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Abstract—Every year, floods cause enormous damage and loss of human life all over the world. Regarding the European Union, extreme floods are the most ...

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 45, NO. 10, OCTOBER 2007

Rapid Response Flood Assessment Using Minimum Noise Fraction and Composed Spline Interpolation Marco Gianinetto, Member, IEEE, and Paolo Villa, Student Member, IEEE

Abstract—Every year, floods cause enormous damage and loss of human life all over the world. Regarding the European Union, extreme floods are the most common types of natural disasters (44% of the total in the last decade), and in the future, the number of flash floods is expected to rise. Recent works of the authors have focused on the development of a straightforward and efficient processing algorithm for analyzing and mapping flood damages using optical remotely sensed satellite data and digital terrain models. In this paper, some improvements of the processing technique, both regarding the flood mapping and the water depth estimation, are presented. With respect to the first issue, a new data transformation is introduced, replacing the spectral–temporal principal component analysis (STPCA) with the spectral–temporal minimum noise fraction (STMNF) transformation, while the peak water depth is obtained through more sophisticated interpolation methods. The STMNF-based technique was applied to the data collected for the worst flood of the 20th Century that struck Piemonte Region, Italy, in 1994. Regarding the flood mapping, the STMNF method allowed an overall accuracy of 97.09% with a kappa coefficient of 0.889 to be established, obtaining a user accuracy of 85.76%, and a producer accuracy of 95.96%, with a lower commission error if compared to the previous STPCA method. Regarding the water depth computation, the best results were obtained using the second-order composed splines interpolator, obtaining an overall agreement with ground reference data of about 83%. Index Terms—Algorithms, hazardous areas, image classification, image processing, interpolation, optical imaging, remote sensing, satellite applications, spline functions.

I. I NTRODUCTION

E

VERY YEAR, floods cause enormous damages and loss of human life all over the world. According to the international emergency disaster database (EM-DAT) containing essential core data on the occurrence and effects of over 12 800 mass disasters in the world from 1900 to present, compiled from various sources, including United Nations agencies, non-governmental organizations, insurance companies, research institutes, and press agencies, and maintained by the Centre for Research on the Epidemiology of Disasters, Manuscript received September 21, 2006; revised December 4, 2006. This work was supported by the Italian Ministry for University and Research within the research program “Tecnologie innovative per la previsione, il controllo e la mitigazione dell’impatto delle emergenze ambientali.” M. Gianinetto is with the Remote Sensing Laboratory, Dipartimento di Ingegneria Idraulica, Ambientale, Infrastrutture Viarie, Rilevamento (DIIAR) Department, Politecnico di Milano University, 20133 Milano, Italy (e-mail: [email protected]). P. Villa is with the Italian National Research Council [Consiglio Nazionale delle Ricerche–Istituto per il Rilevamento Elettromagnetico dell’Ambiente (IREA)], 20133 Milano, Italy (e-mail: [email protected]). Digital Object Identifier 10.1109/TGRS.2007.895414

Brussels, Belgium, in cooperation with the U.S. Office for Foreign Disaster Assistance, in the last decade of the 20th Century, floods killed about 100 000 persons and affected over 1.4 billion people [1]. Looking at global statistics and comparing the decades 1985–1995 and 1995–2005, floods have had an increase in the average duration (+16%), affecting larger regions (+39%), and producing a higher number of casualities (+38%) and people displaced (+102%) [2]. With respect to the European Union, extreme floods are the most common type of natural disasters. Floods vary in frequency, location, and intensity as a result of seasonal and regional variations in precipitation, weather conditions, and more long-term changes in the climate. Climate change, including the increasing intensity of heavy rainfall, is projected to make extreme river floods even more frequent in some areas, particularly in central, northern, and northeastern Europe. In particular, the number of flash floods is expected to rise, which is also likely to increase the risk of casualties [3], [4]. Looking at the flood events recorded in the EM-DAT between 1975 and 2001, the number of flood events per year increased over this period [5]. However, the number of deaths per flood event decreased somewhat, probably due to improved warning and rescue systems [3], [4]. In the period 1900–2006, floods comprised 38% of all disasters in Europe, growing to more than 44% if considering only the last decade. Only in the period 1998–2002, Europe suffered about 100 damaging floods causing some 700 fatalities and the displacement of about half a million people (around 1.5% of the European population) [3], [4]. Regarding their direct economic impact, in Europe, floods cause the 75% of all insurance payments due to natural disasters: at least 25 billion EUR in insured economic losses were reported just only for the period 1998–2002. Furthermore, the indirect economic and social effects, which are more difficult to quantify, can cause a decrease of socio-economic welfare [1]. In this global context, Italy is particularly struck by this type of natural disaster. The results of some major research projects on floods presented in 2003 by the European Research Commissioner Philippe Busquin pointed out that in the last two decades of the 20th Century the greatest number of floods occurred in France (22%), Italy (17%), and the U.K. (12%). However, the highest number of fatalities occurred in Italy (38%), followed by Spain (20%) and France (17%), and the greatest economic losses occurred in Germany and Italy (both 11 billion EUR), followed by Spain and the U.K. (both around 6 billion EUR) [6]. Moreover, if looking at the database of the Aree Vulnerate Italiane da frane ed inondazioni (AVI)

