Estimating leaf nitrogen concentration from similarities in fresh and dry leaf spectral bands using a model population analysis framework

Fresh leaf spectral reflectance is primarily influenced by leaf water content and structural aspects such as the inter-cellular spaces within the spongy mesophyll, which also interfere with the estimation of the leaf nitrogen content. It is therefore essential to identify spectral bands that are least affected by the above perturbing factors for improving leaf nitrogen estimation for fresh leaves across any landscape. Wavelengths selection plays a vital role in identifying the best spectral features for assessing leaf nitrogen concentration from hyperspectral data of dry and fresh leaves. The primary objective of this study was to determine typical optimal bands for leaf nitrogen estimation from spectra (400–2500 nm) of whole fresh and dry leaves for the same specimens of Eucalyptus grandis. This was achieved via the use of competitive adaptive re-weighted sampling (CARS), and Monte Carlo cross-validation-competitive adaptive re-weighted sampling (MCCV-CARS) band selection approaches. Bands selected (931 nm, 1003 nm, 1027 nm, 1036 nm, 1177 nm, and 1180 nm) via the MCCV-CARS approach yielded the highest estimation accuracy for both fresh predicted coefficient of determination (R²_cal) = 0.82 and predicted root mean square error (RMSE_P) = 0.14) and dry leaves (R²_P = 0.88 and RMSE_P = 0.13) when compared to CARS (2044 nm, 2107 nm, and 2188 nm) only. The identified spectral features could be relevant for assessing leaf nitrogen concentration for different seasons, for example, wet to dry season.     

Response of reflectance to dielectric properties of bare tills

Parent tills are routinely exposed as a result of mechanical sitepreparation during post-harvest forest regeneration in northern Fennoscandia. Scots pine (Pinus sylvestris L.), the species most often chosen for artificial reforestation, only thrives on sites with low soil moisture content (θ_v ). Hence objective methods are needed to measure θ_v of bare tills to provide information on suitability of a site for pine. We studied the relationship between the spectral reflectance (350–2500?nm) and dielectric permittivity (?, as dependent on the soil θ_v ) of tills varying in clay fraction content (2.4–5.5%), fine fraction content (23.5–47.1%) and organic matter content (OMC, 0.6–5.8%). Laboratory measured data, analysed with correlation and regression analysis and mixed effect modelling, showed a significant negative correlation between reflectance (500–2500?nm) and the soil ? (i.e. soil θ_v ). In addition, the proposed generic exponential models (y=ae^bx +c) explained the reflectance–soil ? relationship well (adjusted goodness of fit 0.8–0.85) for tills with low OMC (<1.7%). The results suggest that high-resolution remotely sensed data can provide an effective alternative to traditional soil surveys for recognition of soil θ_v patterns on clear-cut mechanically prepared sites.     

土壤重金属Cu含量遥感反演的波段选择与最佳光谱分辨率研究

高光谱数据以其高光谱分辨率和多而连续的光谱波段为预测土壤重金属污染提供了有力工具,但波段选择方法与光谱分辨率的影响不容忽视。利用实验室测定的181个土壤光谱样本数据,利用逐步回归法进行土壤Cu含量反演的波段选择,进而利用偏最小二乘方回归PLSR方法建模,分析了波段数对Cu含量反演的影响;此外,采用高斯响应函数重采样方法,探讨了光谱分辨率降低对反演精度的影响。实验表明,预测重金属元素Cu含量的最佳波段数为10个,模型可决系数R2=0.7523,拟合均方根误差RMSE=0.4699;预测Cu含量的最佳光谱采样间隔为32 nm,R2=0.7028,RMSE=0.5147。该结果可能为将来设计低廉实用的高光谱卫星传感器提供指标论证,为模拟卫星传感器波段预测土壤重金属含量提供理论依据。     

Mapping of heavy metal pollution in stream sediments using combined geochemistry, field spectroscopy, and hyperspectral remote sensing: A case study of the Rodalquilar mining area, SE Spain

