High Accuracy Surface Modeling Method Research Articles

A New HASM-Based Downscaling Method for High-Resolution Precipitation Estimates

Obtaining high-quality precipitation datasets with a fine spatial resolution is of great importance for a variety of hydrological, meteorological and environmental applications. Satellite-based remote sensing can measure precipitation in large areas but suffers from inherent bias and relatively coarse resolutions. Based on the high accuracy surface modeling method (HASM), this study proposed a new downscaling method, the high accuracy surface modeling-based downscaling method (HASMD), to derive high-quality monthly precipitation estimates at a spatial resolution of 0.01° by downscaling the Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG) precipitation estimates in China. A scale transformation equation was introduced in HASMD, and the initial value was set by including the explanatory variables related to precipitation. The performance of HASMD was evaluated by comparing the results yielded by HASM and the combined method of HASM, Kriging, IDW and the geographical weighted regression (GWR) method (GWR-HASM, GWR-Kriging, GWR-IDW). Analysis results indicated that HASMD performed better than the other four methods. High agreement was achieved for HASMD, with bias values ranging from 0.07 to 0.29, root mean square error (RMSE) values ranging from 9.53 mm to 47.03 mm, and R2 values ranging from 0.75 to 0.96. Compared with the original IMERG precipitation products, the downscaling accuracy with HASMD improved up to 47%, 47%, and 14% according to bias, RMSE and R2, respectively. HASMD was able to capture the spatial variation in monthly precipitation in a vast region, and it might be potentially applicable for enhancing the spatial resolution and accuracy of remotely sensed precipitation data and facilitating their application at large scales.

A New Approach for Estimating Dissolved Oxygen Based on a High-Accuracy Surface Modeling Method.

Dissolved oxygen (DO) is a direct indicator of water pollution and an important water quality parameter that affects aquatic life. Based on the fundamental theorem of surfaces in differential geometry, the present study proposes a new modeling approach to estimate DO concentrations with high accuracy by assessing the spatial correlation and heterogeneity of DO with respect to explanatory variables. Specifically, a regularization penalty term is integrated into the high-accuracy surface modeling (HASM) method by applying geographically weighted regression (GWR) with some covariates. A modified version of HASM, namely HASM_MOD, is illustrated through a case study of Poyang Lake, China, by comparing the results of HASM, a support vector machine (SVM), and cokriging. The results indicate that HASM_MOD yields the best performance, with a mean absolute error (MAE) that is 38%, 45%, and 42% lower than those of HASM, the SVM, and cokriging, respectively, by using the cross-validation method. The introduction of a regularization penalty term by using GWR with respect to covariates can effectively improve the quality of the DO estimates. The results also suggest that HASM_MOD is able to effectively estimate nonlinear and nonstationary time series and outperforms three other methods using cross-validation, with a root-mean-square error (RMSE) of 0.20 mg/L and R2 of 0.93 for the two study sites (Sanshan and Outlet_A stations). The proposed method, HASM_MOD, provides a new way to estimate the DO concentration with high accuracy.

A Geomorphological Regionalization using the Upscaled DEM: the Beijing-Tianjin-Hebei Area, China Case Study

Characterizing geomorphological patterns based on digital elevation models (DEMs) has become a basic focus of current geomorphology. A new DEM upscaling method based on the high-accuracy surface modelling method (HASM-US method) has been developed to improve the accuracy of current models and the subjectivity of macroscopic geomorphological patterns. The topographic variables of elevation (EL), slope (SL), aspect (AS), relief amplitude (RA), surface incision (SI), surface roughness (SR), and profile curvature (PC) with a spatial resolution of 1 km × 1 km in the Beijing-Tianjin-Hebei (BTH) area of China have been obtained by using the HASM-US method combined with the principal component analysis (PCA) method in terms of the elevation data of the SRTM-4 DEM, meteorological station location information, and field measurements with a GPS receiver. A geomorphological regionalization pattern has been developed to quantitatively classify the geomorphological types in the BTH area by combining the seven topographic factors of EL, SL, AS, RA, SI, SR, and PC that have significant spatial variation. The results show that the upscaling accuracy of elevation (mean difference only −2.32 m) with the HASM-US method is higher than that with the bilinear interpolation method and nearest neighbour interpolation method. The geomorphologic distribution in the BTH area includes 11 types: low plain, low tableland, low hill, low basin, middle plain, middle hill, low mountain with low RA values, low mountain with medium RA values, middle mountain with low RA values, middle mountain with medium RA values, and middle mountain with high RA values. The low plain is the dominant geomorphological type that covers 40.58% of the whole BTH area. The geomorphological distribution shows the different significant characteristics: the elevation rapidly decreases from the Taihang Mountains to the eastern area, gradually decreases from the Yanshan Mountains to the southern area, and first increases and then decreases from the Bashang Plateau to the southeastern area in the whole BTH area.