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GIANINETTO AND VILLA: FLOOD ASSESSMENT USING NOISE FRACTION AND SPLINE INTERPOLATION

project, a special program promoted by the Department of Civil Protection of the Italian Government to gather general information on all sites affected by landslides or floods in Italy during the last century, containing data on the occurrence of floods between 1918 and 1994 and maintained by the National Group for Prevention of Hydrological Hazards of the Italian National Research Council (GNDCI-CNR), we will find more than 28 000 events which have interested more than 15 000 places all over the country [7]. During the AVI project, more than 300 people, divided into 15 research teams and two support groups, worked for one year on the project. Twenty-two journals were systematically searched for the period 1918–1990, 350 000 newspaper issues were screened, and 39 953 articles were collected. About 150 experts on mass movement and floods were interviewed, and 1482 published and unpublished technical and scientific reports were reviewed [7]. Due essentially to property damage implications, private insurance companies are directly concerned by floods. Insurance companies need information on flood risk zones, economic vulnerability, and the actual occurrence of floods for calculating insurance premiums and quantifying the damage after a flood event [8]. This kind of information is also very useful to the political class (from the local level to the European Commission and the European Parliament level) for taking decisions about the distribution of fundings destined to the reconstruction in the inundated areas, for realizing a more efficient management of the environment and for better estimating future risks [9], [10]. In recent years, remote sensing technology along with Geographic Information System (GIS) has become the key tool for flood monitoring [11]–[16], particularly in providing a synoptic vision over a wide area in a short time and in a very cost effective manner [17], [18]. However, as regards remote sensing applications at local scale, researchers have not yet proved in a completely satisfactory way the competitiveness of satellitebased methods compared with ground measures and aerial surveys [19], [8]. Above all, in the field of natural hazards, remote sensing potentialities are huge and not yet totally explored. Recent works of the authors have focused on the development of a straightforward and efficient processing algorithm for analyzing and mapping flood damages using optical remotely sensed satellite data, both at regional and local scale [9], [10], [20], [21]. The basic idea is to highlight the environment’s changes by processing, through the use of a change detection technique, imagery collected before and after the flood, together with a digital terrain model (DTM). In previous works, the STPCA has been used for delimiting the flooded areas, while the water depths and the volume estimation have been performed through the use of a second order polynomial interpolation [9], [10]. This paper presents some improvements of the processing technique regarding both the flood mapping and the water depth estimation. With respect to the first issue, a new data transformation is introduced, replacing the STPCA with the STMNF transformation, while the peak water depth is obtained through more sophisticated interpolation methods, among which are splines. The improved processing technique was applied to the data of the worst flood of the 20th Century that struck Piemonte

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Region, Italy. In particular, the area studied was the valley of the Tanaro River, between the cities of Asti and Alessandria, one of the most heavily hit in 1994. Here, the accumulated precipitations reached the record values of more than 200 mm with a maximum hourly intensity of 55 mm/h. The consequent flash flood caused 44 victims and over 2000 people homeless and serious damages to buildings and infrastructures [10]. II. D ATASET For the flood assessment analysis, two Landsat-5 Thematic Mapper (TM) scenes were used: one preceding the flood event and one subsequent. The closest preflood cloud free image was collected on October 16, 1994, and the first useful post flood image on January 5, 1995, two months after the end of the inundation. The choice of the Landsat/TM data was considered a good compromise between the spatial resolution (30-m ground resolution), the spectral content (six reflective bands: visible, near infrared, and shortwave infrared), and the area covered by the images (about 35 000 km2 for each scene). As supplementary data, the DTM of Piemonte Region supplied in ASCII format by the Cartographic Office of Piemonte Regional Government was used. The following are the main characteristics of the dataset used: 1) two 30-m Landsat-5/TM scenes (WRS2 path 194, row 28/29), centered at 44◦ 53’ North latitude and 8◦ 19’ East longitude: a) October 16, 1994 (preflood image); b) January 5, 1995 (postflood image); 2) 50-m girded DTM derived from the digitalization of existing 1 : 10 000 scale digital cartography, centered at 44◦ 51’ North latitude and 8◦ 16’ East longitude, with 1-m vertical resolution and 2.5-m rms error (RMSE) vertical accuracy. III. F LOOD M APPING Flood mapping consists in the generation of a map describing the maximum extent of the flooding. Such an issue can be obtained through different methods [17], [18]; however, in any case, it is necessary to separate water related features (linked to inundated terrain) from nonwater related ones, and one possibility is to analyze the spectral differences between the two cited features using a change detection technique. As typical in change detection applications, geocoding and atmospheric correction are always needed. For these purposes, the Landsat-5/TM data were first georeferenced in the UTMWGS84 F32N projection, using as reference data an already geocoded Landsat-7 enhanced thematic mapper plus (ETM+) image. Original at-sensor radiance data were atmospherically corrected using a low-resolution MODTRAN4 model (15 cm−1 ) combined with aerosol retrieval based on band reflectance ratios and with adjacency correction of path radiance [22], [23]. Following the processing scheme of spectral-temporal change detection described in [10], a 12-band file was created, including first the six reflective bands of the preflood scene

