Prediction of an environmental issue of mine blasting: an imperialistic competitive algorithm-based fuzzy system

Ground vibration resulting from blasting is one of the most important environmental problems at open-cast mines. Therefore, accurately approximating the blast-induced ground vibration is very significant. By reviewing the previous investigations, many attempts have been done to create the empirical models for estimating ground vibration. Nevertheless, the performance of the empirical models is not good enough. In this research work, a new hybrid model of fuzzy system (FS) designed by imperialistic competitive algorithm (ICA) is proposed for approximating ground vibration resulting from blasting at Miduk copper mine, Iran. For comparison aims, various empirical models were also utilized. Results from different predictor models were compared by using coefficient of multiple determination (R ²), variance account for and root-mean-square error between measured and predicted values of the PPVs. Results prove that the FS–ICA model outperforms the other empirical models in terms of the prediction accuracy. In other words, the FS–ICA model with R ² of 0.942 can forecast PPV better than the USBM with R ² of 0.634, Ambraseys–Hendron with R ² of 0.638, Langefors–Kihlstrom with R ² of 0.637 and Indian Standard with R ² of 0.519.     

Mathematical expression of discharge capacity of compound open channels using MARS technique

In this paper, analytical methods, artificial neural network (ANN) and multivariate adaptive regression splines (MARS) techniques were utilised to estimate the discharge capacity of compound open channels (COC). To this end, related datasets were collected from literature. The results showed that the divided channel method with a coefficient of determination (R ²) value of 0.76 and root mean square error (RMSE) value of 0.162 has the best performance, among the various analytical methods tested. The performance of applied soft computing models with R ²=0.97 and RMSE = 0.03 was found to be more accurate than analytical approaches. Comparison of MARS with the ANN model, in terms of developed discrepancy ratio (DDR) index, showed that the accuracy of MARS model was better than that of MLP model. Reviewing the structure of the derived MARS model showed that the longitudinal slope of the channel (S), relative flow depth (H _r ) and relative area (A _r ) have a high impact on modelling and forecasting the discharge capacity of COCs.     

Petro-chemical investigation of some perhydrous Indian coals

An attempt has been made to study the petro-chemical characteristics of some high sulphur sub-bituminous coal samples from Makum coalfield, Assam, India. The proximate and ultimate analyes were carried out and forms of sulphur were determined and their relationships with the Maceral constituents (vitrinite, liptinite, and inertinite) were investigated. The macerals (vitrinite+liptinite+inertinite) have significant relationships (R²>0.500) with volatile matter and carbon, whereas weak correlations were seen with rest of the physico-chemical characteristics of the coals. The study reveals that these coals are rich in vitrinites and sulphur and are aromatic in nature. These coals have good hydrocarbon potential.     

Predicting longitudinal dispersion coefficient using ANN with metaheuristic training algorithms

A reliable prediction of dispersion coefficient can provide valuable information for environmental scientists and river engineers as well. The main objective of this study is to apply intelligence techniques for predicting longitudinal dispersion coefficient in rivers. In this regard, artificial neural network (ANN) models were developed. Four different metaheuristic algorithms including genetic algorithm (GA), imperialist competitive algorithm (ICA), bee algorithm (BA) and cuckoo search (CS) algorithm were employed to train the ANN models. The results obtained through the optimization algorithms were compared with the Levenberg–Marquardt (LM) algorithm (conventional algorithm for training ANN). Overall, a relatively high correlation between measured and predicted values of dispersion coefficient was observed when the ANN models trained with the optimization algorithms. This study demonstrates that the metaheuristic algorithms can be successfully applied to make an improvement on the performance of the conventional ANN models. Also, the CS, ICA and BA algorithms remarkably outperform the GA and LM algorithms to train the ANN model. The results show superiority of the performance of the proposed model over the previous equations in terms of DR, R ² and RMSE.     