The aim of this study is to derive parameters from spectral variations associated with heavy metals in soil and to explore the possibility of extending the use of these parameters to hyperspectral images and to map the distribution of areas affected by heavy metals on HyMAP data. Variations in the spectral absorption features of lattice OH and oxygen on the mineral surface due to the combination of different heavy metals were linked to actual concentrations of heavy metals. The ratio of 610 to 500 nm (R_610,500 nm) in the visible and near-infrared (VNIR) range, absorption area at 2200 nm (Area_2200 nm), and asymmetry of the absorption feature at 2200 nm (Asym_2200 nm) showed significant correlations with concentrations of Pb, Zn, and As, respectively. The resulting spectral gradient maps showed similar spatial patterns to geochemical gradient maps. The ground-derived spectral parameters showed a reliable quantitative relationship with heavy metal levels based on multiple linear regression. To examine the feasibility to applying these parameters to a HyMAP image, image-derived spectral parameters were compared with ground-derived parameters in terms of R², one-way ANOVA, and spatial patterns in the gradient map. The R_1344,778 nm and Area_2200 nm parameters showed a weak relationship between the two datasets (R² > 0.5), and populations of spectral parameter values, Depth_500 nm, R_1344,778 nm, and Area_2200 nm derived from the image pixels were comparable with those of ground-derived spectral parameters along a section of the stream channel. The pixels classified in the rule image of Depth_500 nm, R_1344,778 nm, and Area_2200 nm derived from a HyMAP image showed similar spatial patterns to the gradient maps of ground-derived spectral parameters. The results indicate the potential applicability of the parameters derived from spectral absorption features in screening and mapping the distribution of heavy metals. Correcting for differences in spectral and spatial resolution between ground and image spectra should be considered for quantitative mapping and the retrieval of heavy metal concentrations from HyMAP images.     

Scaling-based forest structural change detection using an inverted geometric-optical model in the Three Gorges region of China

We use the Li-Strahler geometric-optical model combined with a scaling-based approach to detect forest structural changes in the Three Gorges region of China. The physical-based Li-Strahler model can be inverted to retrieve forest structural properties. One of the main input variables for the inverted model is the fractional component of sunlit background, which is calculated by using pure reflectance spectra (endmembers) of surface components. In this study, we extract these endmembers from moderate spatial resolution MODIS data using two scaling-based methods (namely, a regional based linear unmixing and a purest-pixel approach) relying on corresponding high spatial resolution Landsat TM images. Then, the forest structural property crown closure (CC) is estimated by inverting the Li-Strahler model based on the extracted endmembers. Changes in CC are mapped using MODIS mosaics dated 2002 and 2004 for the whole Three Gorges region. Validation of the estimated CC using 25 sample sites indicates that the regional scaling-based endmembers extracted using linear unmixing are more suitable to be used in combination with the inverted Li-Strahler model for monitoring the forest CC than the purest-pixel approach, and results in significantly better estimates in both years (R²₂₀₀₂ = 0.614, RMSE₂₀₀₂ = 6%, R²₂₀₀₄ = 0.631 and RMSE₂₀₀₄ = 5.2%). A change detection map of the model derived CC in 2002 and 2004 shows a decrease in CC in the eastern counties of the Three Gorges region located close to the Three Gorges Dam. An increase in CC has been observed in other counties of the Three Gorges region, implying a preliminary positive feedback on certain policy measures taken safeguarding forest structure.     

Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff

This study investigated the effects of upstream stations’ flow records on the performance of artificial neural network (ANN) models for predicting daily watershed runoff. As a comparison, a multiple linear regression (MLR) analysis was also examined using various statistical indices. Five streamflow measuring stations on the Cahaba River, Alabama, were selected as case studies. Two different ANN models, multi layer feed forward neural network using Levenberg–Marquardt learning algorithm (LMFF) and radial basis function (RBF), were introduced in this paper. These models were then used to forecast one day ahead streamflows. The correlation analysis was applied for determining the architecture of each ANN model in terms of input variables. Several statistical criteria (RMSE, MAE and coefficient of correlation) were used to check the model accuracy in comparison with the observed data by means of K-fold cross validation method. Additionally, residual analysis was applied for the model results. The comparison results revealed that using upstream records could significantly increase the accuracy of ANN and MLR models in predicting daily stream flows (by around 30%). The comparison of the prediction accuracy of both ANN models (LMFF and RBF) and linear regression method indicated that the ANN approaches were more accurate than the MLR in predicting streamflow dynamics. The LMFF model was able to improve the average of root mean square error (RMSE_ave) and average of mean absolute percentage error (MAPE_ave) values of the multiple linear regression forecasts by about 18% and 21%, respectively. In spite of the fact that the RBF model acted better for predicting the highest range of flow rate (flood events, RMSE_ave/RBF = 26.8 m³/s vs. RMSE_ave/LMFF = 40.2 m³/s), in general, the results suggested that the LMFF method was somehow superior to the RBF method in predicting watershed runoff (RMSE/LMFF = 18.8 m³/s vs. RMSE/RBF = 19.2 m³/s). Eventually, statistical differences between measured and predicted medians were evaluated using Mann-Whitney test, and differences in variances were evaluated using the Levene's test.     

