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Sluice gates are commonly used to measure water discharge and to adjust the water level in open canals. Sluice gates can also be used at the crest of dam spillways for controlling floods. Estimation of head loss (∆E/E₀) and discharge coefficients (C_d) for a sluice gate is essential for the design of open canals. Depending on the downstream water level, free or submerged flow conditions may occur. Although there have been some investigations on C_d for sluice gates, a comprehensive literature review shows that there are no studies of ∆E/E₀ (to the best knowledge of the authors). Knowledge of ∆E/E₀ is necessary for the design of intakes and irrigation canal inverts. This study uses the physical model of sluice gate to introduce helpful charts for energy loss estimation. Experiments were conducted in the University of Tabriz, department of water engineering. A rectangular canal with length of 12 m, width of 0.5 m and height of 0.8 m was used. Vertical slide gate was installed at the 6 m from canal inlet to permit flow become uniform. Water circulation is carried out using a submerged pump. Water is pumped in a 4.5 m head tank and then inters to canal with pipes. Water level/depth was measured with a point gauge with 0.1 mm accuracy. Discharge was measured with a calibrated rectangular sharp crested weir. Experiments were carried out with different discharges and gate opening. Results show that ∆E for free flow is greater than that for submerged flow conditions. Meanwhile, discharge coefficients in a free flow are greater than those under submerged flow conditions. Relative energy losses (∆E/E₀) have a minimum value of 0.271 and a maximum value of 0.604. These high energy losses cannot be ignored in intake structures and canal-designing processes and their impact on minor canal inverts receiving water from main canals should be considered. The relative energy loss changed from the minimum value of 0.271 to the maximum value of 0.604. Multivariate regression method was used to calculate the relative energy loss and the average of the residuals was -0.004. The maximum and minimum residuals for ∆E/E₀ are 5 and -0.31, respectively. A mathematical equation with a coefficient of determination of 0.925 was presented to separate the boundary of free flow from submerged flow. To estimate the discharge coefficient in submerged flow, a mathematical equation was obtained. For this equation, the average of the residuals was -0.004. The maximum and minimum residuals for the discharge coefficient are -0.084 and 0.116, respectively. Application of multiple non-linear regression (MNR) models are presented for predicting ∆E/E₀ and C_d. The high energy losses cannot be ignored in intake structures and canal designing processes. Their impact on minor canal inverts receiving water from main canals should be considered. Application of MNR was presented from a simple equation to more sophisticated equations by improving regression relations in each step. The MNR method provides accurate equations for predicting performance for both ∆E and C_d.

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Directional felling of trees plays a key role in reducing of damages to forest residual trees and can also facilitate skidding. The aim of this study was presents a practical linear model for estimation of tree falling direction error in an uneven-aged mixed stand in northern forests of Iran. To conduct the study a number of 95 trees of four species Fagus Orientalis Lipsky, Carpinus Betulus L., Alnus Subcordata C.A. May and Acer Platanoides were randomly selected,and assumed felling direction were  marked on the trunk of these trees. The trees felled by experienced chainsaw operators, and the differences between the assumed and actual direction were measured as the felling error. The results showed that among the 12 effective factors, the elements of foot slope, diameter at the breast height (DBH), horizontal and vertical angles and area of the backcut surface (HABS, VABS, BA),vertical angle and area of undercut surface (VAUS, UA) significantly correlated with the felling error, and the determination coefficient (R²) of presented linear model was 52.0 % (P < 0.01). Among the model factors, DBH, VABS, and HABS had the three most pronounce impact on felling error.

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Background: Soil salinization is a world-wide land degradation process in arid and semi-arid regions that leads to sever economic and social consequences.
Materials and Methods: We analyzed soil salinity by two statistical linear (multiple linear regression) and non-linear (artificial neural network) models using Landsat OLI data in Agh-Ghala plain located in north east of Iran. In situ soil electrical conductivity (EC) of 156 topsoil samples (depth of 0-15cm) was also determined. A Pearson correlation between 26 spectral indices derived from Landsat OLI data and in situ measured ECs was used to apply efficient indices in assessing soil salinity. The best correlated indices such as blue, green and red bands, intensity indices (Int1, Int2), soil salinity indices (Si1, Si2, Si3, Si11, Aster-Si), vegetation Indices (NDVI, DVI, RVI, SAVI), greenness and wetness indices were used to develop two models.
Results: Comparison between two estimation models showed that the performance of ANN model (R²=0.964 and RMSE=2.237) was more reliable than that of MLR model (R²=0.506 and RMSE=9.674) in monitoring and predicting soil salinity. Out of the total area, 66% and 55.8% was identified as non-saline, slightly and very slightly saline for ANN and MLR models, respectively.
Conclusions: This shows that remote sensing data can be effectively used to model and map spatial variations of soil salinity. 