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Fig. 1. Flood map derived with STMNF transform and DTM filtering, showing the accordance with ground truth data. Both omission error (4.04%) and commission error (14.24%) spatial distribution are reported.

(from band TM1 to band TM5, plus band TM7) followed by the six homologous bands of the postflood scene. To this spectraltemporal dataset, it was applied the MNF transform. One of the most critical elements of the flood mapping using PCA-class techniques is the choice of the component to be used. When using the STPCA, depending on the relative percentage area of change in the preflood and the postflood image pair, the most significant principal component (PC) should be identified in the higher order PCs or in the lower order PCs. In the case of the Tanaro dataset, the areas inundated were well correlated with the lower order PCs [10]. The use of the STMNF transform here introduced and directly deduced from the STPCA [10], [26] overcame this ambiguity. The MNF is a linear transformation which turns multivariate data with different signal-to-noise ratio (SNR) into a new set of uncorrelated variables, rescaling the noise component in order to obtain MNF components laid in decreasing order of SNR [24], [25]. Thus, for flood mapping, it is expected to find the most significant MNF component among the first components (typically component no. 1 or no. 2). After a first visual check of the STMNF components, the component no. 2 was chosen to be representative of water related features, such as floodwater, wet soil, and deposited sediments. The STMNF component no. 2 was then thresholded and filtered with the help of a terrain slope chart derived from the DTM processing. By visual interpretation of the postflood image, an area certainly flooded and an area certainly nonflooded were selected. For these areas were computed, the histograms and the threshold were chosen by computing the average of the mean values of the two histograms. The filtering was then performed through the exclusion of the areas characterized by a slope greater than 4%, which is extremely unlikely to be covered by water because of the hill area. Both the conditions on the MNF and terrain slope thresholds have to be satisfied at the same time (logical AND). Finally, the flood map was refined with classical segmentation and clumping techniques to boost the spatial coherency and homogeneity of the final mapping. In Fig. 1, the inundation map of the Tanaro River between the cities of Asti and Alessandria showing both the omission and the commission errors when compared to ground truth data is shown.

Fig. 2.

Original signal (line) and noisy samples (dot) randomly extracted.

IV. D ATA I NTERPOLATION In engineering practice, data collected from the field are usually discrete. To estimate the outcomes and, eventually, to have a better understanding of the physical phenomenon, a more analytically controllable and continuous function that fits the field data is desirable. The process of finding the coefficients for the fitting function is called curve fitting, and the process of estimating the outcomes in between sampled data points is called data interpolation. For optimizing the mapping of the flood water depth [10], different interpolators were first tested on a 1-D synthetic dataset, evaluating their performances and the quality of results in generalization capabilities. Testing data were generated by sampling a signal with different rates of variation, trying to simulate the complex frequency structure of real phenomena. In particular, a set of randomly scattered data was extracted from a composed function with an added noise (1), simulating an SNR one order of magnitude smaller than the respective SNR of midresolution satellite images or cartographic DTMs y = sen(20x) +

ex 3

σnoise = 0.085 SNR ∼ = 25 D = [0, π].

(1)

Starting from a noisy sample of 50 elements randomly extracted along the dominion D (Fig. 2), different interpolators were examined in the reconstruction of the original signal of (1): 1) linear regression (LR); 2) polynomial regression; 3) spline interpolation; and 4) composed spline interpolation. As shown in Fig. 3, the resulting interpolated function performed differently depending upon the interpolating function used, and the best results were achieved using composed splines (RMSE = 0.46). A. Cubic Spline Interpolation Spline interpolation is a data interpolation technique based on piecewise polynomials placed over the dominion of interpolation D as kernel functions, while the relative coefficients are

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lating function was used [31]. Thus, the Tychonov regularization function used in (4) had the following form: K(b) = bT Kb

(5)

where K is a square matrix (m × m) containing the secondorder derivatives of the function to be regularized in each grid knot. B. Bicubic Spline Interpolation

Fig. 3. Reconstruction of the original signal from the noisy samples using the following: LR, polynomial regression, spline interpolation, and composed spline interpolation.

