Spatial variability in soil moisture as predicted from airborne thematic mapper (ATM) data

In the first part of this project, the extent to which moisture content of alluvial soils could be predicted from imagery derived from an airborne thematic mapper (ATM) was investigated. From sampling done on the same day as the flight, it was found that digital numbers derived from the thermal channel (waveband 11) were strongly correlated with gravimetric moisture content. From sampling three fields of contrasting land cover, the relationship between waveband 11 values and moisture content was found to be independent of land cover type. Spatial variation in waveband 11 values and thus moisture content were related to palaeochannel patterns on the alluvial land. This was investigated by deriving variograms for long transects from each of the three investigated fields. The range and sills of the variograms are shown to express the nature and pattern of palaeochannels. By the application of such geostatistical techniques, high resolution imagery can thus be used to quantify palaeochannel characteristics on alluvial land.     

Monitoring of the sediment dynamics along a sandy shoreline by means of airborne hyperspectral remote sensing and LIDAR: a case study in Belgium

Airborne hyperspectral data and airborne laserscan or LIDAR data were applied to analyse the sediment transport and the beach morphodynamics along the Belgian shoreline. Between 2000 and 2004, four airborne acquisitions were performed with both types of sensor. The hyperspectral data were classified into seven sand type classes following a supervised classification approach, in which feature selection served to reduce the number of bands in the hyperspectral data. The seven classes allowed us to analyse the spatial dynamics of specific sediment volumes. The technique made it possible to distinguish the sand used for berm replenishment works or for beach nourishments from the sand naturally found on the backshore and the foreshore. Subtracting sequential DTMs (digital terrain models) resulted in height difference maps indicating the erosion and accretion zones. The combination of both data types, hyperspectral data and LIDAR data, provides a powerful tool, suited to analyse the dynamics of sandy shorelines. The technique was demonstrated on three sites along the Belgian shoreline: Koksijde, located on the West Coast and characterized by wide accretional beaches, influenced by dry berm replenishment works and the construction of groins; Zeebrugge, on the Middle Coast, where a beach nourishment was executed one year before the acquisitions started and where the dams of the harbour of Zeebrugge are responsible for the formation of a large accretional beach, and Knokke‐Heist, located on the East Coast and characterized by narrow, locally reflective, beaches, heavily influenced by nourishment activities. The methodology applied allowed retrieval of the main sediment transport directions as well as the amount of sediment transported. It proved to be specifically suited to follow up the redistribution and the re‐sorting of the fill in beach nourishment areas. Copyright © 2007 John Wiley & Sons, Ltd.     

Lichens and mosses moisture content assessment through high‐spectral resolution remote sensing technology: a case study of the Hudson Bay Lowlands,Canada

Assessing moisture contents of lichens and mosses using ground‐based high‐spectral resolution spectrometers offers immense opportunities for a comprehensive monitoring of peatland moisture status by satellite/airborne imagery. This study investigates the impact of various moisture conditions of common subarctic lichen and moss species upon the spectral signatures obtained. The lichens are Cladina stellaris and Cladina rangiferina, and the mosses are Dicranum elongatum and Tomenthypnum nitens. Reflectance and moisture content measurements of these species were made in a laboratory setting, while maintaining the natural moisture conditions of the samples; once the moisture and spectral measurements were complete, the samples were returned to the field and placed in their natural setting, continuously receiving moisture from precipitation and groundwater and losing water through evaporation and drainage. Changes in reflectance of the visible to shortwave infrared (SWIR) range (400–2500 nm) at various moisture contents were examined, as well as the potential of current spectral reflectance indices to evaluate the plants' moisture contents was examined. Results indicate that the SWIR region is useful in identifying variations in plants moisture conditions, while the unique spectral signatures of the lichens and mosses in the visible and near‐infrared range suggest that these species may be detected by satellite and airborne imagery. Of current spectral indices, the normalized difference infrared index (NDII) was most successful in identifying the above plants' moisture content (details are discussed in the paper). Future study should focus on the development of improved moisture content spectral indices, as well as upscaling reflectance data and spectral indices. Copyright © 2010 John Wiley & Sons, Ltd.     