Monthly reservoir inflow forecasting using a new hybrid SARIMA genetic programming approach

Forecasting reservoir inflow is one of the most important components of water resources and hydroelectric systems operation management. Seasonal autoregressive integrated moving average (SARIMA) models have been frequently used for predicting river flow. SARIMA models are linear and do not consider the random component of statistical data. To overcome this shortcoming, monthly inflow is predicted in this study based on a combination of seasonal autoregressive integrated moving average (SARIMA) and gene expression programming (GEP) models, which is a new hybrid method (SARIMA–GEP). To this end, a four-step process is employed. First, the monthly inflow datasets are pre-processed. Second, the datasets are modelled linearly with SARIMA and in the third stage, the non-linearity of residual series caused by linear modelling is evaluated. After confirming the non-linearity, the residuals are modelled in the fourth step using a gene expression programming (GEP) method. The proposed hybrid model is employed to predict the monthly inflow to the Jamishan Dam in west Iran. Thirty years’ worth of site measurements of monthly reservoir dam inflow with extreme seasonal variations are used. The results of this hybrid model (SARIMA–GEP) are compared with SARIMA, GEP, artificial neural network (ANN) and SARIMA–ANN models. The results indicate that the SARIMA–GEP model (R ²=78.8, VAF =78.8, RMSE =0.89, MAPE =43.4, CRM =0.053) outperforms SARIMA and GEP and SARIMA–ANN (R ²=68.3, VAF =66.4, RMSE =1.12, MAPE =56.6, CRM =0.032) displays better performance than the SARIMA and ANN models. A comparison of the two hybrid models indicates the superiority of SARIMA–GEP over the SARIMA–ANN model.     

Prediction of strength parameters of sedimentary rocks using artificial neural networks and regression analysis

Accurate laboratory measurement of geo-engineering properties of intact rock including uniaxial compressive strength (UCS) and modulus of elasticity (E) involves high costs and a substantial amount of time. For this reason, it is of great necessity to develop some relationships and models for estimating these parameters in rock engineering. The present study was conducted to forecast UCS and E in the sedimentary rocks using artificial neural networks (ANNs) and multivariable regression analysis (MLR). For this purpose, a total of 196 rock samples from four rock types (i.e., sandstone, conglomerate, limestone, and marl) were cored and subjected to comprehensive laboratory tests. To develop the predictive models, physical properties of studied rocks such as P wave velocity (V_p), dry density (γ_d), porosity, and water absorption (A_b) were considered as model inputs, while UCS and E were the output parameters. We evaluated the performance of MLR and ANN models by calculating correlation coefficient (R), mean absolute error (MAE), and root-mean-square error (RMSE) indices. The comparison of the obtained results revealed that ANN outperforms MLR when predicting the UCS and E.     

A comparative study of shallow groundwater level simulation with WA–ANN and ITS model in a coastal island of south China

Accurate and reliable prediction of shallow groundwater level is a critical component in water resources management. Two nonlinear models, WA–ANN method based on discrete wavelet transform (WA) and artificial neural network (ANN) and integrated time series (ITS) model, were developed to predict groundwater level fluctuations of a shallow coastal aquifer (Fujian Province, China). The two models were testified with the monitored groundwater level from 2000 to 2011. Two representative wells are selected with different locations within the study area. The error criteria were estimated using the coefficient of determination (R ²), Nash–Sutcliffe model efficiency coefficient (E), and root-mean-square error (RMSE). The best model was determined based on the RMSE of prediction using independent test data set. The WA–ANN models were found to provide more accurate monthly average groundwater level forecasts compared to the ITS models. The results of the study indicate the potential of WA–ANN models in forecasting groundwater levels. It is recommended that additional studies explore this proposed method, which can be used in turn to facilitate the development and implementation of more effective and sustainable groundwater management strategies.     

