Parametric Regression Methods Research Articles

MODELING HYPERTENSION DISEASE RISK IN INDONESIA USING MULTIVARIATE ADAPTIVE REGRESSION SPLINE AND BINARY LOGISTIC REGRESSION APPROACHES

In the pursuit of the Sustainable Development Goals (SDGs), health-related challenges, especially hypertension, remain a significant global issue. The third goal of the SDGs aims to improve the quality of life and well-being of all individuals, but hypertension is a serious problem that can hinder these goals. Often referred to as the "silent killer" by the World Health Organization (WHO), hypertension is exacerbated by low awareness. Globally, more than 1.28 billion adults suffer from hypertension, with most cases in lower to middle-income countries, including Indonesia. Indonesia has an alarming rate of hypertension incidence, ranking fifth highest in the world. Riset Kesehatan Dasar (Riskesdas) 2023 and the Indonesia Family Life Survey (IFLS) are critical for understanding hypertension risk factors in Indonesia. The IFLS data, obtained from www.rand.org, includes observations from October 2014 to April 2015, totalling 85 observations. Despite being over 10 years old, this dataset was selected because it remains the most recent comprehensive data available from RAND, representing 83% of the Indonesian population. The IFLS is conducted every 7-8 years, with the next wave of data expected soon. Most studies on hypertension globally and in Indonesia use parametric regression methods. However, a research gap exists as no studies have used Multivariate Adaptive Regression Splines (MARS) on IFLS data to analyze hypertension risk factors. This study addresses this gap by comparing binary logit regression and MARS. The analysis shows the Apparent Error Rate (APPER) for MARS is 84.706%, while for binary logistic regression it is 80%, indicating MARS is better at classifying hypertension data in Indonesia. Using MARS offers a novel approach to understanding hypertension risk factors in Indonesia. Despite the data's age, it remains relevant as primary causes and risk factors for hypertension have not changed, making the findings valuable for current health policy and strategies.

Modeling and forecasting carbon dioxide emission in Pakistan using a hybrid combination of regression and time series models

Carbon dioxide (CO2) emissions continue to rise globally despite efforts to combat climate change. Energy industry emissions are a pressing global issue, causing devastating impacts. Hence, it is vital to accurately and efficiently forecast CO2 emissions. Thus, this study comprehensively analyzes forecasting CO2 emissions by comparing various hybrid combinations of regression and time series methods to explore the CO2 emissions in Pakistan. First, divide the yearly time series of CO2 emissions into the long-run curve trend series and the residual subseries. The long-run curve trend subseries is modeled using parametric and nonparametric regression methods, while various standard time series models are used to forecast the residual subseries. However, the forecasts of each subseries will be combined to obtain the final forecast of CO2 emissions. This work used four different accuracy mean errors, a statistical test, and a graphical analysis as performance measures to evaluate the proposed hybrid forecasting technique. The findings confirmed that the proposed hybrid combination forecasting technique is highly accurate and efficient in forecasting CO2 emissions. Likewise, according to the proposed final optimal hybrid combination forecasting model, Pakistan's per capita CO2 emissions will be 1.130215 metric tons in 2030. Pakistan's escalating emission trend signals that creative solutions must be implemented to curb it. Thus, the government must price carbon footprints, regulate electricity from zero-carbon sources, reduce population, encourage afforestation in densely populated areas, adopt clean technology, and fund research.

