Hyperspectral Remote Sensing of Total Phosphorus (TP) in Three Central Indiana Water Supply Reservoirs

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1 Water Air Soil Pollut (212) 223: DOI 1.17/s Hyperspectral Remote Sensing of Total Phosphorus (TP) in Three Central Indiana Water Supply Reservoirs Kaishan Song & Lin Li & Shuai Li & Lenore Tedesco & Bob Hall & Linhai Li Received: 11 May 211 / Accepted: 15 September 211 / Published online: 1 October 211 # Springer Science+Business Media B.V. 211 Abstract The connection between nutrient input and algal blooms for inland water productivity is well known but not the spatial pattern of water nutrient loading and algae concentration. Remote sensing provides an effective tool to monitor nutrient abundances via the association with algae concentration. Twenty-one field campaigns have been conducted with samples collected under a diverse range of algal bloom conditions for three central Indiana drinking water bodies, e.g., Eagle Creek Reservoir (ECR), Geist Reservoir (GR), and Morse Reservoir (MR) in 25, 26, and 28, which are strongly influenced anthropogenic activities. Total phosphorus (TP) was estimated through hyperspectral remote sensing due to its close association with chlorophyll a (Chl-a), total suspended matter, Secchi disk transparency (SDT), and turbidity. Correlation analysis was performed to determine K. Song (*) : L. Li : S. Li : L. Tedesco : B. Hall : L. Li Department of Earth Sciences, Indiana University Purdue University, Indianapolis, IN, USA kaissong@iupui.edu K. Song Northeast Institute of Geography and Agricultural Ecology, CAS, Changchun, China L. Tedesco : B. Hall Center for Earth and Environmental Sciences, Indiana University Purdue University, Indianapolis, IN, USA sensitive spectral variables for TP, Chl-a, and SDT. A hybrid model combining genetic algorithms and partial least square (GA-PLS) was established for remote estimation of TP, Chl-a, and SDT with selected sensitive spectral variables. The result indicates that TP has close association with diagnostic spectral variables with R 2 ranging from.55 to.72. However, GA-PLS has better performance with an average R 2 of.87 for aggregated dataset. GA-PLS was applied to the airborne imaging data (AISA) to map spatial distribution of TP, Chl-a, and SDT for MR and GR. The eutrophic status was evaluated with Carlson trophic state index using TP, Chl-a, and SDT maps derived from AISA images. Mapping results indicated that most MR belongs to mesotrophic (48.6%) and eutrophic (32.7%), while the situation was more severe for GR with 57.8% belongs to eutrophic class, and more than 4% to hypereutrophic class due to the high turbidity resulting from dredging practices. Keywords Chl-a. GA-PLS. Hyperspectral. SDT. Total phosphorus. Trophic state index 1 Introduction Human activities can strongly influence light and nutrient availability, sedimentation, disturbance frequency in lake ecosystems (Lawson 1972; Wetzel 21), and ultimately the structure and function of primary producer communities (Malmqvist and Rundle

2 1482 Water Air Soil Pollut (212) 223: ). Because nitrogen (N), phosphorus (P), or light commonly determine the growth of inland water algae, elevated levels of these nutrients, and energy resources often result in nuisance algal blooms (Borchardt 1996). Routine methods for analyzing the relationship between nutrients input to algae blooms or inland water productivity have been well documented through field sampling and laboratory analyses (Vollenweider 1976; Paerl and Huisman 28). Nevertheless, these traditional approaches are ill-suited for monitoring a large number of water bodies at a regional or national scale due to the patchy distribution of nutrients, algal blooms, and total suspended matter (Dekker et al. 1991; Poor 21). Remote sensing provides an effective tool to monitor the algae abundance and its association with corresponding nutrients (Hans et al. 22). Remote estimation for total phosphorus (TP) has been investigated due to its high correlation with optically active constituents (Kutser et al. 1995; Wang et al. 24; Wu et al. 21). Chlorophyll a (Chl-a) is a photosynthetic pigment that is found in all plants, including algae (Wetzel 21). Its concentration is commonly used to represent the density of the algal population in water bodies and productivity (Edmondson 197). The response of average Chl-a concentration to reduced phosphorus loading is well documented in individual lakes (Smith 1982; Malve and Qian 26) and is consistent with positive relationship between Chl-a and TP concentration among lakes (Healey and Hendzel 1979; Busse et al. 26; Liu et al. 21). Recent studies indicate that phosphorus may also determine the Chl-a concentration of tidal lakes, estuaries, and near-shore coastal waters (Meeuwig et al. 2; Hoyer et al. 22; Smith 23). Total suspended matter (TSM) refers to organic and inorganic material suspended in the water column, including mineral particles of terrigenous origin, plankton, detritus (from the decomposition of phytoplankton and zooplankton cells), and particles of anthropogenic origin (Bukata et al. 1995). For case-ii waters, TSM is often related to total primary production, heavy metal fluxes and micro-pollutants. In many turbid waters, TSM is directly tied to sediment transport problems (Fettweis et al. 26) and to the available light for primary production (Ebenhoeh et al. 1997; Doxaran et al. 26). Like Chl-a, TSM is spatially heterogeneous, thus a synoptic view of TSM concentration is difficult to obtain at a regular basis merely using in situ monitoring network. An optimal mapping approach is the combination of remote sensing, in situ measurements, and water quality modeling (Han and Rundquist 1997; Song et al. 211). It has been recognized that nonpoint resources pollution is the major TP source in aquatic system, and generally TP loading was highly correlated with sediment loading (Wang et al. 29). According to Sulliwan et al. (25), there was a general relationship between TP and discharge which is associated with watershed scale and storm events. Water clarity, or transparency, commonly reflected by Secchi disk transparency (SDT) is reduced by the presence of suspended sediment, bits of organic matter, free-floating algae, and zooplankton (Carlson 1977). The accelerated production of algae in a lake is generally the result of excess nutrients, in particular, phosphorus (Busse et al. 26; Paerl and Huisman 28). The depth to which light can penetrate a lake diminishes with more algae and suspended inorganic matter in a lake (Fuller et al. 24). Therefore, SDT, relating to the free-floating algae concentration or noalgal particles in a lake, is often used as a trophic state indicator (Carlson 1977). As aforementioned, TP is closely related to Chl-a concentration, and TSM usually acts as a carrier for TP loading, thus, TP is also closely related to SDT with an exponential equation which is consistent with Carlson s finding (Carlson 1977). Spectral characteristics of phytoplankton and TSM provide a physical basis to quantify the concentrations of these optically active components (OACs) through the use of remote sensing techniques. Furthermore, some water quality parameters that are not directly related to upwelling spectral signals can also be retrieved from remotely sensed data, such as SDT and turbidity because of their close correlation with TSM and phytoplankton (Gitelson 1992; Thiemann and Kaufmann 22). As mentioned above, TP closely relates to phytoplankton (Carlson 1977; Busse et al. 26), TSM, and SDT (Usitalo et al. 2), which set a basis to remotely monitor TP dynamics (Hoyer et al. 22). Multispectral Landsat TM data have been applied to map the TP spatial pattern (Kutser et al. 1995; Wang et al. 24; Wu et al. 21); hyperspectral remote sensing provides more potential to detect material diagnostic spectral band(s) which has not been fully applied for mapping TP concentration distribution. The objectives of this study are to (1) determine optimal relationships of TP concentration with either