Mixed Discontinuous Galerkin Finite Element Method for the Biharmonic Equation

In this paper, we first split the biharmonic equation Δ² u=f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v=Δu and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation v _h of v can easily be eliminated to reduce the discrete problem to a Schur complement system in u _h , which is an approximation of u. A direct approximation v _h of v can be obtained from the approximation u _h of u. Using piecewise polynomials of degree p≥3, a priori error estimates of u−u _h in the broken H ¹ norm as well as in L ² norm which are optimal in h and suboptimal in p are derived. Moreover, a priori error bound for v−v _h in L ² norm which is suboptimal in h and p is also discussed. When p=2, the preset method also converges, but with suboptimal convergence rate. Finally, numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

Responses of the reflectance indices PRI and NDVI to experimental warming and drought in European shrublands along a north-south climatic gradient

The aim of this study was to evaluate the use of ground-based canopy reflectance measurements to detect changes in physiology and structure of vegetation in response to experimental warming and drought treatment at six European shrublands located along a North-South climatic gradient. We measured canopy reflectance, effective green leaf area index (green LAIe) and chlorophyll fluorescence of dominant species. The treatment effects on green LAIe varied among sites. We calculated three reflectance indices: photochemical reflectance index PRI [531 nm; 570 nm], normalized difference vegetation index NDVI₆₈₀ [780 nm; 680 nm] using red spectral region, and NDVI₅₇₀ [780 nm; 570 nm] using the same green spectral region as PRI. All three reflectance indices were significantly related to green LAIe and were able to detect changes in shrubland vegetation among treatments. In general warming treatment increased PRI and drought treatment reduced NDVI values. The significant treatment effect on photochemical efficiency of plants detected with PRI could not be detected by fluorescence measurements. However, we found canopy level measured PRI to be very sensitive to soil reflectance properties especially in vegetation areas with low green LAIe. As both soil reflectance and LAI varied between northern and southern sites it is problematic to draw universal conclusions of climate-derived changes in all vegetation types based merely on PRI measurements. We propose that canopy level PRI measurements can be more useful in areas of dense vegetation and dark soils.     

Using hyperspectral radiometry to predict the green leaf area index of turfgrass

The green leaf area index (LAI) is an important indicator of the photosynthetic capacity of turfgrass canopies. The measurement of LAI is typically destructive and requires large plots to allow for multiple sampling dates. Hyperspectral radiometry may provide a rapid, non-destructive means for estimating LAI. Our objectives were to: (1) evaluate the utility of hyperspectral radiometry to predict the LAI of Kentucky bluegrass (Poa Pratensis L.); and (2) determine regions of the spectrum that provide the best LAI predictions. An empirical prediction model of spectral data for LAI was conducted with partial least squares regression (PLSR). The PLSR method created viable, first-iteration models for five of 11 sampling dates (the coefficient of determination (R²) is 0.52–0.85). Each model had its own set of factors that were analysed to determine their ‘weights’, or specific regions of the spectrum by which they were most strongly influenced. Second iterations of each model were then created using only those regions most strongly influenced, centred on 600, 690, 761, 960, 1330, and 1420 nm (±10 nm). Four of the five second-iteration models had LAI estimation capabilities greater than or similar to the first-iteration models (R² = 0.72–0.86), indicating that the information contained in all other wavelengths was redundant or irrelevant in regard to predictions of LAI. The robustness of prediction models varied over the growing season, possibly related to changes in canopy properties with environmental conditions. Results suggest hyperspectral radiometry has a significant potential to predict LAI in turfgrass, although different models may be required throughout the growing season.     