Dual ensemble approach to predict rice heading date by integrating multiple rice phenology models and machine learning-based genetic parameter regression models

Recent research advances in crop breeding and bioinformatics have revealed several genes that determine the flowering (heading) time in some crops. In this study, we calibrated an integrated rice phenology model that uses the genetic information of the cultivar to estimate the parameters of the models. Differences in the prediction of heading stage were examined using different phenology models and parameter estimation methods. We also proposed a novel approach to construct a dual-integrated ensemble model using both multiple crop phenology and regression models to estimate their parameters based on the haplotype combinations of 11 genes related to the heading date of rice. We used the data of 144 Japanese rice (Oryza sativa L.) cultivars to compare the prediction accuracy of the proposed approach with that of individual integrated phenology models. Subsequently, 4,083 ensemble patterns were analyzed using four rice phenology models (Beta, simplified Beta, ORYZA2000, and SIMIRIW) and three machine learning-based parameter regression methods (support vector, random forest, and ridge regression). The accuracy of the individual integrated model depended on the phenology model and its parameter regression method used. In some cases, the RMSE differed by more than one day. When the individual integrated model with the highest prediction accuracy in the training data was applied to the known and unknown environmental test data sets, the prediction accuracies were about 7.0 d and 8.2 d, respectively in the cross-validation. The prediction accuracy of the dual ensemble model with five ensemble members was approximately 5.9 d and 6.5 d in known and unknown environments. Our results suggest that the dual ensemble approach can enhance crop phenology prediction accuracy and present the importance of ensemble parameterization as well as combining multiple crop models when integrating genomic prediction with crop phenology models.

Bayesian and Classical Semi-parametric Estimation of the Balanced Longitudinal Data Model

The primary objective of this study is to employ semi-parametric regression techniques in the balanced longitudinal data model. Where the parametric regression models are plagued by the problem of strict constraints, while non-parametric regression models, despite their flexibility, suffer from the problem of the curse of dimensionality. Consequently, semi-parametric regression presents a suitable solution to address the problems in parametric and non-parametric regression methods. The advantage of this model is that it contains all the positive properties included in the previous two models such as containing strict restrictions in its parametric component, complete flexibility in its non-parametric component, and clarity of the interaction between its parametric and non-parametric components. According to the above, two methods were used to estimate a semi-parametric balanced longitudinal data model. The first is the Bayesian estimating method; the second is the Speckman method, which estimated the unknown nonparametric smoothing function by employing the kernel smoothing Nadaraya & Watson method. The Aim was to make a comparison between the Bayesian estimation method and the classical estimation method. Based on simulation experiments conducted on three different sample sizes (50, 100, and 200), it was concluded that the Bayes method is best at the variance levels (1,5). In contrast, the Profile least square method is best at the variance level (10).

Aboveground Biomass Prediction of Arid Shrub-Dominated Community Based on Airborne LiDAR through Parametric and Nonparametric Methods

Aboveground biomass (AGB) of shrub communities in the desert is a basic quantitative characteristic of the desert ecosystem and an important index to measure ecosystem productivity and monitor desertification. An accurate and efficient method of predicting the AGB of a shrub community is essential for studying the spatial patterns and ecological functions of the desert region. Even though there are several entries in the literature on the AGB prediction of desert shrub communities using remote sensing data, the applicability and accuracy of airborne LiDAR data and prediction methods have not been well studied. We first extracted the elevation, density and intensity variables based on the airborne LiDAR, and then sample plot-level AGB prediction models were constructed using the parametric regression (nonlinear regression) and nonparametric methods (Random Forest, Support Vector Machine, K-Nearest Neighbor, Gradient Boosting Machine, and Multivariate adaptive regression splines). We evaluated accuracies of all the AGB prediction models we developed based on the fit statistics. Results showed that: (1) the elevation, density and intensity variables obtained from LiDAR point cloud data effectively predicted the AGB of the desert shrub community at a sample plot level, (2) the kappa coefficient of nonlinear mixed-effects (NLME) model obtained was 0.6977 with an improvement by 13% due to the random effects included into the model, and (3) the nonparametric model, such as Support Vector Machine showed the best fit statistics (R2 = 0.8992), which is 28% higher than the NLME-model, and effectively reduced the heteroscedasticity. The AGB prediction model presented in this paper, which is based on the airborne LiDAR data and machine learning algorithm, will provide a valuable tool to the managers and researchers for evaluating desert ecosystem productivity and monitoring desertification.