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Aims: Soil organic carbon (SOC) is contemplated as a crucial proxy to manage soil quality, conserve natural resources, monitoring CO2 and preventing soil erosion within the landscape, regional, and global scale. Therefore, the main aims of this study were to (1) determine the impact of terrain derivatives on the SOC distribution and (2) compare the different algorithms of topographic wetness index (TWI) calculation for SOC estimation in a small-scale loess hillslope of Toshan area, Golestan province, Iran. (3) Comparison between multiple linear regression (MLR) and artificial neural networks (ANN) methods for SOC prediction.
Materials & Methods: total of 135 soil samples were taken in different slope positions, i.e., shoulder (SH), backslope (BS), footslope (FS), and toeslope (TS). Primary and secondary terrain derivatives were calculated using digital elevation model (DEM) with a spatial resolution of 10 m × 10 m. To SOC estimation (dependent variable) was applied two models, i.e., MLR and ANN with terrain derivatives as the independent variables.
Findings: The results showed significant differences using Duncan’s test in where TS position had the higher mean value of SOC (25.90 g kg⁻¹) compared to SH (5.00 g kg⁻¹) and BS (12.70 g kg⁻¹) positions. The present study also revealed which SOC was more correlated with TWIMFD (Multiple-Flow-Direction) and TWIBFD (Biflow-Direction) than TWISFD (Single Flow Direction). The MLR and ANN models were validated by additional samples (25 points) that can be explain 65% and 76% of the total variability of SOC, respectively, in the study area.
Conclusion: These results indicated that the use of terrain derivatives is a beneficial method for SOC estimation. In general, an accurate understanding of TWIMFD is needed to better estimate SOC to evaluate soil and ecosystem related effects on global warming of as this hilly region at a larger scale in a future study.

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In the present study variation of air relative humidity at the inlet and outlet of a cabinet dryer as well as drying kinetic of pear fruit in thin layer were studied.  The experiments were conducted at three temperature levels of 40, 50 and 60^oC and three air velocity levels of 0.5, 1 and 1.5 m/s. It was observed that the difference between input and output air relative humidity increased when drying temperature was increased. This difference followed declining trend at the same level of drying temperature when air velocity was increased. If drying at lower air temperature and higher velocity is desired, for optimum use of energy, a closed loop drying method is appropriate. Otherwise, increasing in air temperature and decreasing in air velocity is recommended. Eight mathematical models were fitted on drying data and the best one was selected according to coefficient of determination (R²) and Chi-square (χ²) statistics for 70 percent of data. The model then validated by statistics of root mean square of error (RMSE), mean bias of error (MBE) and mean relative error (ARE) for 30 percent of remaining data. The approximation of diffusion model with highest R² (0.998), and lowest χ² (0.0001), RMSE (0.01), MBE (0.0008) and ARE (5.2%) was found an appropriate model for estimating the kinetics of thin layer drying of pear cubes drying in a cabinet dryer.  

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Ttriangulation technique is one of the most commonly techniques used in three dimensional measurements. Hardware and software used in 3D scanning systems are main error sources affected the accuracy of scanners. Depth reconstruction accuracy is a direct impact of the quantization process, and so it is related to the pixel size of the sensor. Dithering technique may be used to reduce the errors during quantization. The current study introduces a technique in which a relative fine movement between object and sensor is generated during picture capture. Although, using this technique will improve the accuracy of scanning but changing the hardware set up during the process is also time consuming. So to deal with this problem the dithering technique is simulated using the linear regression to reduce the scanning time. The paper firstly describes the theory of the noise introduction technique followed by modeling and simulation of the process by regression function. The results obtained from simulation show great improvement in measurement accuracy. To evaluate the result in a real world, a control rig was designed and built following which experiment was performed. The results showed considerable improvement in measurement accuracy. The result of both simulation and experiments are reported.