Cloud computing-based high accuracy surface modeling method for China’s Poyang Lake basin DEM generation

The increasing availability of big spatial data demands large-scale surface modeling methods. To find a solution for large-scale surface modeling problem, based on previously developed high accuracy surface modeling (HASM) method, an extended high accuracy surface modeling method utilizing cloud computing is developed. The developed method was run on a Hadoop-based cloud computing environment comprising four computers and applied for China’s Poyang Lake basin digital elevation model construction. The experiments results indicate that the cloud computing-based method outperforms the general sequential method based on single computer significantly and attains three times speedups. Furthermore, the improved schedule algorithm for cloud computing-based HASM has further accelerated the computing speed.

An improved HASM method for dealing with large spatial data sets

Surface modeling with very large data sets is challenging. An efficient method for modeling massive data sets using the high accuracy surface modeling method (HASM) is proposed, and HASM_Big is developed to handle very large data sets. A large data set is defined here as a large spatial domain with high resolution leading to a linear equation with matrix dimensions of hundreds of thousands. An augmented system approach is employed to solve the equality-constrained least squares problem (LSE) produced in HASM_Big, and a block row action method is applied to solve the corresponding very large matrix equations. A matrix partitioning method is used to avoid information redundancy among each block and thereby accelerate the model. Experiments including numerical tests and real-world applications are used to compare the performances of HASM_Big with its previous version, HASM. Results show that the memory storage and computing speed of HASM_Big are better than those of HASM. It is found that the computational cost of HASM_Big is linearly scalable, even with massive data sets. In conclusion, HASM_Big provides a powerful tool for surface modeling, especially when there are millions or more computing grid cells.

An improved statistical downscaling scheme of Tropical Rainfall Measuring Mission precipitation in the Heihe River basin, China

Estimating an accurate spatial distribution of precipitation with high resolution is necessary for hydrological and ecological applications, especially in data‐scarce and terrain‐complicated river basins. Satellite‐based precipitation data have been widely used to measure the spatial patterns of precipitation, but an improvement in accuracy and resolution is needed. In this article, a new statistical downscaling method is proposed to generate improved monthly precipitation fields at a higher spatial resolution of 1 km in Heihe River basin (HRB), China. The presented methods employed the geographical weighted regression (GWR) method to explore the non‐stationarity between precipitation and its factors, and used the high‐accuracy surface modelling method (HASM) to compensate for the errors produced in the GWR downscaling process. The GWR model was first established under five different spatial scales, and the optimal relation between precipitation derived from the Tropical Rainfall Measuring Mission (TRMM) and its influencing factors was found for each month. The errors caused during the scale change were modified by performing HASM as a data merging framework, which considered both the local climate characteristics and meteorological observations. Results showed that the GWR downscaling method could not generate spatial patterns of precipitation similar to those of the original TRMM products. Although the performance of the GWR method after residual interpolations using Kriging, IDW, and tension Spline was improved, there existed significant variations in some regions, and the accuracy of those methods was still not satisfactory. In comparison with the other four models, GWR‐HASM showed better performance in reproducing the precipitation field at a high spatial resolution. Results indicate that the proposed downscaling method appears feasible for precipitation estimation in data‐scarce river basins.

A modified HASM algorithm and its application in DEM construction

In many spatial interpolation fields, high accuracy surface modeling (HASM) has yielded better accuracy than classical interpolation methods. The Gaussian equation is the core of the HASM algorithm; The current version of the HASM method builds the Gaussian equation in Cartesian coordinates and, computes the two partial derivatives of the surface in the horizontal and vertical directions for each grid. In this paper, a modified HASM method is proposed that integrates flow paths to improve the original HASM methodology. The modified HASM approach involves two steps. The first step generates an initial DEM, which is used to compute the flow path. Then, the second step is conducted based on scatter points and the flow direction. The output from this step is better than the initial DEM. First, we used a theoretical mathematical surface to validate the correctness of the modified model. Then, we chose a small study area where the topography is affected by hydrological erosion for analysis. The test results showed that the modified HASM method constructed a DEM with low MAE and RMSE values compared to those of traditional methods, and it more accurately characterized topographic features. Finally, a relatively gently sloping area was selected to validate that the applicability of the new method in other areas.

A multifactor analysis of the spatial distribution of annual mean extreme precipitation-Taking the Yellow River Basin as an example

Because the current interpolation method cannot meet the accuracy specifications, a new method for spatial interpolation of extreme precipitation is developed. It integrates precipitation, longitude and latitude, elevation, and topography data such as slope and aspect, and it is then simulated by the high accuracy surface modelling method and applied in the Yellow River Basin (YRB). Results show that the integrated method affords a very good simulation precision, with its simulation precision error being far below other interpolation methods. In conclusion, the integrated method for spatial interpolation of extreme precipitation can afford a good solution in topographically complex areas.