3 Water Air Soil Pollut (212) 223: in situ collected spectra or airborne hyperspectral (airborne imaging spectrometer for applications (AISA)) image spectra using the genetic algorithm - partial least square modeling approach (GA-PLS); (2) examine optically active compounds of inland waters that govern the relationships between TP concentrations and remotely sensed data; (3) analyze the spatial correlation of TP to Chl-a, TSM concentration, and water physical parameters, e.g., turbidity and SDT; and (4) derive Carlson Trophic Index from AISA imaging data-derived TP, Chl-a, and SDT for assessing water trophic state spatially over Morse Reservoir (MR) and Geist Reservoir (GR). 2 Material and Methods 2.1 Study Area Eagle Creek Reservoir (ECR; W , N ; surface area (A)=5. km 2 ; average depth (Z) =4.2 m), MR (W , N ; A= 6. km 2 ; Z=4.7 m) and GR (W , N ; A=7.5 km 2 ; Z=3.2 m) are the major drinking and recreational water systems supplying potable water for over 9, residents of the Indianapolis Metropolitan region, Indiana (Fig. 1, Table 1). ECR is fed by a 42-km 2 watershed dominated by agricultural (6.1%) with some subwatersheds transitioning to suburban development (Tedesco et al. 25). MR is fed by the 554 km 2 Cicero Creek watershed, where 76.9% of land use is agricultural (Tedesco et al. 25). GR is fed by the 567-km 2 Fall Creek watershed (Tedesco et al. 25) with more than 6% of agricultural practice; dredging practice has been carried out since 25 to remove bottom sediments which are rich in nutrients, e.g., TP and TN. The water quality of these reservoirs is impaired due to high nutrient concentrations (mean TP=96 1 μg/l, mean TN= mg/l) and the occurrence of nuisance algal blooms every summer (Li et al. 26). Indiana Department of Environmental Management (IDEM) has classified three reservoirs as mesotrophic to eutrophic (Indiana Department of Environmental Management IDEM 22). 2.2 In Situ Data Collection Field campaigns were carried out from 6 September 25 to November 28, of which the in situ measurement on 6 September 25 was concurrent with airborne ASIA imagery data acquisition. Samples were taken under a diverse range of algal bloom conditions. In situ water quality parameters were collected with a YSI 6 XLM multiparameter probe (YSI Inc., Yellow Springs, OH) including temperature (degrees Centigrade), turbidity, electricity conductivity (millisiemens), salinity (milligrams per liter), DO (percent and milligrams per liter), and ph value. The spatial coordinates for each sampling station was recorded using a Trimble Pro- Fig. 1 Study area location for three reservoirs in Midwest of USA

4 1484 Water Air Soil Pollut (212) 223: Table 1 Descriptive characteristic of three reservoirs located in Indiana, USA Reservoir Eagle Creek Geist Morse Units Date of service Surface area km 2 Volume million m 3 Mean depth m Residence time days Watershed area km 2 Mean total P μg/l Mean total N Mg/L Percent agriculture in watershed XRS (Trimble Navigation, Inc., Sunnyvale, CA) global positional system (GPS), and water clarity was estimated using a Secchi disk. Surface water grab samples were collected at each location at three layers approximately.25,.5, and 1. m below the water surface. Samples collected were analyzed for TP, TN, Chl-a, and TSM at Indiana University Purdue University Indianapolis (Randolph et al. 28). 2.3 In Situ Spectra Collection At each scheduled sampling station of the three reservoirs, in situ radiance spectra of these waters were collected using an ASD FieldSpec ultraviolet/ visible and near-infrared (ASD, Inc., Boulder, CO) or Ocean Optics USB4 visible and near infrared spectrometer (Ocean Optics, Inc., Dunedin, FL). The detailed measurement procedures for 25 and 26 datasets can be found in Randolph et al. (28). Remote sensing reflectance (R rs ; steradians (sr) per unit solid angle (sr 1 )) was obtained using the ratio of upwelling water-leaving radiance (L w ; watts per unit source area per unit solid angle (W m 2 sr 1 )) at a nadir viewing angle to the downwelling irradiance (E d ; watts per unit source area (W m 2 )): R rs ¼ L wð þ ; lþ E d ð þ ; lþ ð1þ where L w is derived from subtracting the total upwelling radiance (L up ) at 9 nm from L up for each wavelength from 35 to 9 nm; E d denotes downwelling irradiance measured at each sample site using a white reference panel (99% Lambertian reflector). Spectra for 28 was acquired using two intercalibrated dual-head USB4 Spectrometers using CDAP/CALMIT operating system developed by University of Nebraska at Lincoln, detailed procedures can be found in Gitelson et al. (28). Radiometer 1 connected with a cosine collector to measure incident irradiance E inc (l). Simultaneously, radiometer 2, equipped with a 25 field-of-view optical fiber, was used to measure the below-surface upward radiance, L up (l) at nadir at about 5 cm below the water surface. The inter-calibration of the instruments was accomplished by measuring simultaneously the upwelling radiance L cal (l) from a 25% gray Spectralon and the corresponding incident irradiance E cal (l). The remote sensing reflectance at nadir was computed as (Gitelson et al. 28): R rs ðlþ ¼ tfðlþl upe cal ðlþ n 2 pe inc ðlþl cal ðlþ R calðlþ ð2þ where t is the water-to-air transmittance equal to.98, F is spectral immersion factor (Ohde and Siegel 23); n is the refractive index of water relative to air equal to 1.33, and π is used to transform the irradiance reflectance R into remote sensing reflectance, R cal (l) is the reflectance of the Spectralon panel linearly interpolated to match band centers of radiometers. 2.4 Airborne Hyperspectral Image Image Acquisition Airborne hyperspectral imagery data were collected using an AISA-Eagle (Spectral Imaging Ltd. Oulu, Finland) sensor on board a Piper Saratoga airplane owned by the University of Nebraska, Lincoln (UNL). This airborne sensor has a programmable set-up, allowing the collection of data in up to 512