Use of SWAT to determine the effects of climate and land use changes on streamflow and sediment concentration in the Purna River basin,India

A semi-distributed, physically based, basin-scale Soil and Water Assessment Tool (SWAT) model was developed to determine the key factors that influence streamflow and sediment concentration in Purna river basin in India and to determine the potential impacts of future climate and land use changes on these factors. A SWAT domain with a Geographical Information System (GIS) was utilized for simulating and determining monthly streamflow and sediment concentration for the period 1980–2005 with a calibration period of 1980–1994 and validation period of 1995 to 2005. Additionally, a sequential uncertainty fitting (SUFI-2) method within SWAT-CUP was used for calibration and validation purpose. The overall performance of the SWAT model was assessed using the coefficient of determination (R²) and Nash–Sutcliffe efficiency parameter (E_NS) for both calibration and validation. For the calibration period, the R² and E_NS values were determined to be 0.91 and 0.91, respectively. For the validation period, the R² and E_NS were determined to be 0.83 and 0.82, respectively. The model performed equally well with observed sediment data in the basin, with the R² and E_NS determined to be 0.80 and 0.75 for the calibration period and 0.75 and 0.65 for the validation, respectively. The projected precipitation and temperature show an increasing trend compared to the baseline condition. The study indicates that SWAT is capable of simulating long-term hydrological processes in the Purna river basin.     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

Digital soil mapping in a Himalayan watershed using remote sensing and terrain parameters employing artificial neural network model

Digital soil mapping relies on field observations, laboratory measurements and remote sensing data, integrated with quantitative methods to map spatial patterns of soil properties. The study was undertaken in a hilly watershed in the Indian Himalayan region of Mandi district, Himachal Pradesh for mapping soil nutrients by employing artificial neural network (ANN), a potent data mining technique. Soil samples collected from the surface layer (0–15 cm) of 75 locations in the watershed, through grid sampling approach during the fallow period of November 2015, were preprocessed and analysed for various soil nutrients like soil organic carbon (SOC), nitrogen (N) and phosphorus (P). Spectral indices like Colouration Index, Brightness Index, Hue Index and Redness Index derived from Landsat 8 satellite data and terrain parameters such as Terrain Wetness Index, Stream Power Index and slope using CartoDEM (30 m) were used. Spectral and terrain indices sensitive to different nutrients were identified using correlation analysis and thereafter used for predictive modelling of nutrients using ANN technique by employing feed-forward neural network with backpropagation network architecture and Levenberg–Marquardt training algorithm. The prediction of SOC was obtained with an R² of 0.83 and mean squared error (MSE) of 0.05, whereas for available nitrogen, it was achieved with an R² value of 0.62 and MSE of 0.0006. The prediction accuracy for phosphorus was low, since the phosphorus content in the area was far below the normal P values of typical Indian soils and thus the R² value observed was only 0.511. The attempts to develop prediction models for available potassium (K) and clay (%) failed to give satisfactory results. The developed models were validated using independent data sets and used for mapping the spatial distribution of SOC and N in the watershed.     

Data-driven nonlinear modeling studies on removal of Acid Yellow 59 using Si-doped multi-walled carbon nanotubes

Data-driven modeling of removal of color index name of Acid Yellow 59 from aqueous solutions using multi-walled carbon nanotubes by multiple (non)linear regression and artificial neural networks (ANN) models based on leave-one-out cross-validation to predict the adsorbed dye amount per unit mass of adsorbent (mg g^?1) and performance evaluation of the proposed multiple (non)linear regression and ANN models is the main novel contributor of the present study. Initial dye concentration, adsorbent concentration, reaction time, and temperature were determined as explanatory variables and input neurons for multiple (non)linear regression and ANN models, respectively. The total number of experiments was determined as 1280 statistically. The results showed that multilayer perception ANN model (\(R^{2}_{\text{training}}\) = 0.9997, \(R^{2}_{\text{testing}}\) = 0.9993, RMSE = 0.7678, MAE of 0.0007) predicted q _t better than multiple (non)linear regression model (\(R^{2}_{\text{adj}}\) = 0.9645, \(R^{2}_{\text{pred}}\) = 0.9633, SE = 9.55) and MLR (R ² = 0.9543, SE = 10.87) models. The results justified the accuracy of ANN in prediction of q _t , significantly.     