Investigation of submarine groundwater discharge to tidal rivers: Evidence for regional and local scale seepage

Fluxes of submarine groundwater discharge (SGD) were investigated into two tidal rivers on the north and south shore of Long Island, NY, during July 2015. Ground‐based handheld thermal infrared (TIR) imagery, combined with direct push‐point piezometer sampling, documented spatially heterogeneous small‐scale intertidal seepage zones. Pore waters were relatively fresh and enriched in nitrogen (N) within these small‐scale seeps. Pore waters sampled just 20 cm away, outside the boundary of the ground‐based TIR‐located seepage zone, were more saline and lower in N. These ground‐based TIR‐identified seeps geochemically represented the terrestrial fresh groundwater endmember, whereas N in pore waters sampled outside of the TIR‐identified seeps was derived from the remineralization of organic matter introduced into the sediment by tidal seawater infiltration. A ²²²Rn (radon‐222) time‐series was used to quantify fresh SGD‐associated N fluxes using the N endmembers sampled from the ground‐based TIR pore water profiles. N fluxes were up‐scaled to groundwater seepage zones identified from high‐resolution airborne TIR imagery using the two‐dimensional size of the airborne TIR surface water anomalies, relative to the N flux from the time‐series sampling location. Results suggest that the N load from the north‐shore tidal river to Long Island Sound is underrepresented by at least 1.6–3.6%, whereas the N load from SGD to a south‐shore tidal river may be up to 9% higher than previous estimates. These results demonstrate the importance of SGD in supplying nutrients to the lower reaches of tidal rivers and suggest that N loads in other tidal river environments may be underestimated if SGD is not accounted for.     

Development of new spectral reflectance indices for the detection of lichens and mosses moisture content in the Hudson Bay Lowlands,Canada

Assessing moisture contents of lichens and mosses using ground‐based high‐spectral resolution spectrometers offers immense opportunities for a comprehensive monitoring of peatland moisture status by satellite/airborne imagery. This study investigates the impact of various moisture conditions of the lichens Cladina stellaris and Cladina rangiferina, and the mosses Dicranum elongatum and Tomenthypnum nitens on the spectral signatures obtained. Reflectance and moisture content measurements of these species were made in a laboratory setting, while maintaining the natural moisture conditions of the samples; once the moisture and spectral measurements were complete, the samples were returned to the field and placed in their natural setting, continuously receiving moisture from precipitation and groundwater and losing water through evaporation and drainage. Previously, we correlated the present spectral indices with the moisture contents of the above species, whereas the current study developed new species‐specific indices to improve the detection of the plants' moisture contents. The relationship between the plants' moisture content and the water table position was examined as well. It was found that the lichens are not responsive to variations in the water table position, whereas the mosses, specifically D. elongatum, are quite sensitive to changes in the water table position. Thus, the use of the mosses spectral indices may contribute to an indirect evaluation of the water table position. Overall, the results suggest that the unique spectral signatures of the above species can be detected by satellite and airborne imagery, whereas the mosses, can be used as indicators of peatlands moisture status. Copyright © 2010 John Wiley & Sons, Ltd.     

Aeolian sand strip mobility and protodune development on a drying beach: examining surface moisture and surface roughness patterns measured by terrestrial laser scanning

Ephemeral aeolian sand strips are commonplace on beaches. Their formation during high energy sand transport events often precedes the development of protodunes and their dynamics present interesting feedback mechanisms with surface moisture patterns. However, due to their temporary nature, little is known of their formation, mobility or the specifics of their interaction with beach surface characteristics. Similarly surface moisture has an important influence on sediment availability and transport in aeolian beach systems, yet it is difficult to quantify accurately due to its inherent variability over both short spatial and temporal scales. Whilst soil moisture probes and remote sensing imagery techniques can quantify large changes well, their resolution over mainly dry sand, close to the aeolian transport threshold is not ideal, particularly where moisture gradients close to the surface are large. In this study we employed a terrestrial laser scanner to monitor beach surface moisture variability during a three and a half hour period after a rain event and investigated relationships between bedform development, surface roughness and surface moisture. Our results demonstrate that as the beach surface dries, sand transport increases, with sediment erosion occurring at the wet/dry surface boundary, and deposition further downwind. This dynamic structure, dependent upon changing surface moisture characteristics, results in the formation of a rippled sand strip and ultimately a protodune. Our findings highlight dynamic mobility relationships and confirm the need to consider transient bedforms and surface moisture across a variety of scales when measuring aeolian transport in beach settings. The terrestrial laser scanner provides a suitable apparatus with which to accomplish this. Copyright © 2010 John Wiley & Sons, Ltd.     