5 Water Air Soil Pollut (212) 223: discrete channels in spectral range of 4 1, nm. To account for the majority of the geometric distortion that occurs during image collection, a GPS unit (six satellites minimum) is used to collects x, y, and z data of the aircraft. To provide both radiance and atsensor reflectance products, downwelling irradiance is measured at the same time as image acquisition using a spectrometer pointing upward through the aircraft hull. For this study, the AISA-Eagle was set to collect the images with 62 bands in the spectral region of approximately nm with a bandwith of 7 8 nm. The instantaneous field of view of the sensor, across the track is 1 mrad, resulted in 1 m wide pixels and 1, m wide swath from an altitude of 1, m Image Preprocessing The entirety of GR and MR were covered with four and five swaths, respectively. The AISA image data were processed (normalized, registered, mosaicked, and calibrated) using ENVI 4.2 software (Environmental Research Systems, Inc.). Each swath of AISA image was georectified to a 23 aerial photograph of Marion and Hamilton counties (1 m resolution) in Indiana with the projection of Universal Transverse Mercator (UTM) Zone 16 North, WGS-1983 Datum. Ground control points were manually selected between the image swaths and the reference aerial photograph (Sengpiel 27). Because of the high spatial resolution of the images, it is not uncommon for the warp to be off by one or two pixels in some locations, and the final total root mean square errors (RMSEs) are within m. All the swaths over a specific reservoir were mosaicked, and portable field spectrometer (ASD) measurements from the sample locations were used for image calibration through the empirical line calibration technique (Lillesand et al. 23). These were matched by using the spatial coordinates for each sample site and associating each field measurement with a 3 3-m area of the AISA image. By doing this, the AISA image is converted from radiance into reflectance, and the effects of the atmosphere between the sensor and the ground are ideally removed, but most likely significantly minimized (Koponen et al. 22; Li et al. 21). 2.5 Laboratory Analysis Water Quality Parameters TP, total Kjehldahl nitrogen (TKN), Chl-a, TSM, and dissolved organic carbon (DOC) were analyzed at IUPUI laboratories following procedures recommended by the Environmental Protection Agency and American Public Health Association (APHA APHA/AWWA/ WEF 1998). All samples were run in duplicate. Chl-a The 15 to 2 ml of sample was filtered through 47-mm-diameter.45-micron-pore-size acetate filters. Extract was analyzed following the EPA Method 445. (EPA 1997). After a 1:5 or 1:1 dilution, pheophytin-corrected Chl-a was measured fluorometrically with a TD-7 Fluorometer (Turner Designs, Inc., Sunnyvale, CA, USA) equipped with a Daylight White Lamp and Chlorophyll Optical Kit (34 5 nm excitation filter and emission filter> 665 nm). The fluorometer was first calibrated with Chl-a from spinach standard (Sigma-Aldrich 1865). Total Phosphorus The samples were collected in 25- ml high-density polyethylene containers. Samples are preserved in the field with 2 ml of 12.5% H 2 SO 4 / 25 ml (1 ml of conc. H 2 SO 4 /L, ph<2) and stored at 4ºC. In the TP determination, the PO 4 reacts with ammonium molybdate in the presence of H 2 SO 4 to form a phosphomolybdenum complex. Potassium antimonyl tartrate and ascorbic acid are used to reduce the complex, forming a blue color which is proportional to the TP concentration. 2.6 Modeling Approaches This study mainly focused on TP estimation with both in situ collected spectra and airborne imaging spectrometer data. However, models for Chl-a and SDT were also established with AISA image spectra to map the spatial concentration of these two water quality parameters in order to assess the trophic status of MR and GR using Carlson Trophic Index (Carlson 1977). 2.7 Spectra Processing and Regressions Phosphorus does not directly present optically diagnostic signals in water leaving radiance for the water quality remote sensing spectral domain (4 9 nm), thus empirical modeling is considered the most applicable approach for the remote estimation of TP in water column (Triphathi and Patil 24; Wu et al. 21; Song et al. 211). Band ratio and derivative analysis are the major approaches for empirical or semi-empirical models to retrieve Chl-a, TSM, SDT,