Correlation between soil apparent electroconductivity and plant hyperspectral reflectance in a managed wetland

The apparent electrical conductivity (σ_a) of soil is influenced by a complex combination of soil physical and chemical properties. For this reason, σ_a is proposed as an indicator of plant stress and potential community structure changes in an alkaline wetland setting. However, assessing soil σ_a is relatively laborious and difficult to accomplish over large wetland areas. This work examines the feasibility of using the hyperspectral reflectance of the vegetation canopy to characterize the σ_a of the underlying substrate in a study conducted in a Central California managed wetland. σ_a determined by electromagnetic (EM) inductance was tested for correlation with in-situ hyperspectral reflectance measurements, focusing on a key waterfowl forage species, swamp timothy (Crypsis schoenoides). Three typical hyperspectral indices, individual narrow-band reflectance, first-derivative reflectance and a narrow-band normalized difference spectral index (NDSI), were developed and related to soil σ_a using univariate regression models. The coefficient of determination (R ²) was used to determine optimal models for predicting σ_a, with the highest value of R ² at 2206 nm for the individual narrow bands (R ²?=?0.56), 462 nm for the first-derivative reflectance (R ²?=?0.59), and 1549 and 2205 nm for the narrow-band NDSI (R ²?=?0.57). The root mean squared error (RMSE) and relative root mean squared error (RRMSE) were computed using leave-one-out cross-validation (LOOCV) for accuracy assessment. The results demonstrate that the three indices tested are valid for estimating σ_a, with the first-derivative reflectance performing better (RMSE?=?30.3 mS m^?1, RRMSE?=?16.1%) than the individual narrow-band reflectance (RMSE?=?32.3 mS m^?1, RRMSE?=?17.1%) and the narrow-band NDSI (RMSE?=?31.5 mS m^?1, RRMSE?=?16.7%). The results presented in this paper demonstrate the feasibility of linking plant–soil σ_a interactions using hyperspectral indices based on in-situ spectral measurements.     

Spectroscopic determination of leaf water content using continuous wavelet analysis

The gravimetric water content (GWC, %), a commonly used measure of leaf water content, describes the ratio of water to dry matter for each individual leaf. To date, the relationship between spectral reflectance and GWC in leaves is poorly understood due to the confounding effects of unpredictably varying water and dry matter ratios on spectral response. Few studies have attempted to estimate GWC from leaf reflectance spectra, particularly for a variety of species. This paper investigates the spectroscopic estimation of leaf GWC using continuous wavelet analysis applied to the reflectance spectra (350-2500 nm) of 265 leaf samples from 47 species observed in tropical forests of Panama. A continuous wavelet transform was performed on each of the reflectance spectra to generate a wavelet power scalogram compiled as a function of wavelength and scale. Linear relationships were built between wavelet power and GWC expressed as a function of dry mass (LWC_D) and fresh mass (LWC_F) in order to identify wavelet features (coefficients) that are most sensitive to changes in GWC. The derived wavelet features were then compared to three established spectral indices used to estimate GWC across a wide range of species.Eight wavelet features observed between 1300 and 2500 nm provided strong correlations with LWC_D, though correlations between spectral indices and leaf GWC were poor. In particular, two features captured amplitude variations in the broad shape of the reflectance spectra and three features captured variations in the shape and depth of dry matter (e.g., protein, lignin, cellulose) absorptions centered near 1730 and 2100 nm. The eight wavelet features used to predict LWC_D and LWC_F were not significantly different; however, predictive models used to determine LWC_D and LWC_F differed. The most accurate estimates of LWC_D and LWC_F obtained from a single wavelet feature showed root mean square errors (RMSEs) of 28.34% (R² = 0.62) and 4.86% (R² = 0.69), respectively. Models using a combination of features resulted in a noticeable improvement predicting LWC_D and LWC_F with RMSEs of 26.04% (R² = 0.71) and 4.34% (R² = 0.75), respectively. These results provide new insights into the role of dry matter absorption features in the shortwave infrared (SWIR) spectral region for the accurate spectral estimation of LWC_D and LWC_F. This emerging spectral analytical approach can be applied to other complex datasets including a broad range of species, and may be adapted to estimate basic leaf biochemical elements such as nitrogen, chlorophyll, cellulose, and lignin.     