Relationship between apparent redox potential discontinuity (aRPD) depth and environmental variables in soft-sediment habitats

As global temperatures increase and dissolved oxygen(DO) content decreases in marine systems, indices assessing sediment DO content in benthic habitats are becoming increasingly useful. One such measure is the depth to the apparent redox potential discontinuity(aRPD), a transition of sediment color that serves as a relative measure of sediment DO content. We examined spatiotemporal variation of aRPD depth, and the nature of the relationships between aRPD depth and biotic(infauna and epibenthic predators) and abiotic variables(sediment properties), as well as the availability of resources(chlorophyll a concentration, and organic matter content) in the intertidal mudflats of the Bay of Fundy, Canada. aRPD depth varied significantly through space and time, and a combination of biotic(sessile and errant infauna, as well as epibenthic predators), and abiotic(exposure time of a plot, sediment particle size,penetrability, and water content) variables, as well as the availability of resources(sediment organic matter content, and chlorophyll a concentration) were correlated with aRPD depth. As such, knowledge of both biotic and abiotic variables are required for a holistic understanding of sediment DO conditions.Abiotic variables likely dictate a suite of potential aRPD depth conditions, while biota and resource availability, via bioturbation and respiration, strongly influence the observed aRPD depth. As DO conditions in marine systems will continue to change due to global climate change, elucidating these relationships are a key first step in predicting the influence decreasing DO content may have upon marine benthos.     

Potential of support vector regression for prediction of monthly streamflow using endogenous property

In the recent past, a variety of statistical and other modelling approaches have been developed to capture the properties of hydrological time series for their reliable prediction. However, the extent of complexity hinders the applicability of such traditional models in many cases. Kernel‐based machine learning approaches have been found to be more popular due to their inherent advantages over traditional modelling techniques including artificial neural networks(ANNs ). In this paper, a kernel‐based learning approach is investigated for its suitability to capture the monthly variation of streamflow time series. Its performance is compared with that of the traditional approaches. Support vector machines (SVMs) are one such kernel‐based algorithm that has given promising results in hydrology and associated areas. In this paper, the application of SVMs to regression problems, known as support vector regression (SVR), is presented to predict the monthly streamflow of the Mahanadi River in the state of Orissa, India. The results obtained are compared against the results derived from the traditional Box–Jenkins approach. While the correlation coefficient between the observed and predicted streamflows was found to be 0·77 in case of SVR, the same for different auto‐regressive integrated moving average (ARIMA) models ranges between 0·67 and 0·69. The superiority of SVR as compared to traditional Box‐Jenkins approach is also explained through the feature space representation. Copyright © 2009 John Wiley & Sons, Ltd.     

Apparent redox potential discontinuity (aRPD) depth as a relative measure of sediment oxygen content and habitat quality

As hypoxic conditions spread in our oceans, indices that quickly and efficiently assess oxygen content in sediment pore water, and habitat quality are increasingly becoming desirable. Depth to the appa...     

Quantification of bedform dynamics and bedload sediment flux in sandy braided rivers from airborne and satellite imagery

Images from specially-commissioned aeroplane sorties (manned aerial vehicle, MAV), repeat unmanned aerial vehicle (UAV) surveys, and Planet CubeSat satellites are used to quantify dune and bar dynamics in the sandy braided South Saskatchewan River, Canada. Structure-from-Motion (SfM) techniques and application of a depth-brightness model are used to produce a series of Digital Surface Models (DSMs) at low and near-bankfull flows. A number of technical and image processing challenges are described that arise from the application of SfM in dry and submerged environments. A model for best practice is presented and analysis suggests a depth-brightness model approach can represent the different scales of bedforms present in sandy braided rivers with low-turbidity and shallow (< 2 m deep) water. The aerial imagery is used to quantify the spatial distribution of unit bar and dune migration rate in an 18 km reach and three ~1 km long reaches respectively. Dune and unit bar migration rates are highly variable in response to local variations in planform morphology. Sediment transport rates for dunes and unit bars, obtained by integrating migration rates (from UAV) with the volume of sediment moved (from DSMs using MAV imagery) show near-equivalence in sediment flux. Hence, reach-based sediment transport rate estimates can be derived from unit bar data alone. Moreover, it is shown that reasonable estimates of sediment transport rate can be made using just unit bar migration rates as measured from 2D imagery, including from satellite images, so long as informed assumptions are made regarding average bar shape and height. With recent availability of frequent, repeat satellite imagery, and the ease of undertaking repeat MAV and UAV surveys, for the first time, it may be possible to provide global estimates of bedload sediment flux for large or inaccessible low-turbidity rivers that currently have sparse information on bedload sediment transport rates. © 2018 The Authors. Earth Surface Processes and Landforms published by John Wiley & Sons Ltd.     