6 1486 Water Air Soil Pollut (212) 223: and turbidity (Gitelson 1992; Gons 1999; Gitelson et al. 28) based on the absorption trough or scattering peak spectral region (Rundquist et al. 1996; Gons 1999). Correlation analysis was first performed between original reflectance, spectral derivative, and all band ratio combinations (25, pairs of band ratios) and TP, Chl-a, and SDT to select the diagnostic spectral variables. Generally, the most sensitive 3 spectral variables were selected from each of the correlation analysis for running the GA-PLS model, which were accomplished through a program written with Matlab R29 software package (Matlab Inc.). 2.8 GA-PLS Model GA-PLS was used for estimation of TP using in situ spectral data collected with portable spectrometers. Furthermore, TP, Chl-a, and water clarity (SDT) were estimated and mapped using AISA imagery data. GA- PLS combines genetic algorithms with partial least squares regression for spectroscopic analysis of material composition in which genetic algorithms are used for band selection and partial least square (PLS) links the selected bands to the compositional parameters Genetic Algorithm Description Genetic algorithm (GA) is well suitable for generating a subset of spectral variables and removing these which are insensitive to target parameters (Forrest 1993). In a simplified genetic algorithm, there are at least five components: encoding, population initialization, individual selection, crossover, and mutation (Gourvénec et al. 24). Input spectra will be encoded with binary data: zeros and ones as chromosomes (Fig. 2). GA needs a number of possible candidate solutions to start with, such as a first step, all sensitive spectral variables will be selected (S). Fitness of every chromosome will be evaluated using a predefined fitness function associated with material abundance (Y). Then, the fitness will be judged whether satisfies certain constraints. If satisfied, it outputs selected results; if not, chromosomes with better fit will be selected to survive. Then, from crossover and mutation, offspring will be generated (similar to combinations of bands). Fitness of every chromosome will be evaluated again and continue until fitness satisfies the predefined constraints. A subset of spectral related to water quality components will be obtained for further processing by PLS for concentration estimation Partial Least Square Regression Assuming that a system of interest is driven by a few factors or components, PLS determines a few eigenvectors of the explanatory variables such that the corresponding scores not only explain the variance of the explanatory variables but also have a high correlation to the response variables (Wold 1966). A simplified PLS model consists of two outer relations resulting from the eigenstructure decomposition of Fig. 2 Flow chart for GA- PLS model, the left diagram shows how GA processes spectral variables according to water quality parameters and the right diagram shows how PLS performs the regression according both spectral variables determined via GA and water quality parameters

7 Water Air Soil Pollut (212) 223: both the matrix containing explanatory variables (i.e., spectral bands, band ratio, or transformed spectra) and the matrix containing response variables (i.e., water quality parameters), and an inner relation that links the resultant score matrices from these two eigenstructure decompositions (Geladi and Kowalski 1986). The diagram in Fig. 2 shows these three relations, where both X (n m) and Y (n p) represent the explanatory and response variable matrices, respectively. The first outer relation is derived by applying principle component analysis to X, resulting in the score matrix T (n a) and the loading matrix P (m a) plus an error matrix E (n m). In a similar way, the second outer relation is derived by decomposing Y into the score matrix U (n a) and the loading matrix Q (p a) and the error term F (n p). The prime represents matrix transpose. The goal of PLS modeling is to minimize the norm of F while maximizing the covariance between X and Y by the inner relation. This inner relation is a multiple linear regression between U and T in which B is an n n regression coefficient matrix determined via least square minimization. The selection of the optimal number of PLS components (latent variables) is a key step to obtain a model with good predictive power. The cross-validation is performed on the calibration samples, a subset of all available samples, and the remaining are used as validation samples. During the cross-validation, the model is increased one PLS component until the prediction on the calibration samples shows that further PLS components do not improve predictive ability for concentration. In this leave-one-out cross-validation, a calibration PLS model was built using N 1 samples, and the abundance of the sample left out was then predicted (Li et al. 27). The prediction error sum of squares (PRESS) was used to derive the root-meansquare error of cross-validation (RMSECV) which can indicate how well the model predicts new samples. PRESS ¼ XN i¼1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PRESS k RMSECV ¼ N ^ 2 yi y i ð3þ ð4þ ^ where y i is the predicted value for the sample I; yi is measured value of the sample i, and k is the number of components used in a PLS model, and N denotes sample numbers GA-PLS Implementation The major risk of using GA is over-fitting because of too many latent variables (i.e., spectral variables). To minimize this risk, the program was set using the following features: (1) the parameters were set with the highest elitism with the method introduced by Leardi (2); (2) the model was set to be determined after 1 independent, short GA runs; and (3) each run s frequency for selection of the variables was set to be a weighted average between the frequency for selection of the variables in the starting run and the previous run. The fitness function with which the individuals are subject to evaluation is the percentage of predicted variance of a constituent abundance, defined as: (" # " #) X n ^ 2=n 1 y i y i = Xn ^ 2=k y i y i 1 i¼1 i¼1 ð5þ where n is the number of samples to be considered, k=n 1 in the case of cross-validation. The final model is picked via a stepwise regression, and the variables are selected in terms of their frequency. The result of GA-PLS modeling is evaluated based on the root mean square error in the dataset (RMSE). Root-mean-square error of prediction (RMSEP) is written as: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N ^ 2 u t yi y i i¼1 RMSEP ¼ N ^ where N, y i and yi are as defined above. 2.9 Model Assessment ð6þ In this study, samples from each dataset were divided into calibration (67%) and validation (33%) subsets. RMSE, relative RMSE (RMSE %), mean absolute error (MAE) are used to evaluate the model performance. Both MAE and RMSE indicate absolute estimation errors, but RMSE is more sensitive to

8 1488 Water Air Soil Pollut (212) 223: outliers, and thus, RMSE% is also calculated as a complimentary measure. The three parameters for model performance assessment are calculated as the following formulae: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P N ^ 2 u t y i yi i¼1 RMSE ¼ N MAE ¼ P N i¼1 ^ yi y i N and RMSE% ¼ 1 RMSE y ð7þ ð8þ where y denotes the average of measured value. In this study, the percent difference between predicted and measured TP was also calculated with the following equation. ^ y i yi " i ¼ y i 1 ð9þ where " i denotes the absolute percent of TP residuals. To further analyze the performance of the predicted values versus the observed values, two other model performance parameters were applied in this study (Miehle et al. 26; Williams 21): determination coefficient (R 2 ) and ratio of prediction to deviation (RPD). A detail definition and description about these two parameters can be found in Taylor (1997), and RPD is calculated as: RPD ¼ SDP h i ^ yi Þ 2 ^ 2=N yi = ðn 1Þ 1=2 P yi y i ð1þ where SDP is written as: n SDP ¼ X o ^ y 2 i ½ðy ^Þ2 1=2 i =NŠ=ðN 1ÞÞ ð11þ R 2 and RPD indicate strength of statistical correlation between measured and predicted values for various models applied in this study. According to (Williams 21), a model is accurate if R 2 and RPD values are higher than.91 and 2.5, respectively; it can be regarded good prediction when R 2 ranges between.82 and.9 and the RPD is higher than 2; and whereas an approximate prediction is regarded when R 2 lies between.66 and.81 with RPD higher than 1.5, it is generally regarded poor prediction when R 2 ranges between.5 and Water Trophic Assessment A numerical TSI for lakes was developed by Carlson (1977) which can be related to the trophic status classification scheme to group lakes into basic classes of oligotrophic (TSI value<38), mesotrophic (TSI value 38 48), eutrophic (TSI value 49 61), and hypereutrophic (TSI value>61). Carlson s TSI can be calculated from Chl-a, SDT, and TP concentration. The computational forms of the Eqs. 12, 13, and 14 are from Carlson (1977), and an average is taken to derive the final trophic state (Eq. 15) as follows: TSIðTPÞ ¼1 6 ln 48 =lnð2þ ð12þ TP TSIðChl aþ ¼1 6 TSIðSDTÞ ¼1 6 lnðsdtþ lnð2þ 2:4 :68lnðChl aþ lnð2þ ð13þ ð14þ TSIðaverageÞ ¼½TSIðTPÞþTSIðChl aþþtsiðsdtþš ð15þ Of the three measures to compute TSI, SDT, Chl-a, and TP concentration are quantifiable by means of remote sensing techniques and, more specifically, with airborne or satellite imagery (Hans et al. 22; Wu et al. 21) which facilitates mapping TSI for various waters. Any eutrophic status derived from SDT, Chl-a, or TP can be biased, and the averaged TSI can be more objective for assessing eutrophic status for inland waters (Duan et al. 28).