Fluid–rock interaction during seprentinization of oceanic ultramafic rocks hosting the Lost City hydrothermal field, 30° N,MAR

The estimation of the fluid/rock (W/R) ratio during serpentinization on the basis of oxygen isotope characteristics is peculiar, because this process is accompanied by not only changes in the stoichiometric proportions of oxygen in fluid and rock, but also by the formation of associated minerals. These factors should be taken into account for environments when the volume of aqueous fluid is limited, for instance, for serpentinization of the deep-seated rocks of oceanic lithosphere under low spreading rates. We studied isotope characteristics of samples collected in dives of submersible MIR during Cruise 50 of the R/V Akademik Mstislav Keldysh along vertical profile on the southern slope of the Atlantis Massif, which hosts the Lost City hydrothermal field. Almost all studied serpentinites have homogenous strontium isotope composition corresponding to the composition of the modern seawater. Oxygen isotope composition of these serpentinites shows systematic variations from 2. 6 to 6.1‰ with sampling depth, which indicates the preservation of stratigraphic position of samples in the sequence of the Atlantis Massif and the global serpentinization of the entire plutonic sequence. The value of the fluid–rock ratio during serpentinization in a system closed to fluid was estimated using the dissolution–crystallization model. This model takes into account the variable stoichiometry of oxygen and the effect of the simultaneous crystallization of brucite on the oxygen isotope composition of newly formed serpentine. The results show that at moderately elevated temperatures (≈300°C) and 0.1 < W/R < 5, fluid, crystallizing serpentine, and brucite are characterized by sharp variations in oxygen isotope composition: 1.3–7.8, 2.5–8.9, and 4.5–1.9‰, respectively. The model explains the observed range of δ¹⁸O in the serpentinized harzburgites of the Atlantis Massif. According to our estimates, the rocks of the studied sequence of the Atlantis Massif were serpentinized at 270–350°C and W/R = 0.7–3. For lower temperature serpentinization, for instance, at T = 250°C, the W/R ratio can be as high as 6. The present-day serpentinization of the deepseated zones of the Atlantis Massif with the Lost City fluid participance proceeds at T > 270°C and W/R ratio <1. These conditions are similar to those of serpentinization of harzburgites from the lower parts of the studied sequence of the Atlantis Massif.     

Geospatial approach in mapping soil erodibility using CartoDEM – A case study in hilly watershed of Lower Himalayan Range

Soil erodibility is one of the most important factors used in spatial soil erosion risk assessment. Soil information derived from soil map is used to generate soil erodibility factor map. Soil maps are not available at appropriate scale. In general, soil maps at small scale are used in deriving soil erodibility map that largely generalized spatial variability and it largely ignores the spatial variability since soil map units are discrete polygons. The present study was attempted to generate soil erodibilty map using terrain indices derived from DTM and surface soil sample data. Soil variability in the hilly landscape is largely controlled by topography represented by DTM. The CartoDEM (30 m) was used to derive terrain indices such as terrain wetness index (TWI), stream power index (SPI), sediment transport index (STI) and slope parameters. A total of 95 surface soil samples were collected to compute soil erodibility factor (K) values. The K values ranged from 0.23 to 0.81 t ha^?1R^?1 in the watershed. Correlation analysis among K-factor and terrain parameters showed highest correlation of soil erodibilty with TWI (r ²= 0.561) followed by slope (r ²= 0.33). A multiple linear regression model was developed to derive soil erodibilty using terrain parameters. A set of 20 soil sample points were used to assess the accuracy of the model. The coefficient of determination (r ²) and RMSE were computed to be 0.76 and 0.07 t ha^?1R^?1 respectively. The proposed methodology is quite useful in generating soil erodibilty factor map using digital elevation model (DEM) for any hilly terrain areas. The equation/model need to be established for the particular hilly terrain under the study. The developed model was used to generate spatial soil erodibility factor (K) map of the watershed in the lower Himalayan range.     

