to be researched in space and time.The first approach investigates the space variability for fixed time and vice versa; the second approach examines the temporal variability for given space intervals.
To this aim, we used a total of 8  CSK sets (°H V , °H H , °V V and dpr collected at both low and high incidence angles) and 2 VI sets (NDVI and LAI).For each  CSK image, we have considered the nearest VI.
In the first approach, the procedure has been applied with two different schemes (Figure 3): -The first scheme uses VI as the reference image and  CSK as the complementary one; -Conversely, the second scheme uses  CSK as the reference image and VI as complementary.In each scheme, the reference image has been segmented into N-equal intervals (applying the equal interval data classification) and for each interval mean, and standard deviation values have been extracted.The segmented reference image is then used to create a Boolean mask for identifying corresponding pixels of the complementary image and, for each subset of the complementary image, the same statistics have then been calculated.Finally, the statistics of reference and complementary images have been compared to investigate any reciprocal relationship between average values and data variability of  CSK and VI.
In the second approach, a diachronic analysis between variation of VI and  CSK , namely ΔVI and Δ CSK , has been carried out within a set of homogeneous areas to investigate the influence of canopy growth on solar energy absorption/reflection and microwave backscattering.Once selected, for 30 homogeneous areas, characterized by low, moderate and high temporal ΔVI, the corresponding Δ CSK has been derived.An empirical relationship has been sought between the two variations to be successively applied to the whole image.The results have been validated by using in situ data taken at the Improsta farm.