to be calculated with a least squares approach [27], [28]. In a 1-D discrete problem (such as the one described in Fig. 3), the observation equation is as follows: f (xm ) =



bl s∆,l (xm − τl ) + νm

(2)

l

where f (xm ) observed sample value; s∆,l (xm − τl ) = s∆,l (xm ) function determining a translation of the compact support which centers the spline at the generic knot τl ; spline coefficient at the generic knot τl ; bl l knot grid index; ∆ grid step; and the cubic spline s∆ (x) reads as follows:  (4∆+x)3   96 ,    (4∆+x)3 −4(2∆+x)3 s∆ (x) =

96

x ∈ [−4∆, −2∆] ,

(4∆−x) −4(2∆−x)  ,  96    (4∆−x)3 , 96 3

3

x ∈ [−2∆, 0] x ∈ [0, 2∆]

(3)

x ∈ [2∆, 4∆].

The least squares computation of the optimal coefficients for (2) and (3) was done by using the Tychonov regularization: a general approach used to face singularities in the normal matrix and to assure the uniqueness of the least squares solution, even in the presence of irregularly girded data and empty regions over the dominion of interpolation [29]–[31]. The regularized estimator for the b coefficients was therefore obtained by minimizing the linear and nonnegative function   ˆ |2 + µK (b) MinΨ(b) = Min |Y 0 − Y

To process a 2-D discrete field (such as the flood water depth), we must consider more than a single dimension. Referring to the 2-D problem, for the positive quadrant, the bicubic spline form s∆ (x, y) is described as   x ∈ [0, 2∆]   ϕ33 (x, y)     y ∈ [0, 2∆]      ϕ43 (x, y) x ∈ [2∆, 4∆]   y ∈ [0, 2∆] (6) s∆ (x, y) =  x ∈ [0, 2∆]   ϕ (x, y) 34     y ∈ [2∆, 4∆]    x ∈ [2∆, 4∆]   ϕ44 (x, y) y ∈ [2∆, 4∆] where (4∆ − x)3 − 4(2∆ − x)3 (4∆ − y)3 − 4(2∆ − y)3 96 96 (4∆ − x)3 (4∆ − y)3 − 4(2∆ − y)3 = 96 96 (4∆ − x)3 − 4(2∆ − x)3 (4∆ − y)3 = 96 96 (4∆ − x)3 (4∆ − y)3 (7) = 96 96

ϕ33 = ϕ43 ϕ34 ϕ44

and for symmetry, (6) is extended to the other quadrants [31]. A 2-D field can be modeled through composed interpolation, starting from the decomposition of the original field into two components, as described in f (xm , yn ) = h(xm , yn ) + νm,n where f (xm , yn ) observed value; h(xm , yn ) approximated field; overall residual; νm,n m, n knot index. Thus, the field to be interpolated is then decomposed in h(xm , yn ) = T (xm , yn ) + L(xm , yn )

(4)

where |Y0 − Yˆ | usual least squares minimizing function; regularizing positive function; K(b) µ regularization parameter. Different regularization techniques exist. A second derivative regularization that minimized the curvature of the final interpo-

(8)

where T (xm , yn )

L(xm , yn )

(9)

trend component of the field (large scale varying) usually modeled with polynomial fitting and least squares estimation; = h(xm , yn ) − T (xm , yn ) local component (small scale varying) calculated as residual part of the original field once removed the estimated trend.

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Following the above principles, composed bicubic spline interpolator [32] implements two subsequent steps of interpolation, which are performed as a cascade algorithm. The first step is the removal of a regional trend component of the field, which is the term T (xm , yn ) in (9), through a classic polynomial regression and least squares estimation. The second step is the modeling of the residuals, which is the term L(xm , yn ) in (9), derived from detrending of the original sampled field, through bicubic splines and Tychonov regularization. V. W ATER D EPTH C OMPUTATION Using the flood extension map produced with the Landsat images (Fig. 1), the maximum depths reached by the water during the event were estimated by means of interpolating the water level gathered at the border of the flooded area (with a spatial density of 0.7 points/km2 ). Along the borderline separating the flooded and nonflooded areas, a set of randomly collected water depths were collected on both sides of the river valley through the superimposition of the DTM over the flood map and considering the terrain elevation at the border as coincident with the maximum level reached by the flooding waters [10]. As described in the 1-D problem, the randomly collected data were interpolated to derive the surface approximating the peak water depth using the following functions. 1) LR: direct approximation of the water depth with a plane surface T (xm , yn ) = a0 + a1 x + a2 y L(xm , yn ) = 0