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The aim of this study was to explore the minimum amount of urea formaldehyde (UF) resin content and optimum particleboard density while maintaining boards’ quality to reduce production costs. Board density at three levels (520, 620 and 720 kg m^-3) and resin content (6, 7 and 8%) were variable parameters. Stepwise multivariate linear regression models were used to evaluate the influence of board density and resin content on board properties and to determine the most effective parameter. In order to obtain the optimum board density and minimum resin content, contour plots were drawn. Regression models indicated that both board density and resin content were included in Modulus of Rupture (MOR) and Modulus of Elasticity (MOE) models based on the degree of their importance. Internal Bond (IB) model only had one step and resin content positively affected it. The results obtained from contour plots revealed that manufacturing poplar particleboards with density ranging from 600 to 650 kg m^-3 and 6% resin would result in boards with mechanical properties within those required by the corresponding standard. Thickness swelling (TS) values were slightly higher (poorer) than the requirements. The panels required additional treatments such as using adequate amount of water resistant materials to improve thickness swelling after 2 and 24 hours of immersion.

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The objectives of this study were to identify a suitable mathematical model for describing the growth curve of Baluchi sheep based on monthly records of live weight from birth to yearling; and to evaluate the efficacies of nonlinear mixed effect model (NLMM) and the nonlinear fixed effect model (NLM) methodologies. Growth models were fitted to a total of 16,650 weight–age data belonging to 2071 lambs. Five nonlinear growth functions of von Bertalanffy, Gompertz, Brody, Logistic, and Richards and two linear polynomial functions were applied. The growth models were compared by using the Akaike’s information criterion (AIC) and residual mean square (MSE). Among all nonlinear fixed effect models, the Brody function had the smallest AIC and MSE values, indicating the best fit for both sexes. The Brody fixed effect model compared with NLMM including one random effect of asymptotic mature weight. The model evaluation criteria indicated that the Brody mixed effect model fitted the data better than the corresponding fixed effect model. It can be concluded that, among the linear models, the polynomial of the third order and, among nonlinear models, Brody mixed model were found to best fit the Baluchi sheep growth data.

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The use of different synthetic dyes in textile industries has increased in recent decay, resulting in the release of dye-containing industrial effluents into natural aquatic ecosystem. Since most of dyes are usually very recalcitrant to microbial degradation, therefore dye removal from effluent is a main concern in many studies. Different process was used for the treatment of dye effluent. In the last few years, studies were focused on advanced oxidation process (AOPs) methods such as UV-ZnO, UV-H2O2, UV-O3 and UV-TiO2. Photocatalytic process such as UV-ZnO is an efficient method that treats non-degradable wastewater by active radicals. The photocatalysis needs a photo-reactor that contacts reactant, products and light. In recent years, different types of photo-reactors have been used for wastewater treatment. In some reactors, nano-photocatalysts are utilized in slurry form, and the other particles are coated on bed. In Photocatalytic reactors with fixed bed, nano-photocatalysts are immobilized on bed and do not need the separation unit, but the main disadvantage of this photo-reactors is the low mass transfer rate between wastewater and nano-photocatalysts. Consequently, Different optimal photo-reactors were developed for increasing mass transfer rate. In this study, a novel photocatalytic cascade disc reactor coated with ZnO nano-photocatalysts was applied and in order to increase mass transfer rate artificial roughness were created on the surface of disks. Applying artificial roughness changes mass transfer rate by providing vertical mixing, creating secondary currents and increasing the Reynolds number. This photo-reactor has a number of advantages that include eliminating the need for catalyst separation units as the catalyst is immobilized, creating the flow mixing by non-mechanical method, increasing the transport of oxygen from the gas phase to the photocatalyst surface by providing the flow cascade pattern. The photo-reactor was used in order to remove Reactive Yellow 81 (RY81) dye from textile industry effluent, by means of UV-ZnO process. RY81 is a reactive dye composed of 10 Benzene rings and two –N=N azo bonds. The effect of different operational parameters such as initial Concentration of dye, pH, Catalyst surface loading and flow rate in removal efficiency was investigated, and the optimal value of those parameters were 50 mg/L, 8, 40 gr/m2 and 80 cc/s, respectively. A rate equation for the removal of RY81 was obtained by mathematical kinetic modeling. The Langmuir-Hinshelwood kinetic model is one of the most common kinetic models that are used for studying the kinetics of heterogeneous photo-catalysis. The results of reaction kinetic modeling indicate the conformity of removal kinetics with Langmuir-Hinshelwood model, and the constants kL-H and Kads were obtained 7.17 mg L-1 hr-1, 0.122 mg-1 L, respectively.
One way of inserting various operational parameters to a rate equation is regression analysis. Therefore, in this study, nonlinear regression model was developed for prediction pseudo- first order rate constant as a function of initial concentration of dye, pH, catalyst surface loading and flow rate. This equation could properly predict (R2=0.95) the removal rate constant of RY81 removal in the photocatalytic cascade disk reactor under different operational conditions and a good consistency was observed between the calculated results and experimental findings.