Approach 1: Image Segmentation
From the different VI and  CSK datasets considered in scheme 1, the existence of a general exponential relationship between the averages of VI and the corresponding  CSK value was found: Figure 4(a,b) refers to the application of schemes 1 and 2, respectively.In Figure 4(a), VI is the reference image, whilst in Figure 4(b),  CSK has been used as the reference, according to the scheme 2.
In scheme 1, best fitting (N = 10; r 2 ~ 0.79, Figure 4(a)) resulted when considering LAI for VI and dpr for  CSK collected at high angles only (dpr high ), thus reducing the available dataset to five couples of DEIMOS-1 and CSK images.The choice of N in the segmentation did not influence the results if N is greater than 10.The relationship is applicable if LAI ranges between 0.5 and 3.For LAI < 0.5, the soil roughness is strong enough to influence the backscattering; diversely, for LAI > 3, the relationship tends to a vertical asymptote, which can be considered as the upper limit of validity.
Other VI- CSK returned lower correlations compared to the findings of Figure 4(a).As a consequence, SP images (acquired in co-polarized mode only) and PP low have not been considered for further setting up and/or calibrating the model.A discrepancy in the backscattering levels between SP and PP has been also found.
In particular, the SP vs. PP revealed only a moderate r 2 (~0.59); this is due both to differences in the look angles (21° and 41° for SP, 27° and 46° for PP) and to differences of the image generation between PP and SP having great influences, especially regarding the focusing azimuth process, and thus, in the backscattering level.
The relationship (1) was in line with expectations deriving from a physical interpretation of the backscattering phenomenon, with more vegetation showing higher difference between cross-polarized and co-polarized backscattering.Furthermore, the disaggregation between two different dates showed the relationship to be almost temporally invariant.However, relationship (1) has been retrieved between average values of both VI and  CSK variables.Actual standard deviation values of  CSK found for each VI interval are very high, meaning that the variability of the independent variable cannot be fully explained by that observed for the dependent variable.
For this reason, the average values of the independent variable are actually constrained in a limited range.These results are ever observable between variables that are moderately or coarsely pixel-wise correlated (as occurring in this case).
Indeed, the standard deviation values of dpr (dpr st.dev ) within LAI intervals are high, especially for the lowest LAI ranges (dpr st.dev ranges from 3.7 to 3 dB for 3 August and it ranges from 5.5 to 2.8 dB for 5 September).This means that an average dpr value (dpr avg ) of −10 dB represent dpr values ranging from −16 to −3 dB (considering two-times the dpr st.dev ).
For the above-mentioned reasons, scheme 2, which was based on the segmentation of  CSK , did not confirm, as expected, the previous finding (Figure 4(b)).Different  CSK classes produced similar VI averages, with significant differences for distinct acquisition dates.
Furthermore, we notice that the maximum LAI observed in the different intervals of backscattering used for the segmentation is 1-1.5 m 2 • m −2 (Figure 4(b)), that is comparable (i.e., the average plus the standard deviation is up to 2.7 m 2 • m −2 ) to the maximum value of 3 m 2 • m −2 , which is possible to infer according to scheme 1 (Figure 4(a)).It means that the segmentation based on backscattering determines areas characterized by a larger variability of LAI compared to the opposite scheme 1.This highlights that it is not possible to apply a relationship similar to Equation (2) to infer LAI avg starting from average  CSK values.
One reason for these findings could be due to the effect of residual speckle, even after the de-speckling pre-processing, thus leading to the evidence that dpr average variability cannot be fully explained by LAI averages and vice versa.
A larger kernel could be used to further reduce the speckle, but this choice is limited by the average size of the agricultural plots of the Sele plain (land heterogeneity).In the second approach, the relationship between the variation of both  CSK and VIs between two consecutive acquisitions has been analyzed (ΔVI and Δ CSK , respectively).Firstly, we have selected a limited subset of the image, corresponding to homogeneous vegetation cover (i.e., characterized by low coefficient of variation) and different average LAI values.We have analyzed the variation of both VI and  CSK between a reference date (3 August) and subsequent acquisitions; this leads to four different sets of ΔVI and Δ CSK .Another two additional sets of variation have been calculated considering as the reference date the acquisition of 19 August and the two subsequent images.
Among all the possible couples of ΔVI and Δ CSK , the best fitting was found when considering NDVI for VI and °H V,high (r 2 = 0.75), the latter corresponding to the acquisition mode PP high (Section 2.2.1), hereinafter °H V for the sake of brevity.This result confirms previous findings, i.e., °p q (backscattering acquired in cross-polarization) is more sensitive than like-polarized backscattering, °p p , to the temporal variations of vegetation biomass [35].
Knowing NDVI ti at a reference time, t i , and the variation of backscattering, Δ°H V,(ti + 1) − ti , between times, t i + 1 and t i , it is then possible to infer NDVI ti + 1 by means of a linear relationship: where ΔNDVI (ti + i) − ti is the variation of NDVI and γ and δ are empirical coefficients determined by using the observed variations within the spatial subsets and for the acquisitions mentioned above.Within the above relationship (2), NDVI ti accounts for the spatial pattern, while (γ•Δ°H V,(ti + 1) − ti + δ) describes its temporal variability.In other words, the variability of the two sets, NDVI and °C SK , is determined by different interactions between the surface and the active/passive signals, whilst the response in two consecutive images shows a similar behavior (linear proportionality in increments or decrements).This procedure does not require a preliminary segmentation of the image, as in Approach (1). Figure 6 shows the relationship between ΔNDVI (ti + 1) − ti and Δ°H V,(ti + 1) − ti using the calibration dataset.