9 Water Air Soil Pollut (212) 223: Results and Discussion 3.1 Water Quality Characterization The concentrations of the major water quality parameters, e.g., Chl-a, TSM, SDT, TP, and TN for the combined dataset in 25 are shown in Table 2. It can be seen that the combined dataset shows a large range in TSM ( mg/l) and Chl-a ( μg/l) concentration. High concentrations of TSM and phytoplankton result in low water clarity (SDT, cm) and larger variation of turbidity ( NTU). TN concentration shows a relatively large variation ranging from.6 to 2.8 mg/l with average value of 1.7 mg/l. TP ranges from.23 to.2 mg/l with average values less than.8 mg/l. TP and TN concentrations are relatively high in the study waters indicating higher nutrients concentration available for the potential algal bloom. Datasets for 26 and 28 show similar trends for all parameters (see Table 2). For three datasets, optical active parameters, such as Chl-a and TSM show spatiotemporal variability. Chl-a concentration is low before June and late October and high in July and August, which is caused by nutrients availability, light, river discharge, and algal species habitat (Tedesco and Clercin 211). Also, phytoplankton (Chl-a) was prevalent in ECR and MR than that in GR. For this case study, TP concentration revealed a close relation to Chl-a concentration (R 2 =.46, p.5; see Fig. 3a). Comparable correlation between TP concentration and TSM presented in Fig. 3b (R 2 =.47, p.5), and even higher correlation between TP and SDT was observed by an R 2 =.62 and p.5 (see Fig. 3c). Similarly, turbidity is the comprehensive result of TSM and phytoplankton in waters, and TP is also closely related to turbidity in our dataset (R 2 =.69, p.1; see Fig. 3d). This Table 2 Summary statistics of water quality parameters for Eagle Creek, Morse and Geist Reservoirs in 25, 26, and 28 Parameter Mean Median Minimum Maximum σ N 25 two field campaigns field campaigns 28 four field campaigns MR+GR SDD (cm) Turbidity (NTU) TSM (mg/l) DOC (mg/l) Chl-a (μg/l) Total P (μg/l) Total N (mg/l) ECR+MR+GR SDD (cm) Turbidity (NTU) TSM (mg/l) DOC (mg/l) Chl-a (μg/l) Total P (μg/l) Total N (mg/l) ECR+MR SDD (cm) Turbidity (NTU) TSM (mg/l) DOC (mg/l) Chl-a (μg/l) Total P (μg/l) Total N (mg/l)

10 149 Water Air Soil Pollut (212) 223: Predicted TP (mg/l) Measured TP (mg/l) (a). TP vs. Chl-a y =.9x R 2 =.46 p<.5 n = Measured Chl-a (ug/l) (c) TP vs. SDD Measured SDD (cm) y =.21e -.1x R 2 =.62 p <.5 n = 234 Measured TP (mg/l) Measured TP (mg/l) (b) TP vs. TSM y =.37x +.37 R 2 =.47.5 p<.5 n = Measured TSS (mg/l) (d) TP vs. Turbidity y =.67x +.25 R 2 =.69.5 p<.1 n= Measured Turbidity (NTU) Fig. 3 Correlation analysis between TP and four water quality parameters, a chlorophyll a, b total suspended matter, c Secchi disk depth, d turbidity relationship between TP and corresponding water physical chemical parameters set up as basis for remote sensing monitoring of TP at various scales (Kutser et al. 1995; Wu et al. 21). 3.2 TP Modeling with In Situ Data Correlation Analysis To examine the association of spectral reflectance and its derivative with TP concentration, correlation analysis was applied to 5 spectral bands between 4 and 9 nm of reflectance datasets collected in 25, 26, and 28, respectively, resulting in the corresponding correlogram of TP concentration versus reflectance (Fig. 4a) and TP versus derivative (Fig. 4b). It can be observed from Fig. 4a that a broad region of relatively low correlation coefficient exhibits in the blue and green spectral regions and higher correlation coefficient in the near infrared (NIR) region for 25 dataset. Likewise, it shows relative high correlation coefficient from the green to NIR spectral region for 26 dataset, but no significant correlation for 28 dataset. One narrow region around 7 nm (chlorophyll-a florescence peak) has a high correlation coefficient, yet it is not significant for 28 dataset indicating that Chl-a acts as a bridge for the correlation between TP and remote sensing reflectance. Similar analysis applied to Chl-a revealed the same trend for the correlation coefficient curve vs. wavelength, implying that original reflectance spectra is apt to sun target sensor geometry variation and ambient environment factors(partial cloud, wind speed, etc), and derivative is more effective to reduce these factors as shown below. The reflectance derivative exhibits a relatively high correlation coefficient in the blue, green edge, red edge, and NIR regions, especially in the red edge