A recurrent support vector regression model in rainfall forecasting

To minimize potential loss of life and property caused by rainfall during typhoon seasons, precise rainfall forecasts have been one of the key subjects in hydrological research. However, rainfall forecast is made difficult by some very complicated and unforeseen physical factors associated with rainfall. Recently, support vector regression (SVR) models and recurrent SVR (RSVR) models have been successfully employed to solve time‐series problems in some fields. Nevertheless, the use of RSVR models in rainfall forecasting has not been investigated widely. This study attempts to improve the forecasting accuracy of rainfall by taking advantage of the unique strength of the SVR model, genetic algorithms, and the recurrent network architecture. The performance of genetic algorithms with different mutation rates and crossover rates in SVR parameter selection is examined. Simulation results identify the RSVR with genetic algorithms model as being an effective means of forecasting rainfall amount. Copyright © 2006 John Wiley & Sons, Ltd.     

Physical environmental controls on riparian root profiles associated with black poplar (Populus nigra L.) along the Tagliamento River,Italy

Tree roots contribute to the resistance of riparian sediments to physical deformation and disintegration. Understanding reinforcement by roots requires information on root distributions within riparian soils and sediments. Continuous‐depth models or curves have been proposed to describe vertical root density variations, providing useful indicators of the types of function that may be appropriate to riparian trees, but have generally been estimated for terrestrial species or broad vegetation types rather than riparian species or environments. We investigated vertical distributions of roots >0.1 mm diameter of a single riparian tree species (Populus nigra L.) along the middle reaches of a single river (Tagliamento River, Italy), where Populus nigra dominates the riparian woodland. Root density (hundreds m^?2) and root area ratio (RAR in cm² m^?2) were measured within 10 cm depth increments of 24 excavated bank profiles across nine sites. Sediment samples, extracted from distinct strata within the profiles, were analysed for moisture content, organic matter content and particle size. Statistical analyses identified two groups of wetter and drier profiles and five sediment types. Following log_e‐transformation of root density and RAR, linear regression analysis explored their variation with depth and, using dummy variables, any additional influence of moisture and sediment type. Significant linear regression relationships were estimated between both root density and RAR and depth which explained only 15% and 8% of the variance in the data. Incorporating moisture and then sediment characteristics into the analysis increased the variance explained in root density to 29% and 36% and in RAR to 14% and 26%. We conclude that riparian tree root density and RAR are highly spatially variable and are poorly explained by depth alone. Complex riparian sedimentary structures and moisture conditions are important influences on root distributions and so need to be incorporated into assessments of the contribution of roots to river bank reinforcement. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterisation and sediment–source linkages of intertidal sediment of the UK’s north Sefton Coast using magnetic and textural properties: findings and limitations

Sediment pathways and links to offshore processes are considered in the textural and magnetic characteristics of sediments of the intertidal flats and salt marshes of the north Sefton Coast, UK. In addition, sediment from a range of intertidal, marine and fluvial locations within the northwest region has similarly been characterised. Subsequently, the characteristics of these regional sediments, using a multivariate statistical approach of R- and Q-mode factor analyses, have been used to investigate the sediment transport pathways of the north Sefton Coast sediment. The benefits of fractionating sediment samples have been observed, and by using combinations of textural and isothermal remanent magnetic measurements, specific environments within the research have been successfully differentiated and characterised. Linkages between potential sediment source areas have also been established on a particle size-related basis.     