(10)

where aj are the parameters of the polynomial regression to be estimated (j = 0, 1, 2). 2) Third-order polynomial regression (P3R): direct approximation of water depth with a third-order polynomial surface T (xm , yn ) = a0 + a1 x + a2 y + a3 xy + a4 x2 + a5 y 2 + a6 x2 y + a7 xy 2 + a8 x3 + a9 y 3 L(xm , yn ) = 0 (11) where aj are the parameters of the polynomial regression to be estimated (j = 0, 1, . . . , 9). 3) Composed spline interpolation (SP2): detrending with second order polynomial regression and modeling of the residuals through bicubic splines T (x, y) = a0 + a1 x + a2 y + a3 xy + a4 x2 + a5 y 2  L(xm , yn ) = bp,q s∆,p,q (xm , yn ) (12) p,q

where aj bp,q m×n

parameters of the polynomial regression to be estimated (j = 0, 1, . . . , 5); spline coefficients to be estimated; total number of splines.

Fig. 4. Water depth estimation using second-order composed spline interpolation (SP2).

Spline interpolation based on (6) and Tychonov regularization on the second derivative were performed with the following parameters: a) regularization parameter µ = 0.5; b) low spatial density: Mean mutual distance [∆ value in (6) and (7)] among radial basis function centers of about 1000 m (p × q = 416 splines functions over the dominion). 4) Composed spline interpolation (SP3): detrending with third order polynomial regression and modeling of the residuals through bicubic splines: T (x, y) = a0 + a1 x + a2 y + a3 xy + a4 x2 + a5 y 2 + a6 x2 y + a7 xy 2 + a8 x3 + a9 y 3  L(xm , yn ) = bp,q s∆,p,q (xm , yn )

(13)

p,q

where aj

parameters of the polynomial regression to be estimated (j = 0, 1, . . . , 9); spline coefficients to be estimated; bp,q m × n total number of splines. Spline interpolation based on (6) and Tychonov regularization on the second derivative were performed with the following parameters: a) regularization parameter µ = 0.1; b) medium spatial density: mean mutual distance [∆ value in (6) and (7)] among radial basis function centers of about 500 m (p × q = 1581 spline functions over the dominion). Fig. 4 shows the results for the second order composed spline interpolation. VI. R ESULTS AND D ISCUSSION The mapping accuracy of the STMNF-based classification (Fig. 1) was tested using as ground truth data an inundation map supplied by the Cartographic Office of Piemonte Regional Government and produced using aerial photos and ground surveys. The confusion matrix is shown in Table I. The STMNF method allowed to establish an overall accuracy of 97.09% with a kappa coefficient of 0.889, obtaining a user

GIANINETTO AND VILLA: FLOOD ASSESSMENT USING NOISE FRACTION AND SPLINE INTERPOLATION

TABLE I FLOOD MAPPING USING STMNF CONFUSION MATRIX BASED ON AVAILABLE GROUND MEASUREMENTS SUPPLIED BY THE CARTOGRAPHIC OFFICE OF THE PIEMONTE REGION GOVERNMENT, ITALY

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TABLE II WATER DEPTH COMPUTATION. ACCURACY OBTAINED BY USING DIFFERENT INTERPOLATION FUNCTIONS. (LR = LINEAR REGRESSION P3R = THIRD-ORDER POLYNOMIAL REGRESSION; SP2 = SECOND-ORDER COMPOSED SPLINE INTERPOLATION; AND SP3 = THIRD-ORDER COMPOSED SPLINE INTERPOLATION)

TABLE III WATER VOLUME ESTIMATION. ACCURACY OBTAINED BY USING DIFFERENT INTERPOLATION FUNCTIONS. (LR = LINEAR REGRESSION P3R = THIRD-ORDER POLYNOMIAL REGRESSION; SP2 = SECOND-ORDER COMPOSED SPLINE INTERPOLATION; AND SP3 = THIRD-ORDER COMPOSED SPLINE INTERPOLATION)

Fig. 5. Flood mapping comparison between STPCA and STMNF-based classifications showing commission and omission errors.

accuracy of 85.76% and a producer accuracy of 95.96%. The very low omission error (4.04%) showed that all the inundated areas were correctly mapped, with an overestimation outlined by the commission error (14.24%). The advantage of using the method here described instead of the STPCA-based method [10] is actually in terms of commission error. Fig. 5 shows the comparison of commission errors for both the STMNF and STPCA-based methodologies: Both the mapping have limited omission errors, while the commission error is greater for the STPCA mapping method. Regarding the water depth computation, results were tested using as ground truth the data in situ hydrometric levels measured during the days subsequent to the flood, which are again supplied by the Cartographic Office of Piemonte Regional Government. All the parameters computed (RMSE, absolute standard deviation, negative values, estimated total water volume, and volume overestimation) showed that the best results were obtained using the bicubic spline interpolator. In Table II, the statistics for the water depth maps are shown: the rmse and the standard deviation σ for the absolute residuals were computed from 55 ground control points with known peak water depths (derived from the local surveys), while the negative values (modeling errors) were computed with respect to the flood map of Fig. 1. Looking at Table II, it is evident that the poor fitting of data (RMSE = 1.456 m) for the LR, both the third-order polynomial regression (P3R) and the third-order composed