X Per and V725 Tau: infrared variations on timescales longer than fifteen years

The results of infrared observations of the two Be stars X Per and V725 Tau, which are the optical components of X-ray binary systems, obtained in 1994–2016 are presented. The observations cover Be-star phases as well as shell phases. The data analysis shows that the radiation observed from the binaries at 1.25, 3.5, and 5 μm can be explained as the combined radiation from the optical components and variable sources (shells/disks) that emit as blackbodies (BBs). Emission from a source with the color temperature T _c ~1000?1500 K was detected for X Per at λ ≥ 3.5 μm. The highest IR-brightness variation amplitudes for X Per were 0.9?1.2 ^m (JHK magnitudes) and ~1.45 ^m (LM magnitudes); for V725 Tau, they were 1.1?1.4 ^m and ~1.7 ^m (L magnitudes). The parameters of the optical components and interstellar extinction during the Be phases were estimated: the color excesswasE(B?V) = 0.65±0.08 ^m and 0.77 ± 0.03 ^m for X Per and V725 Tau, respectively. Light from the variable sources (disks/shells) was distinguished and their color temperatures, radii, and luminosities estimated for different observation epochs in a BB model. The variations of the binaries’ IR brightness and colors are shown to be due to changing parameters of the variable sources. The mean color temperature of the cool source (disk/shell) and the mean radius and mean luminosity of X Per are 9500± 2630 K, (35 ± 10) R_⊙, and (9100± 540) L_⊙. For V725 Tau, these parameters are 6200 ± 940 K, (27 ± 6) R_⊙, and (980 ± 420) L_⊙. The 1.25–5 μm radiation from X Per at different epochs can be represented as a sum of contributions from at least three sources: the optical component and two objects emitting as BBs. To reproduce the 1.25–3.5 μm radiation from V725 Tau, two components are sufficient: the optical component and a single variable BB object. For both binary systems, orbital variations of the IR brightness can be noted near the Be-star phase. The amplitudes of the J-band variations of X Per and V725 Tau are about 0.3 ^m and 0.1 ^m , respectively.     

Using Stable Isotopes to Assess the Contribution of Terrestrial and Riverine Organic Matter to Diets of Nearshore Marine Consumers in a Glacially Influenced Estuary

Terrestrial and marine ecosystems in Southeast Alaska are linked by the flow of freshwater from precipitation and glacial runoff, which transports nutrients and organic matter (OM) downstream to estuaries. We examined the contribution of terrestrial-riverine and marine OM to diets of fishes (N = 257, four species) and invertebrates (N = 90, six species) collected from glacially influenced estuaries in Southeast Alaska using multiple stable isotopes (δ¹³C, δ¹⁵N, and δ³⁴S). Multivariate analysis of similarity (ANOSIM) was used to quantify variation in stable isotope composition of consumers across 6 months and three sites with watersheds that differed in their glacier and forest composition. Fishes showed weak differences (ANOSIM R = 0.141) in stable isotope composition among sampling months, moderate differences (ANOSIM R = 0.375) among sites, and strong differences (ANOSIM R = 0.583) among species. Invertebrates showed moderate differences (ANOSIM R = 0.352) in stable isotope composition among sampling months and strong differences among sites (ANOSIM R = 0.710) and species (ANOSIM R = 0.858). We found the greatest differences in stable isotope composition between the two estuary sites with watersheds containing the highest and lowest glacial coverage, indicating that the contribution of allochthonous OM to consumer diets varies across watershed types. Invertebrates collected from the site with the lowest glacial coverage in the watershed were more depleted in δ¹³C and δ³⁴S, indicating higher use of terrestrial-riverine OM, than those at sites with higher watershed glacial coverage. High variation in stable isotope composition among species, months, and sites underscores the complexity of estuary food web responses to future glacier loss.     

Prediction of local scour around complex piers using GEP and M5-Tree

Local scour around piers is one of the main causes of bridge failures. In this study, three robust techniques, artificial neural networks (ANNs), M5-Tree, and Gene Expression Programming (GEP), were employed for prediction of scour depth around complex piers. The clear water condition was chosen for all experimental tests. The results indicated that pier diameter (b _c) and foundation level (Y) are the main parameters for local scour. Furthermore, the minimum scour depth occurs in range of Y/b _c = 1.1~1.3. In next step, to evaluate the mentioned techniques, a wide range of dataset was collected from the present study and literature. The radial base function (RBF) with R ² = 0.945 and RMSE = 0.031 provides better prediction in comparison with conventional equations, M5-Tree (R ² = 0.883, RMSE = 0.292) and the GEP techniques (R ² = 0.811 and RMSE = 0.263). The equations developed by M5-Tree and GEP are more useful for practical purposes and can be easily employed to predict the depth of scour at complex piers.     