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Nowadays, the world is facing to increasing loss of fossil resources, energy crisis and environmental problems. On the other hand, diesel engines due to wide application in various sectors such as transport, agriculture, industry, etc., are the main sources of emissions and fuel consumption. Accurate measurement of fuel consumption and engine pollution is time-consuming and costly. Hence, the main objective of this study was to develop proper linear regression models of some important performance parameters of ITM285 tractor engine based on engine torque and engine speed. Experiments were carried out in 11 levels of primary engine speed (1063, 1204, 1346, 1488, 1629, 1771, 1818, 1913 and 2054 rpm) by 10 N.m steps of torque from zero (no load) to full load. The measured parameters include fuel consumption mass flow, exhaust temperature, instantaneous engine speed, maximum and mean exhaust opacities. Four different linear regression models were used to estimate the parameters. The results of regression models performance evaluation showed that quadratic model had the highest efficiency and the lowest RMSE for all parameters. The maximum and minimum effects of engine torque were on exhaust temperature and instantaneous engine speed, respectively; while, this result was completely reverse for primary engine speed. The results of regression models evaluation showed a high adaptation between the output of each model and the desired output. Also, the fuel mass flow and exhaust temperature were highly correlated to the maximum and mean exhaust opacity with correlation coefficients of 0.96 and 0.99, respectively.

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Solar radiation data play an important role in solar energy relevant researches. These data are not available for some locations due to the absence of the meteorological stations. Therefore, solar radiation data have to be predicted by using solar radiation estimation models. This study presents an integrated Artificial Neural Network (ANN) approach for estimating solar radiation potential over Iran based on geographical and meteorological data. For this aim, the measured data of 31 stations spread over Iran were used to train Multi-Layer Perceptron (MLP) neural networks with different input variables, and solar radiation was the output. The accuracy of the models was evaluated using the statistical indicators of Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and Correlation Coefficient (R); hence, the best model in each category was identified. The Stepwise Multi NonLinear Regression (MNLR) method was used to determine the most suitable input variables. The results obtained from the ANN models were compared with the measured data. The MAPE and RMSE were found to be 2.98% and 0.0224, respectively. The obtained R value was about 99.85% for the testing data set. The results testify to the generalization capability of the ANN model and its excellent ability to predict solar radiation in Iran.

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Trip generation is the first stage of the conventional four-step travel forecasting framework that estimates the number of trips to and from a traffic analysis zone. Using linear regression model is common in this step and generates an acceptable level of performance from the perspective of transport planning, however this model does not incorporate traveler behavior, integer and non-negative nature of trips. To overcome these limitation, several models have been suggested: censored model such as Tobit for deleting negative values; count data models such as negative binomial and Poisson for deleting continuous and negative values; and discrete choice models such as ordered logit and probit for incorporating traveler behavior and preventing continuous and negative values. Given the importance of trip generation stage and lack of sufficient and quantitive attention to various trip production models, this paper develops alternative trip production models. The purpose of this paper is a structural analysis for various trip production models and comparison of their performance in prediction. Four representative models (regression, Tobit, Poisson and ordered logit) are applied to the educational trips in Qazvin city. The modeling unit employed in this study is the household. Sample is included econometric- social attributes 4734 houshols. 85% of the data used for estimation and the rest to validation. The models are assessed by how closely they are able to replicate trips ,made by each household in the estimation and validation dataset. in order to compare the performance of models in prediction, each of the models is developed on estimation dataset, and the models are used to predict the trips made by each household in validation and estimation dataset. Measures assessing how well the predicted number of trips made daily by each houshold by each of the models compared to the observed number of trip made by the houshold are evaluated and compared. The four measure for assessing performance are the mean absolute error, regression of the predicted number of household- trips against the observed number of household trip in term of goodness of fit and coefficient of determination, and compare plot of observed and predicted aggregate trip shares. In order to modeling is used stata software. The result show that, In every four models, number of school students, number of university students, and household car ownership have been statistically significant. The performance of each of the models are different in term of various measures (mean absolute error, regression of the predicted number of household- trips against the observed number of household trip in term of goodness of fit and coefficient of determination, and compare plot of observed and predicted aggregate trip shares).From mean absolute error perspective, ordered Logit and linear regression models have the best performance, but from goodness of fit regression of the predicted number of household- trips against the observed number of household trip, Tobit models have the best performance. Ordered Logit models have the best performance in terms of coefficient of determination of the predicted number of household- trips against the observed number of household trip and comparision of predicted share of every trip rate level with observed share. The performance of each of the models are similar in prediction of validation and estimation dataset.