11 Water Air Soil Pollut (212) 223: Correlation Coefficient (R) (a) Reflectance Wavelength (nm) Correlation Coefficient (R) 1.5 (b) Derivative Wavelength (nm) Fig. 4 Correlation analysis on original spectra (a) and derivative (b) against TP concentration for each wavelength with various datasets region (69 7 nm) and NIR (around 79 nm); but in the blue, red, and NIR spectral region, the correlation coefficient varies (Fig. 4b). Although the correlation coefficient values for the 3-year datasets show significant variation, the highest correlation coefficients are observed in the red edge spectral region (chlorophyll-a florescence peak), ranging from.72 to.84, further confirm that Chl-a is acting as a bridge for remote estimation of TP. It indicates that spectral reflectance derivative analysis is an effective approach for spectroscopic analysis for water quality parameters quantification (Rundquist et al. 1996; Han and Rundquist, 1997; Han 25). Furthermore, it is worth noting that derivatives from these datasets have similar correlation trends to TP (both sensitive spectral regions and amplitude), while this was not the case for the reflectance spectra from 28 dataset due to more random sun target sensor geometry variation (Han and Rundquist 1997) Band Ratio Analysis For a preliminary analysis, 2-D correlograms of coefficient were generated by sequential regression of reflectance ratios against TP concentration for various datasets (Fig. 5). The reflectance band ratios include all possible pair combinations of narrow bands in the range 4 9 nm (25, combinations). Several hot spots in the diagram represent relatively broad regions of high correlation between band ratio and TP concentration. Apparently, correlation coefficient (R) across datasets varied for samples collected in different seasons, and the maximum correlation coefficient value ranges from.81 (the 26 dataset) to.92 (the 25 dataset). It can be seen that the best-performing band combination locations are not consistent for datasets collected in various years. However, the overall pattern for the 25 dataset is similar to that for 26 dataset and aggregated dataset (25, 26, and 28). For the 28 dataset, the higher correlation band ratio pairs locating in red (around 69 nm) and NIR spectral region for TP (around 71 nm), which is consistent with band ratio analysis for Chl-a empirical models (Schalles and Yacobi 2). Also, it is worthwhile to notice that the correlation coefficient seems symmetric along the diagonal element. However, the difference is subtle and the relationship between band ratios of A i /B j and B j /A i has different relationships to TP concentration where A i and B j denote reflectance at wavelength i and j, respectively GA-PLS Models Application of GA-PLS algorithms for retrieval of TP with the aggregated 25 dataset yielded an R 2 value of.89, with slope and intercept.81 and.125 μg/l, respectively (Fig. 6a). The " distribution pattern for the 25 dataset is presented in Fig. 6b with an average value of 18.7%. Comparison of estimated and measured TP concentration for the 25 dataset yielded an RMSE of.19 mg/l for both calibration and validation datasets (Table 3). It can be seen from Fig. 6b that the " i distribution mainly concentrates between 5 and +5, indicating a good performance of GA-PLS. The GA-PLS model has good prediction

12 1492 Water Air Soil Pollut (212) 223: Fig. 5 Correlation analysis between all band ratios vs. TP concentration for various datasets, a Morse and Geist reservoir dataset in 25; b Eagle Creek, Morse and Geist reservoir dataset in 26; c Eagle Creek and Morse Reservoir dataset in 28; d aggregated dataset ability according to William s criteria as both R 2 and RPD values illustrated in Table 3. Application of GA-PLS algorithms for the aggregated 26 dataset yielded a low R 2 (.67), and the slope and intercept for 1:1 line were significantly far from one to zero (see Fig. 6c). The " distribution pattern is presented in Fig. 6d with a much higher value of 27.9%, showing that most of the residual distributed in 5% and 1%. Comparison of estimated and measured TP concentration for 26 dataset yielded an RMSE of.24 mg/l for calibration and.26 mg/l for validation (Table 3). The GA-PLS model has an approximate performance according to William s criteria with both R 2 and RPD value in Table 3. Application of GA-PLS algorithms for the aggregated 28 dataset yielded a higher R 2 value of.9, and the slope and intercept for 1: 1 line were close to unity and zero (see Fig. 6e). Comparison of estimated and measured TP concentration for 28 dataset yielded an RMSE of.1 mg/l for calibration and.28 mg/l for validation (Table 3). The GA-PLS model has an accurate performance according to William s criteria with both R 2 and RPD shown in Table 3. The " distribution pattern also indicates that the GA-PLS model performed good with the 28 dataset (Fig. 6f), which is much better than that with the 26 dataset and marginally better than that with the 25 dataset. Both MAE and relative RMSE indicate that GA-PLS had better performances for both the 25 and 28 datasets; the result is not so promising for the 26 dataset. 3.3 TP Modeling with AISA Image Spectra Extracted AISA image spectra were preprocessed with the similar method as that applied to in situ spectra data. Application of GA-PLS for retrieval

13 Water Air Soil Pollut (212) 223: Predicted TP(mg/L) (a) Dataset in 25 Calibration Validation 1:1 Line.5 y =.835 x R 2 =.892, n = Measured TP(mg/L) Normalized Frequency (%) (b) Residual-25 ε, = 18.7% n = % Residual TP(mg/L) Predicted TP(mg/L) (c) Dataset-26 Calibration Validation 1:1 Line.5 y =.62 x R 2 =.67, n = Measured TP(mg/L) Normalized Frequency (%) (d) Residual-26 ε, = 27.9% n = % Residual TP(mg/L) Predicted TP(ug/L) (e) Dataset-28 Calibration Validation 1:1 Line.1 y = 1.17 x R 2 =.94, n = Measured TP(ug/L) Normalized Frequency (%) (f). Residual-28 ε, = 14.3% n = % Residual TP(ug/L) Fig. 6 Scatter plot of measured vs. predicted TP for GA-PLS and error residual histogram for various datasets, a 25 dataset; b 26 dataset; c 28 dataset of TP over MR yielded an R 2 value of.82 and a " value of 24.7%, respectively (Fig. 7a, b). Comparison of estimated and measured TP concentration for MR yielded a RMSE of.2 and.3 mg/l, respectively. The GA-PLS model had good prediction ability according to William s criteria with both R 2 and RPD summarized in Table 4. Compared with Figs. 6a, b and 7a, b indicate that GA-PLS resulted in a similar pattern but at a lower accuracy. Generally speaking, atmospheric conditions will introduce some