Estimation of Winter Wheat Plant Nitrogen Concentration from UAV Hyperspectral Remote Sensing Combined with Machine Learning Methods

Nitrogen is one of the most important macronutrients and plays an essential role in the growth and development of winter wheat. It is very crucial to diagnose the nitrogen status timely and accurately for applying a precision nitrogen management (PNM) strategy to the guidance of nitrogen fertilizer in the field. The main purpose of this study was to use three different prediction methods to evaluate winter wheat plant nitrogen concentration (PNC) at booting, heading, flowering, filling, and the whole growth stage in the Guanzhong area from unmanned aerial vehicle (UAV) hyperspectral imagery. These methods include (1) the parametric regression method; (2) linear nonparametric regression methods (stepwise multiple linear regression (SMLR) and partial least squares regression (PLSR)); and (3) machine learning methods (random forest regression (RFR), support vector machine regression (SVMR), and extreme learning machine regression (ELMR)). The purpose of this study was also to pay attention to the impact of different growth stages on the accuracy of the model. The results showed that compared with parametric regression and linear nonparametric regression, the machine learning regression method could evidently improve the estimation accuracy of winter wheat PNC, especially using SVMR and RFR, the training set of the model at flowering and filling stage explained 93% and 92% of the PNC variability respectively. The testing set of the model at flowering and filling stages explained 88% and 91% of the PNC variability, the root mean square error of the validation set (RMSEtesting) was 0.82 and 1.23, and the relative prediction deviation (RPD) was 2.58 and 2.40, respectively. Therefore, a conclusion was drawn that it was the best choice to estimate winter wheat PNC at the flowering and filling stage from UAV hyperspectral imagery. Using machine learning methods, SVMR and RFR, respectively, could achieve the most outstanding estimation performance, which could provide a theoretical basis for putting forward the PNM strategy.

Parametric expectile regression and its application for premium calculation

Premium calculation has been a popular topic in actuarial sciences over the decades. Generally, a two-stage model is used to develop the premium calculation process. It can be decomposed into estimating the probability of having at least one claim by the logistic regression in the first stage and calibrating the severity in the second stage. Existing methods for the second stage include generalized linear models (GLMs) and quantile regression. However, the GLMs fail to provide information associated with the extreme claim amount and the quantile is not sensitive to the size of the extreme losses. Given that the magnitude of the extreme claim amount may lead to a huge loss for the insurer, we introduce the expectile risk measure into premium calibration and propose an expectile-based risk premium, which outperforms other methods for heavy-tailed distributions. Naively adopting the conventional expectile regression in the second stage is not preferred because it would be over-parameterized and time-consuming if the portfolio contains a large number of risk classes. Thus, we put forward a two-stage parametric expectile regression (TSPER) with parametric expectile regression (PER) method used in the second stage. The consistency and asymptotic normality of the proposed PER estimator are established under mild conditions. We also propose a novel Expectile Premium Principle to allocate the total premium for each policy. In the analysis of the automobile insurance data set, the proposed TSPER method outperforms other two-stage methods in terms of the ordered Lorenz curve and the Gini index.

Estimation of Winter Wheat Canopy Chlorophyll Content Based on Canopy Spectral Transformation and Machine Learning Method