splines (SP3) performed similarly (RMSE = 0.958 m for P3R, and RMSE = 0.922 m for SP3) while the second order composed splines (SP2) showed the best performance (RMSE = 0.794 m). This behavior is confirmed by the smaller absolute standard deviation for SP2 (σ = 0.562 m), compared to LR (σ = 1.099 m), P3R (σ = 0.737 m), and SP3 (σ = 0.694 m). Water depth negative values represent modeling errors. As shown in Fig. 4 for the SP2 interpolation, negative values were primarily gathered at the classification borders, thus not representing a serious problem for the flood assessment. Again, SP2 minimized this kind of errors (see Table II). Finally, Table III shows the computed total volumes of water and sediments carried by the flooding on the basis of the flood map of Fig. 1, of the water depth estimations (such as that shown in Fig. 4 for SP2), using the DTM. On a regional scale, when comparing the esteemed total volumes derived with the LR (183.66 × 106 m3 ), the P3R (180.29 × 106 m3 ), the SP2 (155.87 × 106 m3 ), and the SP3 (175.31 × 106 m3 ) methods, with the esteemed total volume derived from the ground surveys and in situ measures (129.64 × 106 m3 ), again, the second order composed splines performed better, with an overall agreement with reference data of about 83%. Regarding the overall computational complexity of each method, they can be ranked in terms of number of parameters to be estimated. 1) The simplest method is the LR. The LR needs the computation of three parameters (three aj coefficients), but the model performed poorly on the data.

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2) The P3R model needs the computation of ten parameters (ten aj coefficients). This model performed better than the simple LR. 3) The SP2 model needs the computation of 422 parameters (6 aj coefficients + 416 spline functions). This model showed the best performance on the data. 4) SP3 model needs the computation of 1681 parameters (10 aj coefficients + 1581 spline functions). This model showed on the data a performance comparable to the simplest P3R model but with a higher overall computational complexity. VII. C ONCLUSION The method presented here has proved to be very effective in deriving inundation maps and water depths. This makes the methodology a useful tool for precisely defining the flood extension, for obtaining an accurate chart of the peak level reached by waters during the flood, and finally, for assessing flood damages. The use of the STMNF instead of the STPCA and the use of a second order polynomial regression for regional component with a loose bicubic spline interpolation with Tychonov regularization for local part, instead of a simpler second order polynomial regression, lead to an increment in the overall accuracy of the flood mapping. Enrichment with GIS datasets of local infrastructures (e.g., linear and punctual infrastructures) and land use could help during the postflood decisional phase, resulting in a rapid response method of analysis and a decision-support tool for governments, local administrative units, and also insurance companies. ACKNOWLEDGMENT The authors would like to thank the Italian National Research Council (CNR-IREA, Milano) for supplying the Landsat-7/ ETM+ image taken over Piemonte, Italy, on April 24, 2003 (path 194, row 28/29) that was used for georeferencing the Landsat TM-5/images and the Cartographic Office of Piemonte Regional Government for supplying the DTM of the Tanaro basin and the in situ ground truth data. The authors would also like to thank Dr. M. Reguzzoni (Politecnico di Milano University–Polo Regionale di Como) for supplying the software (GeoSPLINTER v.1.0) used for the spline interpolation. R EFERENCES [1] S. N. Jonkman, “Global perspectives on loss of human life caused by floods,” Nat. Hazards, vol. 34, no. 2, pp. 151–175, 2005, Hanover, New Hampshire. [2] G. R. Brakenridge, Dartmouth Flood Observatory, Hanover, New Hampshire, 2006. [3] European Environment Agency, EEA Briefing 01/2005, EU, Climate change and river flooding in Europe, p. 4, 2005. [Online]. Available: http://reports.eea.europa.eu/briefing_2005_1/en/tab_content_RLR [4] Impacts of Europe’s Changing Climate: An Indicator Based Assessment, Eur. Environ. Agency, Luxembourg, 2004. [5] Université Catholique de Louvain, Brussels, Belgium, EM-DAT: The OFDA/CRED International Disaster Database. [Online]. Available: http://www.em-dat.net [6] European Commission, Brussels, Belgium, Press Release IP/03/1381, 2003.