Consensus scoring model for the molecular docking study of mTOR kinase inhibitor

The discovery of mammalian target of rapamycin (mTOR) kinase inhibitors has always been a research hotspot of antitumor drugs. Consensus scoring used in the docking study of mTOR kinase inhibitors usually improves hit rate of virtual screening. Herein, we attempt to build a series of consensus scoring models based on a set of the common scoring functions. In this paper, twenty-five kinds of mTOR inhibitors (16 clinical candidate compounds and 9 promising preclinical compounds) are carefully collected, and selected for the molecular docking study used by the Glide docking programs within the standard precise (SP) mode. The predicted poses of these ligands are saved, and revaluated by twenty-six available scoring functions, respectively. Subsequently, consensus scoring models are trained based on the obtained rescoring results by the partial least squares (PLS) method, and validated by Leave-one-out (LOO) method. In addition, three kinds of ligand efficiency indices (BEI, SEI, and LLE) instead of pIC₅₀ as the activity could greatly improve the statistical quality of build models. Two best calculated models 10 and 22 using the same BEI indice have following statistical parameters, respectively: for model 10, training set R² = 0.767, Q² = 0.647, RMSE = 0.024, and for test set R² = 0.932, RMSE = 0.026; for model 22, raining set R² = 0.790, Q² = 0.627, RMSE = 0.023, and for test set R² = 0.955, RMSE = 0.020. These two consensus scoring model would be used for the docking virtual screening of novel mTOR inhibitors.     

Evaluating the severity level of cotton Verticillium using spectral signature analysis

High spatial or spectral resolution remote sensing might be an efficient method for estimating Verticillium wilt incidence in cotton. The objectives of this study were to characterize leaf spectra and the physiological and biochemical parameters of cotton (Gossypium hirsutum) damaged by Verticillium dahliae Kleb. (simply, Verticillium) to determine the wavelengths of those leaves that were most responsive to cotton with Verticillium and to develop a spectral model to predict the severity levels (SLs) of Verticillium through evaluation of the SLs of cotton leaves with Verticillium at different growth stages using reflectance and the first derivative (FD) spectrum. The study revealed that the values of the physiological and biochemical parameters all gradually decreased with increasing SLs in cotton leaves infected with Verticillium. The spectral characteristics of cotton leaves infected with Verticillium were significant compared to healthy ones. The reflectance of cotton leaves increased with increasing SLs of SLs disease in the range of 400–2500 nm (excluding 700–900 nm). The values of FD spectrum changed significantly at the red edge of the chlorophyll absorption feature (680–740 nm). The wavelength position of the red edge shifted towards shorter wavelengths and the red-edge swing decreased with respect to increasing SLs. From this study, the raw spectral bands of 437–724 and 909–2500 nm and the FD spectra bands of 535–603 and 699–750 nm can be selected as sensitive bands for estimating the SLs of disease in cotton leaves. Inversion models have been established to estimate the SLs of cotton leaves infected with Verticillium. Of all models, the model of R _700nm/R _825nm was superior for quantitatively estimating the disease SLs of cotton leaves infected with Verticillium in practice: its root mean square error (RMSE) was 0.866 and relative error (RE) was only 0.012. Thus, both the selected wavelength ranges and the chosen reflectance models were good indicators of damage caused by Verticillium to cotton leaves. The results provide theoretical support for large-scale monitoring of cotton infected with Verticillium by air- and spaceborne remote sensing.     

Exploring the potential of leaf reflectance spectra for retrieving the leaf maximum carboxylation rate

The maximum carboxylation rate (V_cmax) is a key photosynthetic parameter that is determined by the leaf biochemistry and environmental conditions. Numerous studies have shown that plant biochemical, physiological and structural parameters can be estimated from reflectance spectra. Therefore, it is reasonable to assume that V_cmax can be spectrally determined. Here, we investigate the potential of leaf reflectance spectra for retrieving the maximum carboxylation rate of leaves. Measurements of leaf reflectance, carbon dioxide (CO₂) response curves, leaf chlorophyll-a + b (chl-a + b) etc., were made on 80 crop, shrub and tree leaves. Then, the leaf V_cmax,25 was linked to leaf biochemistry and spectral reflectance. A reliable relationship, with a coefficient of determination (R²) value of 0.75, was found between the leaf chl-a + b content and V_cmax,25. The leaf V_cmax,25 values were also significantly correlated with chl-a + b-sensitive spectral indices with the highest R² value that was found being 0.83 for the ratio spectral index (RSI) using reflectances at 1089 nm and 695 nm. Finally, multiple stepwise regression (MSR) and a partial least-squares regression (PLSR) modelling approach were used to estimate V_cmax,25 from leaf reflectances. The results confirmed that V_cmax,25 can be reliably estimated from leaf reflectance spectra and give an R² value >0.80. These findings show that leaf chl-a + b can be used as a proxy for leaf V_cmax,25 and that leaf V_cmax,25 can be spectrally determined using leaf reflectance data.     