Canopy chlorophyll content (CCC) is closely related to crop nitrogen status, crop growth and productivity, detection of diseases and pests, and final yield. Thus, accurate monitoring of chlorophyll content in crops is of great significance for decision support in precision agriculture. In this study, winter wheat in the Guanzhong Plain area of the Shaanxi Province, China, was selected as the research subject to explore the feasibility of canopy spectral transformation (CST) combined with a machine learning method to estimate CCC. A hyperspectral canopy ground dataset in situ was measured to construct CCC prediction models for winter wheat over three growth seasons from 2014 to 2017. Sensitive-band reflectance (SR) and narrow-band spectral index (NSI) were established based on the original spectrum (OS) and CSTs, including the first derivative spectrum (FDS) and continuum removal spectrum (CRS). Winter wheat CCC estimation models were constructed using univariate regression, partial least squares (PLS) regression, and random forest (RF) regression based on SR and NSI. The results demonstrated the reliability of CST combined with the machine learning method to estimate winter wheat CCC. First, compared with OS-SR (683 nm), FDS-SR (630 nm) and CRS-SR (699 nm) had a larger correlation coefficient between canopy reflectance and CCC; secondly, among the parametric regression methods, the univariate regression method with CRS-NDSI as the independent variable achieved satisfactory results in estimating the CCC of winter wheat; thirdly, as a machine learning regression method, RF regression combined with multiple independent variables had the best winter wheat CCC estimation accuracy (the determination coefficient of the validation set (Rv2) was 0.88, the RMSE of the validation set (RMSEv) was 3.35 and relative prediction deviation (RPD) was 2.88). Thus, this modeling method could be used as a basic method to predict the CCC of winter wheat in the Guanzhong Plain area.

Online monitoring of the voltage stability margin using local minimax concave penalty regression and adaptive database

A novel online monitoring method for the voltage stability margin (VSM) based on local minimax concave penalties (LocMCP) regression and adaptive database is proposed to ameliorate the weak model interpretability and insufficient generalization ability of the existing online monitoring methods. In this paper, the minimax concave penalty (MCP) is applied for VSM online monitoring for the first time. Compared with the multiple linear regression model (MLRM) and the local least absolute shrinkage and selection operator (LocLASSO), better prediction accuracy can be obtained through LocMCP. The MCP and local regression are combined to find the mapping relationship between VSM and reactive power reserves (RPRs) and to obtain the VSM online monitoring model composed of various local models. To further enhance the generalization ability of the model, an adaptive database is proposed. The data updating of the database is triggered when the local root mean square error (LocRMSE) exceeds the limit or is triggered in the case that the planned operation is performed. Furthermore, the local model can be updated according to the data updating results of the database. The 3-bus system, IEEE 30-bus system, and 1951-bus system are selected for verification, and the test results show that the proposed method is effective and has better generalization ability compared with other parameter regression methods.

Investigation of Parametric, Non-Parametric and Semiparametric Methods in Regression Analysis

Regression analysis is known as statistical methods applied to model and analyze the relationship between variables. Regression method can be examined as parametric, non-parametric and semiparametric regression methods.
 The parametric regression method assumes that the dependent variable is in a linear relationship with the independent variables and that the shape of the relationship is known. If these assumptions are not met, non-parametric regression methods are applied. However, these methods cause difficulties especially in the interpretation part due to the problem of multidimensionality when there is more than one independent variable. Thus, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while the other part may be in a nonlinear relationship. Thus, in order to model these relationships, semiparametric regression methods, which are the additive combination of parametric and non-parametric regression methods, are used.
 In this study, parametric regression method, definition of non-parametric regression method and assumption conditions are given. It has been shown that the semiparametric regression method can be applied in cases where these assumptions are not met. Thus, in the study, regression methods were examined in three different parts, and parametric, non-parametric and semiparametric regression methods were examined theoretically.

Different Modelling Approaches to Determine Suitable Areas for Conserving Egg-Cone Pine (Pinus oocarpa Schiede) Plus Trees in the Central Part of Mexico