Risk assessment and prediction of safety factor for circular failure slope using rock engineering systems

Circular failure is generally observed in the slope of soil, highly jointed rock mass, mine dump and weak rock. Accurate estimation of the safety factor (SF) of slopes and their performance is not an easy task. In this research, based on rock engineering systems (RES), a new approach for the estimation of the SF is presented. The introduced model involves six effective parameters on SF [unit weight (γ), pore pressure ratio (r _u), height (H), angle of internal friction (φ), cohesion (C) and slope angle (\(\beta\))], while retaining simplicity as well. In the case of SF prediction, all the datasets were divided randomly to training and testing datasets for proposing the RES model. For comparison purposes, nonlinear multiple regression models were also employed for estimating SF. The performances of the proposed predictive models were examined according to two performance indices, i.e., coefficient of determination (R ²) and mean square error. The obtained results of this study indicated that the RES is a reliable method to predict SF with a higher degree of accuracy in comparison with nonlinear multiple regression models.     

Orthogonal test and regression analysis of the strain on silty soil in Shanghai under metro loading

Cyclic triaxial test by means of the geotechnical digital system is conducted for the soil near the Guoquan Road Station of Metro Line 10 in Shanghai to analyze the strain characteristics and the variation law of saturated silty soil under subway loading. Orthogonal design method is used to arrange the experiment, considering the following factors: frequency ratio f _R, cyclic stress ratio σ _R, vibration time ratio N _R, and the interaction function among them. Results show that the cyclic stress ratio σ _R, the frequency ratio f _R, the vibration time ratio N _R, and the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R have a significant effect on the axial strain of the subway tunnel. The effect of the interaction between the cyclic stress ratio σ _R and the vibration time ratio N _R is also significant. From the analysis of variance and regression theory, the nonlinear regression equation of the cumulative plastic strain of silty soil under subway loading is established. Residual analysis proves that the equation is ideal and credible. The results have important value for the design of subway tunnels.     

Accuracy assessment of near-shore bathymetry information retrieved from Landsat-8 imagery

The improvement in the capabilities of Landsat-8 imagery to retrieve bathymetric information in shallow coastal waters was examined. Landsat-8 images have an additional band named coastal/aerosol, Band 1: 435–451 nm in comparison with former generation of Landsat imagery. The selected Landsat-8 operational land image (OLI) was of Chabahar Bay, located in the southern part of Iran (acquired on February 22, 2014 in calm weather and relatively low turbidity). Accurate and high resolution bathymetric data from the study area, produced by field surveys using a single beam echo-sounder, were selected for calibrating the models and validating the results. Three methods, including traditional linear and ratio transform techniques, as well as a novel proposed integrated method, were used to determine depth values. All possible combinations of the three bands [coastal/aerosol (CB), blue (B), and green (G)] have been considered (11 options) using the traditional linear and ratio transform techniques, together with five model options for the integrated method. The accuracy of each model was assessed by comparing the determined bathymetric information with field measured values. The standard error of the estimates, correlation coefficients (R ² ) for both calibration and validation points, and root mean square errors (RMSE) were calculated for all cases. When compared with the ratio transform method, the method employing linear transformation with a combination of CB, B, and G bands yielded more accurate results (standard error = 1.712 m, R ² _calibration = 0.594, R ² _validation = 0.551, and RMSE =1.80 m). Adding the CB band to the ratio transform methodology also dramatically increased the accuracy of the estimated depths, whereas this increment was not statistically significant when using the linear transform methodology. The integrated transform method in form of Depth = b ₀  + b ₁ X _CB  + b ₂ X _B  + b ₅ ln(R _CB )/ln(R _G ) + b ₆ ln(R _B )/ln(R _G ) yielded the highest accuracy (standard error = 1.634 m, R ² _calibration = 0.634, R ² _validation = 0.595, and RMSE = 1.71 m), where R _i (i = CB, B, or G) refers to atmospherically corrected reflectance values in the i ^th band [X _i  = ln(R _i -R _{deep water})].