14 1494 Water Air Soil Pollut (212) 223: Table 3 Performance summaries for GA-PLS model on estimated TP with in situ spectra datasets collected in 25, 26, and 28 Datasets Model calibration Model validation RMSE RMSE% MAE RPD R 2 RMSE RMSE% MAE RPD R 2 Dataset Dataset Dataset uncertainty which will ultimately affect the model performance. Application of GA-PLS for retrieval of TP for GR from AISA image spectra yielded an R 2 value of.83 and a " value of 11.1%, respectively (Fig. 7c, d). Comparison of estimated and measured TP concentration for GR yielded a RMSE of.1 mg/l for calibration and.3 mg/l for validation, respectively (Table 4). The GA-PLS model revealed good performance according to William s criteria with both R 2 and RPD being summarized in Table TP Modeling with In Situ and Image Spectra The result derived from GA-PLS modeling with all datasets (in situ datasets for 25, 26, 28, and AISA image spectra in 25) versus measured TP is plotted in Fig. 8a, and residual error (TP predicted Predicted TP (mg/l) (a) MR AISA data Calibration Validation 1:1 Line.5 y =.89 x R 2 =.821, n = Measured TP (mg/l) Normalized Frequency (%) (b) MR AISA data ε, = 24.7% n = % Residual TP (mg/l) Predicted TP (mg/l) (c) GR AISA data Calibration Validation.5 y =.886 x +.8 R 2 =.834, n = Measured TP (mg/l) Normalized Frequency (%) (d) GR AISA data ε, =17.1% n = % Residual TP (mg/l) Fig. 7 Scatter plot of measured vs. predicted TP using AISA imaging spectra via GA-PLS model, a GA-PLS for MR; b residual distribution for MR; c GA-PLS for GR; d residual distribution for GR

15 Water Air Soil Pollut (212) 223: Table 4 Performance summaries for GA-PLS performance on estimated TP, Chl-a, and SDT with AISA images acquired in 25 over MR and GR Datasets Model calibration Model validation RMSE RMSE% MAE RPD R 2 RMSE RMSE% MAE RPD R 2 MR TP (mg/l) Chl-a(μg/L) SDT (cm) GR TP (mg/l) Chl-a(μg/L) SDT (cm) TP measured ) is plotted against measured TP (Fig. 8b). The relationship between predicted and measured TP could be fitted with a linear regression, with the coefficient of determination being.84 and the slope value (.84) close to unity (Fig. 8a). It could be concluded that GA-PLS performs well with remotely sensed data collected in this study. For the GA-PLS model, the highest relative error (under- or over-estimation) occurred randomly with TP concentration (Fig. 8b), implying that TP can be reliably estimated in this case study. The scatter plot of residual error versus measured TP (Fig. 8b) showed significant differences across various datasets with GA-PLS model. Underestimating TP concentration with the 26 dataset can be ascribed to the complex relationship between TP and other OACs in the water column, which need additional data to confirm (Tedesco and Clercin 211). Most of residual errors range from.6 to.6 μg/l with the maximum value of.87 mg/l, indicating a relatively good performance for TP estimation with remote sensing data. 3.5 Chl-a and SDT Modeling with AISA Image Spectra Application of GA-PLS for retrieval Chl-a and SDT from the MR AISA spectra yielded an R 2 value of.96 and.93, respectively (Fig. 9a, b). Comparison of estimated and measured Chl-a concentration for MR yielded a RMSE of 8.87 μg/l for calibration and 9.8 μg/l for validation (Table 4). The GA-PLS model also yielded an accurate performance for SDT estimation according to William s criteria(21)considering R 2 and RPD values (Table 4). The RMSE and MAE for the calibration dataset are 5.69 and 4.61 cm, respectively, and and 9.28 cm for validation dataset..4 (a) Aggregated data.1 (b). Residual vs TP Predicted TP (mg/l) AISA 8.1 y =.845x +.13 R 2 = MeasuredTP (mg/l) Redidual AISA Measured TP (mg/l) Fig. 8 Scatter plot of predicted and measured TP with aggregated dataset including AISA imagery data (a), and residual distribution (b)

16 1496 Water Air Soil Pollut (212) 223: Predicted Chl-a (ug/l) (a) MR AISA Chl-a Calibration Validation 1:1 Line 3 y = 1.6 x R 2 =.961, n = Measured Chl-a (ug/l) Predicted SDT (cm) (b) MR AISA SDT Calibration Validation 1:1 Line 4 y = 1.11 x R 2 =.937, n = Measured SDT (cm) Fig. 9 a Scatter plot of predicted and measured Chl-a and b SDT for Morse Reservoir with AISA imagery data Similarly, GA-PLS estimation of Chl-a and SDT from the GR AISA image spectra resulted in an R 2 value of.87 and.74, respectively (Fig. 1a, b). Comparison of estimated and measured Chl-a concentration for GR yielded a RMSE of μg/l for calibration and 1.55 μg/l for validation (Table 4). Chl-a can be accurately estimated with R 2 and RPD presented in Table 4. However, the GA- PLS yielded approximate performance for SDT estimation (Table 4). Dredging took place in GR during our field campaigns which modified the relationship between inherent optical properties and apparent optical properties of natural waters, i.e., suspended particle size and composition and coating effect of CDOM with mineral particles (Binding et al. 28). 3.6 Trophic Status Mapping According to Carlson (1977), once TP, Chl-a, and SDT have been derived or mapped, then trophic status can be evaluated. GA-PLS models were applied to AISA images to map TP, Chl-a, and SDT over MR (Fig. 11a c). The TP concentration over MR had an average value of 94.6 μg/l and a big gradient as indicated by a standard deviation (SD) of μg/l, with 99.2% of pixels being less than μg/l. This pattern can be observed for the Chl-a spatial concentration pattern in MR. The Chl-a concentration of MR had an average value of 82.1 μg/l and a large gradient as also indicated by SD of 68.5 μg/l, with 99% of pixels being less than μg/l. These observations suggest that TP and Chl-a demonstrate a Predicted Chl-a (ug/l) (a) GR AISA Chl-a Calibration Validation y =.819 x R 2 =.872, n = Measured Chl-a (ug/l) Predicted SDT (cm) (b) GR AISA SDT Calibration Validation 4 y =.732 x R 2 =.742, n = Measured SDT (cm) Fig. 1 a Scatter plot of predicted and measured Chl-a concentration and b SDT for Geist Reservoir with AISA imagery data