Figure 6. ΔNDVI (ti + 1) − ti vs. Δ°H V,(ti + 1) − ti .
Once Equation ( 2) has been applied to the whole study area, the method has been validated on a subset of homogeneous areas.These areas were selected by classifying the NDVI time series by using a k-means algorithm [36].Thus, five clusters of NDVI showing similar temporal behavior were determined.
In Figure 7, we compare average and st.dev values of NDVI (Figure 7(a,b), respectively) retrieved from Equation (3), NDVI CSK and the corresponding original ones from DEIMOS images.The average values, μ NDVICSK vs. μ NDVI , are significantly correlated (r 2 ≈ 0.90, m ≈ 1.10, q ≈ 0.03); as expected, the standard deviation of  NDVICSK is higher than  NDVI .Figure 8 shows the temporal behavior of NDVI and NDVI CSK for a corn and an alfalfa plot of the Improsta farm (Figure 3).NDVI CSK has been derived using the acquisition of 3 August as the reference time, t i .Better agreement between NDVI CSK and NDVI has been found for corn rather than alfalfa plots, especially for the second acquisition date; this result has been also confirmed for other irrigation units.NDVI CSK vs. NDVI on corn was characterized by r 2 ≈ 0.98; NDVI is slightly overestimated by NDVI CSK for NDVI CSK > 0.67 (m ≈ 1.38, q ≈ −0.25), whereas the dispersion in alfalfa plots has a lower r 2 (≈0.66), and the linear regression line has a lower offset (m ≈ 0.83, q ≈ 0.14).
Successively, we have applied the exponential empirical relationship defined in Section 2.2.2 to NDVI CSK to retrieve LAI CSK .Figure 9 shows the correlation between LAI and LAI CSK for alfalfa and corn u.i.; dots represent minima, maxima and averages values (during the period 3 August-5 September).
Finally, Table 3 reports field temporal averages, temporal st.dev and S.E. of the LAI CSK vs. LAI for corn and alfalfa.The S.E. of the LAI ranges between 0.29 and 0.84 (m 2 • m −2 ) over corn plots, whereas it is higher for alfalfa (up to 1.41 m 2 • m −2 ).The lower agreement for alfalfa is probably related to irrigation, which could affect more strongly the backscattering of this kind of canopy.Unluckily, in situ measures of soil water content and soil surface roughness were not available to assess how these variables affect the proposed procedure.However, at the X-band, the backscattering results mainly from the upper part of the canopy and leaves, with little contribution due to the underlying soil surface [37][38][39].Table 3.Comparison between LAI CSK and LAI: field temporal average, temporal average st.dev and S.E.calculated over corn (ui09, ui11, ui12, ui17, ui18, ui20) and alfalfa (ui04, ui05, ui15) plots over the time series.

Conclusions
The possibility of using backscattering SAR images to assess vegetation development and LAI has been investigated within this paper, by comparing optical and X-band SAR images from the novel COSMO-SkyMed constellation, which has a great potential in terms of spatial and temporal resolution.LAI maps derived from DEIMOS optical sensors have been used as the reference.
Areas with a similar value of LAI, in the range 0-3 m 2 •m −2 , respond in a similar way to X-band backscattering, as shown in the first part of the study; an empirical relationship has been observed between average LAI and average backscattering depolarization difference.However, the large variability of backscattering within a cluster of pixels with similar LAI values does not allow its retrieval directly from backscattering.This could be explained by the joint effect of residual speckle and soil water content on backscattering.
The suitability of CSK data to infer NDVI maps (at DEIMOS-1 spatial resolution) has been demonstrated by coupling optical and cross-polarized backscattering (°H V ).The method only requires the NDVI spatial distribution from optical images at a reference time and the °H V temporal variation.High correlation was found between NDVI estimated from °H V and the one calculated from optical reflectances (r 2 ≈ 0.98 on corn; ≈0.66 on alfalfa), moreover standard error over corn and alfalfa fields within the experimental farm ranged between 0.05 and 0.26 (−).The comparison in terms of LAI showed a good agreement on corn, but with a lower determination coefficient, r 2 (≈0.83), with a higher standard error (0.29-1.41 m 2 •m −2 ).

Figure 7 .
Figure 7. NDVI CSK vs. normalized difference vegetation index (NDVI) scatterplot of (a) average values and (b) st.dev within homogeneous areas selected using the k-means algorithm.

Table 1 .
Acquisition time of in situ leaf area index (LAI), DEIMOS-1 and COSMO-SkyMed (CSK) images (SP in single polarization and PP in dual polarization).