Various spatial modelling methods and tools have been used in ecology and biogeography. The application of these options serves a dual function: first, they offer information about the potential distribution of species to understand the richness and diversity of unassessed areas. Second, spatial modelling methods employ these predictions to select relevant sites to determine natural conservation areas. In this study, we compared three methods for modelling the spatial distribution of Egg-cone Pine (Pinus oocarpa Schiede), an important non-timber pine in Mexico. The final goal is to estimate suitable areas for the conservation and reproduction of superior individuals (plus trees) of P. oocarpa as a conservation strategy outside the known distribution since this species possesses a high ecological and economic value. The model used were a generalised linear model (GLM) as a parametric regression method, random forest (RF) as a machine-learning method, and the MaxEnt model, a standard procedure, implemented using the Kuenm R package. The results suggest that the models used performed well since the AUROC was between 0.95 and 0.98 in all cases. MaxEnt and random forest approaches provided more conservative predictions for the distribution of suitable areas of plus trees of P. oocarpa than the generalised linear model, but the random forest algorithm achieved the best performance. The results of the study allowed the determination of ex situ conservation areas for P. oocarpa plus trees outside of their known distribution.

A PDEM-based non-parametric seismic fragility assessment method for RC structures under non-stationary ground motions

To alleviate the consequential influences of earthquakes, many seismic performance evaluation methods have been developed over the past century. Fragility assessment is an effective approach to evaluate the structural response under earthquake excitation, among which the classic parametric linear regression method (LRM) is one of the most popular ones. However, the classic parametric LRM method adopts a lognormal distribution assumption, and the assumption may not be satisfied under highly nonlinear scenario thus leading to inaccurate fragility curves. To overcome this issue, a PDEM-based non-parametric seismic fragility assessment framework without pre-defined distribution of the structural demand and performance is proposed in this paper. Non-stationary ground motions generated by the spectral representation method are employed for deeper representation of the earthquake excitation uncertainty, and two RC frames are designed to exhibit the performance of the proposed assessment framework. The results indicate that the proposed framework can conduct the fragility assessment effectively and perform a better accuracy than the classic parametric LRM method under the same number of dynamic calculations. Additionally, the PDEM-based framework requires much fewer samples compared to the benchmark Monte Carlo simulation (MCS), thus resulting in a less calculation burden.

Semiparametric Regression Models and Applicability in Agriculture

Parametric regression models assume that the dependent variable is a linear relationship with the independent variables and the form of the relationship is known. Nonparametric regression methods are applied in cases where the relationship type is not known or assumptions cannot be provided. However, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while some may be in a nonlinear relationship. In order to model these variables, semiparametric regression models, which are a combination of parametric and nonparametric regression methods, are used. In this study parametric, nonparametric and semiparametric regression models, parametric estimates, fit statistical values of the models, confidence intervals and standard error values were calculated. As a result of the analysis, the parameters of the milking unit and the quarantine area among the parametric variables, the operation area, the ventilation area, the number of ventilation, the quarantine area, the infirmary area, the manure pit and the distance to the center among the non-parametric variables were found to be statistically very important (P

Cumulative Racial and Ethnic Disparities Along the School-to-Prison Pipeline

Using the cumulative disadvantage theoretical framework, the current study explores whether school suspension and expulsion provide an indirect path through which race and ethnicity affect the likelihood of experiencing arrest, any incarceration, and long-term incarceration in adulthood. To address these issues, we use data from Waves I, II, and IV of the Add Health survey (N = 14,484), and we employ generalized multilevel structural equation models and parametric regression methods using counterfactual definitions to estimate direct and indirect pathways. We observe that Black (but not Latinx) individuals are consistently more likely than White persons to experience exclusionary school discipline and criminal justice involvement. However, we find a path through which race and Latinx ethnicity indirectly affect the odds of adulthood arrest and incarceration through school discipline. Disparate exposure to school suspension and expulsion experienced by minority youth contributes to racial and ethnic inequalities in justice system involvement. By examining indirect paths to multiple criminal justice consequences along a continuum of punitiveness, this study shows how discipline amplifies cumulative disadvantage during adulthood for Black and, to a lesser extent, Latinx individuals who are disproportionately funneled through the “school-to-prison pipeline.”