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One of the most important pollutants that its surveillance in the atmosphere by remote sensing is possible is the suspended particles density using the MODIS sensor images. In the analyzing related to pollution study, the studies of distribution and relation between variables have an important role that the regression analyzing applications in these studies is inevitable. The main goals of this paper is preparing the particulate matter less than 10 micron distribution in Khuzestan province in both hourly/daily periods using the linear regression models the AOD product, the MODIS sensor also the ground stations data of the atmosphere pollution measurement and lateral insight of Ahvaz city in 2009 in order to estimating the pm10 were used. The results showed MODIS data have high accuracy to estimate the atmosphere pollutions and results indicates that the hourly period with R square 90% against daily period with R square 76% have a higher coefficient. After the model estimating correction by interpolating the produced plots by using the resultant relation in both time periods the suspended particles distribution maps were prepared. Key Word: ,MODIS,Ahvaz, suspended particles;linear regression Key Word: ,MODIS,Ahvaz, suspended particles;linear regression Key Word: ,MODIS,Ahvaz, suspended particles;linear regression Key Word: ,MODIS,Ahvaz, suspended particles;linear regression

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Organic agriculture in the Czech Republic is taking on a greater importance: the number of the organic farms is increasing and the availability of bio products is rising too. The aim of this study was to evaluate and compare the economic situation of organic, biodynamic, and conventional farms by using financial analysis indicators, performance indicators, economic efficiency indicator, and multidimensional intercompany comparison methods. Furthermore, the subsidies impact on farms’ profits, sales, and return on assets indicators by a linear regression model with AR (AutoRegressive 1) process was analyzed. A total of 389 Czech farms receiving subsidies from 2007 to 2012 were selected. From these, 273 farms were conventional, 112 organic, and 4 biodynamic. Organic farms were the most profitable and got the best results on the economic efficiency indicator and took the first place in the intercompany comparison. Subsidies worsen the organic farms’ economic situation, however, without statistical significance. Biodynamic farms received the highest amount of subsidies. In some years, these farms did not gain profit. Despite the worst results of economic efficiency indicator, biodynamic farms were placed as second in the intercompany comparison. Subsidies improved the biodynamic farms’ economic situation (statistically insignificant) and could play a role as a motivating factor. Conventional farms had the highest values of input and output indicators (except profit) and they received the lowest amount of subsidies. Subsidies had a statistically significantly positive effect on the profitability of these farms, though with a negative effect on sales.

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One of the concerns of designers of engineering structures is structural failure due to stress concentration caused by geometric discontinuities in the structures. Therefore, by considering that perforated composite plates are used in most engineering structures, their study is very important. The purpose of this paper is to present a new model based on the regression method for estimating stress concentration factor of a circular hole in orthotropic plates. One of the important applications of providing stress distribution around holes in terms of mechanical properties is the use of these relationships in the stress analysis of perforated viscoelastic plate using the effective modulus method or Boltzmann's superposition principle. First, using different values of the mechanical properties of the composites plates, and employing an analytical solution based on the complex variable method, the stress concentration factor of circular hole is calculated for a number of these materials. Then, using multiple linear regression, an explicit expression for the stress concentration factor is given in terms of mechanical properties. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of less than 1%.