太湖水体3种典型水质参数的高光谱遥感反演

以富营养化污染严重的太湖为研究区,设计并实施了2次太湖航空遥感综合实验,获取了太湖7条航带、冬夏两个时相的航空高光谱遥感图像;通过6次太湖地面试验,采集了多时相的太湖水体固有光学量和表观光学量数据,分析了它们的空间分布规律,建立了单化固有光学量数据库;面向叶绿素、悬浮物和黄色物质3种典型水质参数,发展了基于生物光学模型和单位固有光学量数据库的水质参数反演分析方法;利用航空高光谱遥感器Will图像和航天高光谱遥感器CHRIS图像对这些方法进行了检验,获得了较好的水质参数图像反演结果.     

Support vector regression for estimating earthquake response spectra

This study uses support vector regression (SVR), a supervised machine learning algorithm, to model the average horizontal response spectrum as a nonparametric function of a set of predictor ground motion variables. Traditional ground motion prediction equations (GMPEs) are derived using parametric regression, where a fixed functional form is selected, and the model coefficients are determined by minimizing the errors on the training set. The SVR model is nonparametric; there is no need to assume a fixed functional form. Using nonlinear basis functions, the data points are mapped into a high dimensional feature space, where nonlinear input-output relationships can be expressed as a linear combination of nonlinear functions, using a subset of the data points. The combination weights are determined by minimizing the generalization error, using a formal mechanism to characterize the trade-off between the model complexity and the quality of fit to the data. Minimization of the generalization error instead of the fitting error leads to better generation to unseen data, and thus reduces the risk of over-fitting for a given number of data points. The SVR model is not based on a specific probability distribution, and is readily applicable to non-Gaussian data. An example application is presented for vertical strike-slip earthquakes, and the predictions from the SVR model are compared to the recently developed GMPEs. The results demonstrate the validity of the proposed model, and suggest that it can be used as an alternative to the conventional ground motion prediction models.     

Surficial sediment erodibility from time-series measurements of suspended sediment concentrations: development and validation

Numerical models of fine sediment transport depend on different approaches to parameterize the erosion properties of surficial sediment strata. These properties, namely the critical shear stress for erosion and the erosion rate coefficient, are crucial for reproducing the short-term and long-term sediment dynamics of the system. Methods to parameterize these properties involve either specialized laboratory measurements on sediment samples or optimization by model calibration. Based on observations of regular patterns in the variation of suspended sediment concentrations (SSC) over the tidal cycle in a small, narrow estuary, an alternate approach, referred to as the entrainment flux method, for quantifying the erosion properties of surficial bed strata is formulated and applied. The results of this method are shown to be analogous to the erosion data used to formulate the standard linear erosion formulation developed by various authors. The erosion properties inferred from the entrainment flux method are also compared to direct measurements of erodibility on sediment samples from the same site using the Gust microcosm apparatus. The favorable comparison of the two approaches suggests that the entrainment flux method can be used to infer and quantify the erodibility of surficial sediment strata in similar small and narrow estuaries. This method has certain advantages, chiefly its ease of implementation and the fact that it uses SSC time series which would typically be expected to be available for the study of or for model application at a given site. Guidelines for selecting the appropriate dataset for the application of the method are also presented.     

Estimation of suspended sediment concentration and yield using linear models,random forests and quantile regression forests

For sediment yield estimation, intermittent measurements of suspended sediment concentration (SSC) have to be interpolated to derive a continuous sedigraph. Traditionally, sediment rating curves (SRCs) based on univariate linear regression of discharge and SSC (or the logarithms thereof) are used but alternative approaches (e.g. fuzzy logic, artificial neural networks, etc.) exist. This paper presents a comparison of the applicability of traditional SRCs, generalized linear models (GLMs) and non‐parametric regression using Random Forests (RF) and Quantile Regression Forests (QRF) applied to a dataset of SSC obtained for four subcatchments (0·08, 41, 145 and 445 km²) in the Central Spanish Pyrenees. The observed SSCs are highly variable and range over six orders of magnitude. For these data, traditional SRCs performed inadequately due to the over‐simplification of relating SSC solely to discharge. Instead, the multitude of acting processes required more flexibility to model these nonlinear relationships. Thus, alternative advanced machine learning techniques that have been successfully applied in other disciplines were tested. GLMs provide the option of including other relevant process variables (e.g. rainfall intensities and temporal information) but require the selection of the most appropriate predictors. For the given datasets, the investigated variable selection methods produced inconsistent results. All proposed GLMs showed an inferior performance, whereas RF and QRF proved to be very robust and performed favourably for reproducing sediment dynamics. QRF additionally provides estimates on the accuracy of the predictions and thus allows the assessment of uncertainties in the estimated sediment yield that is not commonly found in other methods. The capabilities of RF and QRF concerning the interpretation of predictor effects are also outlined. Copyright © 2008 John Wiley & Sons, Ltd.     