Design and Hysteresis Modeling of a Miniaturized Elastomer-Based Clutched Torque Sensor

Elastic torque sensors have been widely used for small-scale robots such as hand exoskeletons to achieve torque control. However, designing a miniaturized and lightweight elastic torque sensor with human–machine interaction safety is still a challenge. In this article, a novel miniaturized and lightweight elastomer-based clutched torque sensor is presented. A rubber spring is designed and used to reduce its volume and weight. A wafer disk clutch is devised to improve mechanical safety. The torque sensor is 29.5 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times18$ </tex-math></inline-formula> mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times24$ </tex-math></inline-formula> mm in dimension and weighs 23 g. Compared with the state-of-the-art elastic torque sensors for hand exoskeletons, the volume-to-torque ratio is reduced by 15.48%, and its weight is reduced by 23.33%. Since the hysteresis characteristics of the rubber spring leads to a nonlinear deformation–torque relationship, an improved parametric Gaussian process regression (PGPR) method based on the nonlinear autoregressive moving average structure with exogenous inputs (NARMAX) is proposed. A combined kernel function for the improved PGPR is designed to improve the fitting performance. Finally, experiments have been conducted to verify the mechanical safety and torque sensing performance. The force caused by collision on the proposed torque sensor is less than that on the torque sensor without the clutch (reduced by 51.78%). The proposed hysteresis model can reduce the maximum absolute modeling error to 7% compared with those of other intelligent hysteresis models (the modeling error is 12.32%). Therefore, the experimental results indicate that the proposed torque sensor can improve the mechanical safety and achieve accurate torque sensing.

The convergence of PM2.5 concentration in Chinese cities: a distribution dynamic approach

To fill the gap in the research on the convergence trend of air pollutants since 2013 in China and overcome the Galton fallacy caused by the parametric regression method, this study examines the convergence trend of the annual average concentration of fine particulate matter 2.5 (PM2.5) in China’s prefecture-level cities after 2013 using a distribution dynamic approach. The winter PM2.5 pollution in Chinese cities is severe. Hence, the convergence of the average winter PM2.5 concentration of prefecture-level cities is also explored in this study. The results show that during 2015–2019, the annual average PM2.5 concentration level improved significantly. However, the average PM2.5 winter concentration level in 2015–2018 did not significantly decrease, with some cities showing severe pollution levels. The annual average PM2.5 of China's prefecture-level cities exhibit club convergence, while the PM2.5 concentration in winter exhibits ‘unikurtosis’. In the long run, the annual average PM2.5 clusters around two levels, at approximately 35 μg/m3 and 60 μg/m3, while the average PM2.5 in winter is concentrated at 100 μg/m3. In the long run, in the central region, PM2.5 pollution is more severe than in northern and southern areas, regardless of the annual or winter average PM2.5 concentration.

Use of Shape Restricted Regression Methods for Fitting Model of Per Capita GDP: A Global Economic Scenario of 2018

The aim of the study is to analyze the pattern of Gross domestic product (GDP) according to Human development index (HDI) for 184 countries of the world. GDP per capita indicates only economic prosperity but not the overall development of the citizens of a country. This research tries to find out the beneath relationship of the financial state and human development of countries using the data of 2018. For demonstrating this analysis several parametric and non-parametric regression methods subject to shape restriction have been used. The study targets to shed light on comparative performance of shape constrained regression with cone projection, polynomial regression, LOESS, Istonic regression with pooled adjacent violators algorithm, Kernel regression, smoothing spline and generalized additive model in convex situation.

Using Soft Sensors as a Basis of an Innovative Architecture for Operation Planning and Quality Evaluation in Agricultural Sprayers