[7] F. Guzzetti, “Landslide fatalities and the evaluation of landslide risk in Italy,” Eng. Geol., vol. 58, no. 2, pp. 89–107, 2000. [8] H. Bach, F. Appel, K. Fellah, and P. de Fraipont, “Application of flood monitoring from satellite for insurances,” in Proc. IEEE Int. Geosci. and Remote Sens. Symp., Seoul, Korea, 2005, CD-ROM. [9] M. Gianinetto and P. Villa, “Monsoon flooding response: A multiscale approach to water-extent change detection,” in Proc. Int. Archive Photogrammetry, Remote Sens. and Spatial Inf. Sci., Enschede, The Netherlands, 2006, CD-ROM. [10] M. Gianinetto, P. Villa, and G. Lechi, “Post-flood damage evaluation using Landsat TM and ETM+ data integrated with DEM,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 1, pp. 236–243, Jan. 2006. [11] Y. Wang, J. D. Colby, and K. A. Mulcahy, “An efficient method for mapping flood extent in a coastal flood plain using Landsat TM and DEM data,” Int. J. Remote Sens., vol. 23, no. 18, pp. 3681–3696, 2002. [12] S. Ali, A. Hassan, T. C. Martin, and Q. K. Hassan, “Geospatial tools for monitoring flood plain water dynamics,” in Remote Sensing and Hydrology 2000, M. Owe, K. Brubaker, J. Ritchie, and A. Rango, Eds. Oxford, U.K.: IAHS, 2001. [13] P. A. Brivio, R. Colombo, M. Maggi, and R. Tomasoni, “Integration of remote sensing data and GIS for accurate mapping of flooded areas,” Int. J. Remote Sens., vol. 23, no. 3, pp. 429–441, 2002. [14] A. S. Dhakal, T. Amda, M. Aniya, and R. R. Sharma, “Detection of areas associated with flood and erosion caused by a heavy rainfall using multi temporal Landsat TM data,” Photogramm. Eng. Remote Sens., vol. 68, no. 3, pp. 233–239, 2002. [15] M. M. Islam and K. Sadu, “Satellite remote sensing data analysis for flood damaged zoning with GIS for flood management,” J. Hydraul. Eng., vol. 44, pp. 301–306, 2000. [16] W. Quan, M. Watanabe, S. Hayashi, and S. Murakami, “Using NOAA AVHRR data to assess flood damage in China,” Environ. Monit. Assess., vol. 82, no. 2, pp. 119–148, Mar. 2003. [17] J. Sanyal and X. X. Lu, “Application of remote sensing in flood management with special reference to monsoon Asia: A review,” Nat. Hazards, vol. 33, no. 2, pp. 283–301, Oct. 2004. [18] L. C. Smith, “Satellite remote sensing of river inundation area, stage and discharge: A review,” Hydrol. Process., vol. 11, no. 10, pp. 1427–1439, 1997. [19] L. Jianping and Z. Bai, “A GIS-based study on the model for evaluation of direct submerging damage of flood disaster,” in Proc. IEEE Int. Geosci. and Remote Sens. Symp., Seoul, Korea, 2005, pp. 1807–1810, CD-ROM. [20] P. Villa and M. Gianinetto, “Multispectral transform and spline interpolation for mapping flood damages,” in Proc. IEEE Int. Geosci. and Remote Sens. Symp., Denver, CO, 2006, pp. 275–278, CD-ROM. [21] P. Villa and M. Gianinetto, “Inundated area delineation using MODIS data: Towards a global scale geo-database of flood events,” in Proc. Int. Archive Photogrammetry, Remote Sens. and Spatial Inf. Sci., Goa, India, CD-ROM. [22] M. W. Matthew, S. M. Adler-Golden, A. Berk, S. C. Richtsmeier, R. Y. Levine, L. S. Bernstein, P. K. Acharya, G. P. Anderson, G. W. Felde, M. P. Hoke, A. Ratkowski, H. Burke, R. D. Kaiser, and D. P. Miller, “Status of atmospheric correction using a MODTRAN4based algorithm,” in Proc. SPIE Algorithms Multispectral, Hyperspectral, and Ultraspectral Imagery VI, 2000, vol. 4049, pp. 199–207. [23] A. Berk, G. P. Anderson, L. S. Bernstein, P. K. Acharya, H. Dothe, M. W. Matthew, S. M. Adler-Golden, J. H. Chetwynd, Jr., S. C. Richtsmeier, B. Pukall, C. L. Allred, L. S. Jeong, and M. L. Hoke, “MODTRAN4 radiative transfer modeling for atmospheric correction,” in Proc. SPIE, Opt. Spectroscopic Techn. and Instrum. Atmospheric and Space Res. III, 1999, vol. 3756, pp. 348–353. [24] A. A. Green, M. Berman, P. Switzer, and M. D. Craig, “A transformation for ordering multispectral data in terms of image quality with implications for noise removal,” IEEE Trans. Geosci. Remote Sens., vol. 26, no. 1, pp. 65–74, Jan. 1988. [25] T. M. Tu, H. C. Shyu, Y. S. Sun, and C. H. Lee, “Determination of data dimensionality in hyperspectral imagery—PNAPCA,” Multidimens. Syst. Signal Process., vol. 10, no. 3, pp. 255–273, Jul. 1999. [26] R. A. Schowengerdt, Remote Sensing-Models and Methods for Image Processing, 2nd ed. New York: Academic, 1997. [27] J. H. Ahlberg, E. N. Nilson, and J. L. Walsh, The Theory of Splines and Their Applications. New York: Academic, 1967. [28] M. Unser, “Splines: A perfect fit for signal and image processing,” IEEE Signal Process. Mag., vol. 16, no. 6, pp. 22–38, Nov. 1999. [29] H. Mitasova and L. Mitàs, “Interpolation by regularized spline with tension: I. Theory and implementation,” Math. Geol., vol. 25, no. 6, pp. 641–655, 1993.