In situ and high frequency monitoring of suspended sediment properties using a spectrophotometric sensor

It is well known that sediment properties, including sediment‐associated chemical constituents and sediment physical properties, can exhibit significant variations within and between storm runoff events. However, the number of samples included in suspended sediment studies is often limited by time‐consuming and expensive laboratory procedures after stream water sampling. This restricts high frequency sampling campaigns to a limited number of events and reduces accuracy when aiming to estimate fluxes and loads of sediment‐associated chemical constituents. In this study, we address the potential of a portable ultraviolet–visible spectrophotometer (220–730 nm) to estimate suspended sediment properties in a resource efficient way. Several field deployable spectrophotometers are currently available for in‐stream measurements of environmental variables at high temporal resolution. These instruments have primarily been developed and used to quantify solute concentrations (e.g. dissolved organic carbon and NO₃‐N), total concentrations of dissolved and particulate forms (e.g. total organic carbon) and turbidity. Here we argue that light absorbance values can be calibrated to estimate sediment properties. We present light absorbance data collected at 15‐min intervals in the Weierbach catchment (NW Luxembourg, 0.45 km²) from December 2013 to January 2015. In this proof‐of‐concept study, we performed a local calibration using suspended sediment loss‐on‐ignition (LOI) measurements as an example of suspended sediment property. We assessed the performance of several regression models that relate light absorbance measurements with the percentage weight LOI. The MM‐robust regression method presented the lowest standard error of prediction (0.48%) and was selected for calibration (adjusted r² = 0.76 between observed and predicted values). The model was then used to predict LOI during a storm runoff event in December 2014. This study demonstrates that spectrophotometers can be used to estimate suspended sediment properties at high temporal resolution and for long‐time spans in a simple, non‐destructive and affordable manner. Copyright © 2016 John Wiley & Sons, Ltd.     

Morphodynamics and sediment dynamics on intertidal mudflats in China (1961–1994)

This paper presents an overview of the significant research on morphodynamics and sediment dynamics on intertidal mudflats in China (1961–1994), particularly in the past 15 years (1980–1994). Development of intertidal mudflats has long been regarded as the response of the intertidal profile to tides, waves and storms. It has been found that there were long-term and short-term cyclic developments of intertidal mudflats in China. Three sedimentological zones have generally been identified from land to sea within the intertidal zone: high mudflat, middle mudflat and low mudflat. In addition, the sediments in the middle mudflat are relatively coarser than those in the high mudflat and low mudflat. Storms have great impacts on the intertidal morphology, sediment textures and sedimentary structures. Based on field investigations of intertidal sedimentary processes, many researchers have found that “settling and scour lags” were only applicable to intertidal cohesive sediment transport during periods of weak waves, but not during storms. In fact, flood fronts, waves, storm surges and longshore drift play important roles in suspended sediment transport on open intertidal mudflats in China. Despite of these extensive studies in the past several decades, there is still a need for an improved understanding of fundamental physical and biological processes governing erosion and deposition of cohesive fine sediment within the intertidal zone in China.     

Simulating monthly streamflow using a hybrid feature selection approach integrated with an intelligence model

ABSTRACT

Streamflow prediction is useful for robust water resources engineering and management. This paper introduces a new methodology to generate more effective features for streamflow prediction based on the concept of “interaction effect”. The new features (input variables) are derived from the original features in a process called feature generation. It is necessary to select the most efficient input variables for the modelling process. Two feature selection methods, least absolute shrinkage and selection operator (LASSO) and particle swarm optimization-artificial neural networks (PSO-ANN), are used to select the effective features. Principal components analysis (PCA) is used to reduce the dimensions of selected features. Then, optimized support vector regression (SVR) is used for monthly streamflow prediction at the Karaj River in Iran. The proposed method provided accurate prediction results with a root mean square error (RMSE) of 2.79 m³/s and determination coefficient (R² ) of 0.92.