One of the major problems facing humanity in the coming decades is the production of food on a large scale. The production of large quantities of food must be conducted in a sustainable and responsible manner for nature and humans. In this sense, the appropriate application of agricultural pesticides plays a fundamental role since pesticide application in a qualified manner reduces human and environmental risks as well as the costs of food production. Evaluation of the quality of application using sprayers is an important issue, and several quality descriptors related to the average diameter and distribution of droplets are used. This paper describes the construction of a data-driven soft sensor using the parametric principal component regression (PCR) method based on principal component analysis (PCA), which works in two configurations: with the input being the operating conditions of the agricultural boom sprayers and its outputs being the prediction of the quality descriptors of spraying, and vice versa. The soft sensor provides, in one configuration, estimates of the quality of pesticide application at a certain time and, in the other, estimates of the appropriate sprayer-operating conditions, which can be used for control and optimization of the processes in pesticide application. Full cone nozzles are used to illustrate a practical application as well as to validate the usefulness of the soft sensor designed with the PCR method. The selection of historical data, exploration, and filtering of data, and the structure and validation of the soft sensor are presented. For comparison purposes, the results with the well-known nonparametric k-Nearest Neighbor (NN) regression method are presented. The results of this research reveal the usefulness of soft sensors in the application of agricultural pesticides and as a knowledge base to assist in agricultural decision-making.

COVID-19: Mechanistic model calibration subject to active and varying non-pharmaceutical interventions

Mathematical models are useful in epidemiology to understand COVID-19 contagion dynamics. We aim to demonstrate the effectiveness of parameter regression methods to calibrate an established epidemiological model describing infection rates subject to active, varying non-pharmaceutical interventions (NPIs). We assess the potential of established chemical engineering modelling principles and practice applied to epidemiological systems. We exploit the sophisticated parameter regression functionality of a commercial chemical engineering simulator with piecewise continuous integration, event and discontinuity management. We develop a strategy for calibrating and validating a model. Our results using historic data from 4 countries provide insights into on-going disease suppression measures, while visualisation of reported data provides up-to-date condition monitoring of the pandemic status. The effective reproduction number response to NPIs is non-linear with variable response rate, magnitude and direction. Our purpose is developing a methodology without presenting a fully optimised model, or attempting to predict future course of the COVID-19 pandemic.

Comparison of Different Methods for Spatial Downscaling of GPM IMERG V06B Satellite Precipitation Product Over a Typical Arid to Semi-Arid Area

Spatial downscaling is an effective way to obtain precipitation with sufficient spatial details. The performance of downscaling is typically determined by the empirical statistical relationships between precipitation and the used auxiliary variables. In this study, we conducted a comprehensive comparison of five empirical statistical methods for spatial downscaling of GPM IMERG V06B monthly and annual precipitation with a relatively long time series from 2001 to 2015 over a typical semi-arid to arid area (Gansu province, China). These methods included two parametric regression methods (univariate regression, or UR; multivariate regression, or MR) and three machine learning methods (artificial neural network, or ANN; support vector machine, or SVM; random forests, or RF), which were used to downscale the satellite precipitation from 0.1° (∼10 km) to 1 km spatial resolution. Five commonly used indices which were normalized differential vegetation index (NDVI), elevation, land surface temperature (LST), and latitude and longitude were selected as auxiliary variables. The downscaled results were validated using a total of 80 rain gauge station data during 2001–2015. Results showed that latitude had the overall largest correlation with IMERG annual precipitation, also evidenced by feature importance measurements in RF. The downscaled results at monthly scale were overall consistent with the results at annual scale. The machine learning-based methods had better predictive ability of the original IMERG precipitation than parametric regression methods, with larger coefficient of determination (R2) and smaller root-mean-square error (RMSE) as well as relative root-mean-square error (RRMSE). The downscaled 1 km IMERG precipitation by parametric regression methods had obvious underestimations (positive residual errors) in the south and east of Gansu province and overestimations (negative residual errors) in the west. In addition, the validation results of parametric regression downscaling methods showed large improvements after residual correction, while the improvements were small in the machine learning-based methods. However, the interpolation algorithm included in residual correction can cause certain errors in the downscaled results due to the ignorance of precipitation spatial heterogeneity. The machine learning-based RF downscaling had the smallest residual errors and the overall best validation results, showing great potentials to provide accurate precipitation with high spatial resolution. (Less)