17 Water Air Soil Pollut (212) 223: Fig. 11 Water quality parameters distribution maps estimated with AISA imagery data: a TP map, b Chl-a map, c SDT map, and d TSI map for Morse Reservoir similar spatial pattern because TP is highly correlated with Chl-a concentration in the reservoir. SDT revealed an average value of.83 m and demonstrated a large variation by showing a higher standard deviation (SD.57 m). It can be observed from Fig. 11c that water clarity is inversely related to Chl-a concentration pattern in the reservoir, i.e., the higher the Chl-a concentration is, the lower the SDT tends to be. This makes sense as phytoplankton and inorganic matter concentrations are the major factors that determine water clarity (Carlson 1977; Goodin et al. 1993; Hans et al. 22). In our study, phytoplankton contributes the major portion of suspended matter resulting in Chl-a inversely related to SDT. Applying Eqs. 12, 13, and 14, the TSI value was calculated from TP, Chl-a, and SDT respectively, and then the average TSI for MR was computed using

18 1498 Water Air Soil Pollut (212) 223: Eq. 15 shown in Fig. 11d. The TSI map presents a mean value of with SD value of 1.1. According to the Carlson TSI, 18.7% of MR belongs to oligotrophic class, 48.6% to mesotrophic class, and 32.7% to eutrophic class, which is consistent with finding from Indiana Department of Environmental Management (IDEM 22). The TSI distribution matches the Chl-a spatial pattern, reflecting that phytoplankton is the result of TP distribution working with temperature, while SDT is somehow the result of phytoplankton and inorganic matter abundance in the water. The TP, Chl-a, and SDT maps for GR derived by GA-PLS are presented in Fig. 12a c. TP concentration has an average value of 15.1 μg/l with a small gradient (SD 34.1 μg/l), and 99.8% of Fig. 12 Water quality parameters distribution maps estimated with AISA imagery data: a TP map, b Chl-a map, and c SDT map, and d TSI map for Geist Reservoir

19 Water Air Soil Pollut (212) 223: pixels are less than 32. μg/l. Chl-a shows an average value of 88.2 μg/l, and a relatively small gradient indicated by a SD of 33.1 μg/l with 99.9% of pixels being less than 15. μg/l. Overall, Chl-a shows a similar spatial pattern to TP concentration, but some variations do exist in the lower reach. This follows because the dredging practice disturbed the hydrologic process which modified the pattern of nutrient and phytoplankton spatial distribution (Randolph et al. 28), leading to the effects similar to that generated by wind working on the lake surface (Hunter et al. 29). SDT has an average value of.44 m and demonstrated a small variation (SD.7). It is obvious that the water of GR is more turbid as revealed by low SDT values, which is also due to the dredging practice disturbing the sediment distribution in the water column. It can be seen from Fig. 12c that water clarity is inversely related to Chl-a concentration, and this is similar to that for MR. The averaged TSI value is shown in Fig. 12d. The TSI map has a mean value of 59.95, SD of 3.1. According to the Carlson TSI, 1.7% can be ascribed to mesotrophic class, 57.8% to eutrophic class, and more than 4% to hypereutrophic class. By comparison, the TSI spatial distribution positively resembles Chl-a and is inversely related to SDT. A high TP and low water clarity lead to high TSI in most of GR. As a result, almost the whole lake belongs to eutrophic or hypereutrophic class. We suspect that the dredging practice played an important role for the trophic state in this reservoir which might have enhanced the P release from the bottom sediment, changed SDT, and thus both have driven the TSI distribution in GR. Given the Chl-a concentration, MR is more eutrophic than GR. However, the higher total suspended matter and especially high turbidity in GR resulted in a high TSI value. performed well when applied to the aggregated datasets from 25 to 28. Differences in phytoplankton community structure and suspended sediment and its relationship with TP from various seasons (17 field trips) could partly explain the low performance for the aggregated dataset in 26. TP highly related to sediment loading with watershed scale, however, there is a time lag for phytoplankton to consume TP in the reservoir, which make the relationship between TP and Ch-a or TSM more complicated. GA-PLS performs well with AISA image spectra for TP concentration mapping in both MR and GR, showing that simple models can result in relatively accurate estimation of TP from hyperspectral imaging data and demonstrating that these techniques can be applied across sensors and sensor platforms (e.g., field, airborne, and satellite sensors) with similar spectral infrastructure. Spatial water eutrophic information can be derived from remotely inversed TP, Chl-a, and SDT result for driving Carlson trophic state index. These can be used as decision-making support information for environmental management agencies. Based on this preliminary finding, future research will focus on improving our techniques for predicting water quality from hyperspectral data, especially TP concentration spatial distribution. This will include (1) increasing the number of water quality parameters retrieved from remotely sensed data and investigate the remote sensing basis for TP estimation by relating with other optically active constituents; (2) expanding our understanding to develop algorithms for reliable TP inversion models based on remotely sensed data; and (3) scaling up our use of spectroradiometer platforms to include satellite imagery sensors in larger water bodies. 4 Conclusions This study shows the feasibility of using hyperspectral remote sensing techniques as a rapid assessment tool for determining the concentration and spatial distribution of TP in Indianapolis' drinking water resources. GA modeling resulted in the selection of spectral variables most related to Chl-a or suspended sediment which are highly related to TP as reported in the literature. GA-PLS derived algorithms Acknowledgments This research was mainly supported by the National Aeronautics and Space Administration (NASA) HyspIRI preparatory activities using existing imagery (HPAUEI) program. Veolia Water Indianapolis, LLC, and Indiana Department of Natural Resource Lake and River Enhancement Program are also acknowledged for financial support on AISA imagery data acquisition. The authors thank the students, staff, and faculty in the Department of Earth Sciences at IUPUI for participating in the field sampling campaign. We are grateful to two anonymous reviewers for the constructive comments and recommendations in improving and strengthening this paper.