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The construction and maintenance of structural pavement was a high-cost problem in last decade. The mechanical properties of self compacting concrete (SCC) required important factors .From its mechanical properties, the compressive strength (CS) is necessary to investigate experimental and computational intelligence analysis in construction materials. Developing models with accurate estimation for this key property caused to saving costs and time and producing an optimal blend. Because of the many advantages, using of SCC in structures is increasing. Construction of precast-prefabricated components, with the use of concrete has also recently been considered. Concrete properties have significant role in precast-prefabricated girders behavior. Exact prediction of these properties is the base of member’s analysis and design. The main purpose of this study is presents new formulation to estimate the compressive strength of self-compacting concrete containing rice husk ash (RHA) using robust variant of genetic programming, namely gene expression programming (GEP) method. To evaluate the performance of the GEP-based proposed model, prediction was also done using classical data driven methods named artificial neural network (ANN) and multiple linear regression (MLR) models.  A large and reliable experimental database containing the results of 156 compressive strength of SCC incorporating RHA is collated through an extensive review of the literature. The performance of proposed models of CS is then assessed using the database, and the results of this evaluation are presented using selected performance measures. New expressions for the estimation of CS of SCC are developed based on the database. To evaluate the modeling performances of the proposed GEP models for CS, different statistical metrics were used. Correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE) were used as the measure of precision. The results showed that the models developed using the aforementioned methods have accuracy over 90 percent in prediction of CS of SCC. The results of testing datasets are compared to experimental results and their comparisons demonstrate that the GEP model (R=0.94, RMSE= 4.308 and MAE=4.916) outperforms ANN (R=0.92, RMSE= 5.136 and MAE=5.624) and MLR (R=0.89, RMSE= 8.212 and MAE=9.472). Proposed models have a strong potential to predict compressive strength of self compacting concrete incorporating rice husk ash with great precision. The importance of different input parameters is also given for predicting the compressive strengths at various ages using gene expression programming. Performed sensitivity analysis to assign effective parameters on compressive strength indicates that cementitious binder content is the most effective variable in the mixture. The assessment results present that the performance of the proposed models are in close agreement with the experimental results. Moreover, the new GEP-based formulation provides improved estimates of the compressive strength of SCC compared to ANN and MLR models. The proposed design equation can readily be used for pre-design purposes or may be used as a fast check on deterministic solutions.
 

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Structural parameter estimation of the forests including deciduous and coniferous is required for understanding environmental cycles including Carbone cycle, hydrological cycle and etc., in a global scale, and sustainable management of the forests, in local scale. Although, the feasibility of different remotely sensed data including optical, radar and Lidar as reliable alternatives for conventional inventory methods have been frequently used for estimating forest structural parameters, the use of multi-temporal radar data have been studied less than the other options for this purpose. In this study the radar images acquired in different dates, were utilized to estimate the structural parameters of a pine plantation. For this purpose, geometric correction and speckle noise reduction methods were applied on multi-polarized Advanced Land Observing Satellite (ALOS)-Phased Array type L-band Synthetic Aperture Radar (PALSAR) data. Afterwards, different backscatter derivatives along with their corresponding textural information were extracted using grey level co-occurrence matrix (GLCM) for different window sizes and orientations. Afterwards, a stepwise multiple-linear regression was applied to model the relationship between structural parameters and synthetic aperture radar (SAR) attributes. The results indicated that the models based on multi-date SAR data performed better than those derived from single-date SAR data. Moreover, it was shown while the estimation error of mean height is 20.7%, the other parameters were estimated with error of more than 30%. Finally, the effects of slope and tree age on the estimation accuracy of structural parameters were investigated.

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Crop load regulation is vital for achieving excellence in orchards, particularly in terms of consistent yields and high-quality fruit. It also has a direct impact on tree nutrition. The objective of this study was to investigate the relationship between crop load and tree nutrition using segment linear regression models. The focus was on identifying any breakpoints in this relationship and exploring the connection between leaf nutrient contents and fruit quality characteristics. Additionally, the study aimed to determine the critical crop load level that influences biennial bearing. The research was conducted in a high-density 'Golden Delicious'/M.9 apple orchard located in the Lake Region of Turkey over three consecutive years (2013-2015). Twenty-four different crop load levels were examined to assess the impact of the number of fruits on leaf nutrient contents. The critical threshold levels were determined as follows: potassium [0.91 kg cm^-2 Trunk Cross-Sectional Area (TCSA)], phosphorus (0.96 kg cm^-2 TCSA), magnesium (0.97 kg cm^-2 TCSA), manganese (0.99 kg cm^-2 TCSA), zinc (1.0 kg cm^-2 TCSA), and iron (1.15 kg cm^-2 TCSA). This suggests that a crop load ranging from 3.71 to 4.69 fruit/cm² TCSA could be considered critical depending on the specific nutrient in tree nutrition. The results revealed significant negative correlations between leaf mineral contents and overall fruit quality characteristics. Moreover, the critical crop load threshold for biennial bearing (0.77 kg cm^-2 TCSA) was found to be lower than the nutrient threshold. Building on previous studies, this research significantly contributes by clarifying the critical crop load level at which a sudden change occurs in macro- and micro-nutrients, as well as biennial bearing.