Predicting C3 and C4 grass nutrient variability using in situ canopy reflectance and partial least squares regression

The use of hyperspectral data to estimate forage nutrient content can be a challenging task, considering the multicollinearity problem, which is often caused by high data dimensionality. We predicted some variability in the concentration of limiting nutrients such as nitrogen (N), crude protein (CP), moisture, and non-digestible fibres that constrain the intake rate of herbivores. In situ hyperspectral reflectance measurements were performed at full canopy cover for C3 and C4 grass species in a montane grassland environment. The recorded spectra were resampled to 13 selected band centres of known absorption and/or reflectance features, WorldView-2 band settings, and to 10 nm-wide bandwidths across the 400–2500 nm optical region. The predictive accuracy of the resultant wavebands was assessed using partial least squares regression (PLSR) and an accompanying variable importance (VIP) projection. The results indicated that prediction accuracies ranging from 66% to 32% of the variance in N, CP, moisture, and fibre concentrations can be achieved using the spectral-only information. The red, red-edge, and shortwave infrared (SWIR) wavelength regions were the most sensitive to all nutrient variables, with higher VIP values. Moreover, the PLSR model constructed based on spectra resampled around the 13 preselected band centres yielded the highest sensitivity to the predicted nutrient variables. The results of this study thus suggest that the use of the spectral resampling technique that uses only a few but strategically selected band centres of known absorption or reflectance features is sufficient for forage nutrient estimation.     

Spectral slope based analysis and classification of stressed speech

In this study, spectral slope based features are investigated for characterization and classification of stressed speech. The vocal tract spectrum is modulated with glottal flow spectra, resulting a tilt in the overall spectrum. In this study, spectral tilt is analyzed for different stress classes. Relative formant peak displacement (RFD) is proposed as the displacement of formant peaks from the 1 ^st formant peak. The displacement of 2 ^nd , 3 ^rd and 4 ^th formant peaks from 1 ^st formant peak is termed as RFD ₂, RFD ₃ and RFD ₄, respectively. The features are extracted from linear prediction coefficient (LPC) and cepstrally smoothed log spectrum, respectively. Analysis shows that stress effects higher formant region more than lower formant region. To evaluate the effectiveness of this feature for different stress classes, the performance of stress classification is evaluated. A simulated stressed speech database is collected under four stress conditions, namely, neutral, angry, sad and Lombard from fifteen speakers. The performance of RFD feature is similar to Mel-frequency cepstral coefficient (MFCC). This shows that RFD feature have approximately same discrimination capability for stress as MFCC. Further, the performance of cepstrally smoothed log spectra derived RFD are higher than LPC derived RFD feature. RFD features are combined with MFCC in feature, score and rank level and found improved performance.     

Using the artificial neural network model for modeling the performance of the counter flow vortex tube

In this study, the effect of the nozzle number and the inlet pressure on the heating and cooling performance of the counter flow type vortex tube has been modeled with artificial neural networks (ANN) by using the experimentally obtained data. ANN has been designed by Pithiya software. In the developed system output parameter temperature gradient between the cold and hot outlets (ΔT) has been determined using inlet parameters such as the inlet pressure (P_inlet), nozzle number (N), and cold mass fraction (μ_c). The back-propagation learning algorithm with variant which is Levenberg–Marquardt (LM) and Fermi transfer function have been used in the network. In addition, the statistical validity of the developed model has been determined by using the coefficient of determination (R²), the root means square error (RMSE) and the mean absolute percentage error (MAPE). R², RMSE and MAPE have been determined for ΔT as 0.9947, 0.188224, and 0.0460, respectively.