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Marco Gianinetto (M’07) received the Laurea (M.S.) degree in environmental engineering and the Ph.D. degree in geodesy and geomatics (summa cum laude) from Politecnico di Milano University, Milano, Italy, in 2000 and 2006, respectively. From 2001 to 2002, he was Research Assistant at the Italian National Research Council (CNR-Istituto per il Rilevamento Elettromagnetico dell’Ambiente), Milano, working on Italian Space Agency’s research contract. From 2002, he is Research Fellow at the Dipartimento di Ingegneria Idraulica, Ambientale, Infrastrutture Viarie, Rilevamento (DIIAR) Department, Politecnico di Milano University. From 2004 to 2005, he was Contract Professor of Geographic Information Systems (GIS) and Remote Sensing at the Politecnico di Milano University–Polo Regionale di Lecco, Lecco, Italy, and he is currently Adjunct Professor of GIS and remote sensing with Remote Sensing Laboratory, DIIAR Department, Politecnico di Milano University. His main research activity is in the area of multispectral remote sensing, hyperspectral remote sensing, and high-resolution satellite’s data processing (analysis of multitemporal data, data fusion, natural hazards and disaster assessment, urban mapping, image registration and rectification, algorithm development, image classification, multitemporal analysis and change detection, accuracy assessment, sensor calibration, sensor validation and verification, and feature extraction). He conducts research on these topics within the frameworks of several national and international projects. He is the author (or coauthor) of more than 40 technical publications in Information and Communication Technology (I&CT) and the author (or coauthor) of more than 35 scientific publications in remote sensing, including journals, book chapters, and conference proceedings. He is a Referee for Remote Sensing of Environment, International Journal of Remote Sensing, ISPRS Journal of Photogrammetry and Remote Sensing, Photogrammetric Engineering and Remote Sensing, Journal of Imaging Science and Technology, Computers & Geosciences and committee member of many international conferences. He was Remote Sensing Scientist (cultore) at the First Faculty of Architecture, Politecnico di Milano University, from 2001 to 2003. He is Coinvestigator in the Cartosat-1 Scientific Assessment Programme for the Department of Space of the Government of India and Research Group Leader for Politecnico di Milano University. Since December 2006, he is Associate Editor of the Journal of Applied Remote Sensing and since April 2007 he is Associate Editor of the International Journal of Navigation and Observation. Dr. Gianinetto was awarded the Young Researcher Award from Politecnico di Milano University in 2006. He is member of the scientific team involved in the Canadian/Italian Joint Hyperspectral Mission planning. Since 2004, he is a member of the Scientific Committee of the Italian Journal of Remote Sensing. He is member of the experts board for Regione Lombardia Government within the Ingenio Program for supporting research, enterprise creation, and technological transfer. He is a member of the International Society for Photogrammetry and Remote Sensing, of the American Society for Photogrammetry and Remote Sensing, of the IEEE Geoscience and Remote Sensing Society, of the Remote Sensing and Photogrammetry Society, of the Italian Association for Remote Sensing (AIT), and of the Italian Society for Photogrammetry and Topography (SIFET).

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Paolo Villa (S’06) received the Laurea (M.S.) degree in environmental engineering (magna cum laude) from Politecnico di Milano University, Milano, Italy, in 2004, where he is currently working toward the Ph.D. degree in geomatics. From 2004 to 2006, he was with the Remote Sensing Laboratory, Dipartimento di Ingegneria Idraulica, Ambientale, Infrastrutture Viarie, Rilevamento (DIIAR) Department, Politecnico di Milano University, working in the area of change detection with midresolution satellite data for urban and flood monitoring studies. He recently began working with the Italian National Research Council-Institute for Electromagnetic Sensing of the Environment (CNR-Istituto per il Rilevamento Elettromagnetico dell’Ambiente), Milano, where he joined the special interest group of geoinformation, participating in European projects dealing with the preparation and implementation phase of a European Spatial Data Infrastructure (ESDI) and Global Monitoring for Environment and Security (GMES) program.

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