Mapping temperature using a Bayesian statistical method and a high accuracy surface modelling method in the Beijing-Tianjin-Hebei region, China

A more accurate Bayesian statistical technique together with a high accuracy surface modelling method (HASM) was used to improve the accuracy of temperature fields in the Beijing–Tianjin–Hebei (BTH) region, China. Bayesian statistical inference theory was first applied to fill missing daily values for meteorological stations on an annual scale. A mixed interpolator was then employed to simulate the annual mean temperature and was compared with other methods. The annual mean temperature was produced and the inter-decade change was investigated. The results show that the values filled by Bayesian statistical inference theory agree well with actual observations. A comparison with other interpolators shows that combining the Bayesian estimation method with the HASM gives better results than those of the other methods tested in this study. The construction of the annual mean temperature for 10 years shows the change interval and the spatial distribution of temperature in the BTH region. The annual temperature over 10 years changed from less than −1 °C in the northwest to more than 14 °C in the southeast. From 1981–1990 (T1) to 1991–2000 (T2) and T2 to 2001–2010 (T3) the temperature change was spatially stationary and varied mainly from −0.05 °C to 0.05 °C, except for some areas such as the southwest of Tangshan city and the south of Tianjin city where land cover and land use has exhibited large decadal variation during the past 30 years.

A high accuracy surface modeling method based on GPU accelerated multi‐grid method

AbstractA high accuracy surface modeling method (HASM) has been developed to provide a solution to many surface modeling problems such as DEM construction, surface estimation and spatial prediction. Although HASM is able to model surfaces with a higher accuracy, its low computing speed limits its popularity in constructing large scale surfaces. Hence, the research described in this article aims to improve the computing efficiency of HASM with a graphic processor unit (GPU) accelerated multi‐grid method (HASM‐GMG). HASM‐GMG was tested with two types of surfaces: a Gauss synthetic surface and a real‐world example. Results indicate that HASM‐GMG can gain significant speedups compared with CPU‐based HASM without acceleration on GPU. Moreover, both the accuracy and speed of HASM‐GMG are superior to the classical interpolation methods including Kriging, Spline and IDW.

A convergence criterion for a high accuracy surface modelling method

Recently, a new surface modelling method, High Accuracy Surface Modelling (HASM), is developed to give a relatively more accurate result than other classical methods. However, in the absence of a common convergence criterion, further applications of HASM have been limited. In this paper, we propose a convergence criterion for HASM which is based on the theoretical basis of it, allowing one to reliably determine a good termination point for the iterations. We then use numerical experiments and real-world applications to test the performance of this stopping criterion. Results show that the simulation accuracy is much improved and a convergence solution for HASM is obtained. In addition, for end-users, this criterion gives a quantitative indicator for the stopping rule of HASM and further makes HASM widely accepted by the general public.

Statistical downscaling of precipitation using local regression and high accuracy surface modeling method

Downscaling precipitation is required in local scale climate impact studies. In this paper, a statistical downscaling scheme was presented with a combination of geographically weighted regression (GWR) model and a recently developed method, high accuracy surface modeling method (HASM). This proposed method was compared with another downscaling method using the Coupled Model Intercomparison Project Phase 5 (CMIP5) database and ground-based data from 732 stations across China for the period 1976–2005. The residual which was produced by GWR was modified by comparing different interpolators including HASM, Kriging, inverse distance weighted method (IDW), and Spline. The spatial downscaling from 1° to 1-km grids for period 1976–2005 and future scenarios was achieved by using the proposed downscaling method. The prediction accuracy was assessed at two separate validation sites throughout China and Jiangxi Province on both annual and seasonal scales, with the root mean square error (RMSE), mean relative error (MRE), and mean absolute error (MAE). The results indicate that the developed model in this study outperforms the method that builds transfer function using the gauge values. There is a large improvement in the results when using a residual correction with meteorological station observations. In comparison with other three classical interpolators, HASM shows better performance in modifying the residual produced by local regression method. The success of the developed technique lies in the effective use of the datasets and the modification process of the residual by using HASM. The results from the future climate scenarios show that precipitation exhibits overall increasing trend from T1 (2011–2040) to T2 (2041–2070) and T2 to T3 (2071–2100) in RCP2.6, RCP4.5, and RCP8.5 emission scenarios. The most significant increase occurs in RCP8.5 from T2 to T3, while the lowest increase is found in RCP2.6 from T2 to T3, increased by 47.11 and 2.12 mm, respectively.

A Comparison of Methods for Solving High Accuracy Surface Modeling in DEM Construction

High accuracy surface modeling method (HASM) has the capacity of constructing a surface with a higher accuracy than classical methods. However, surface construction with HASM requires a large amount of computing time due to the intensive computing arising from solving the large linear systems. An effective linear system solving method is essential to cutting down the computing time so that HASM could be applied in constructing large scale surface with high resolution. This paper aims to study the performances of seven linear system solution methods, including HASM-GS, HASM-MGS, HASM-DSPM, HASM-CG, HASM-PCG, HASM-GCG and HASM-GPCG, thus providing a guideline for choosing the right method for HASM under different situations of computing environment. These seven methods were tested against a real-world DEM surface in the Boyang lake basin, which owns a complex topography. Three performance metrics were used, including convergence rates, computing time and consumed memory size. We found that to attain the same accuracy HASM-DSPM method consumed the least memory, HASM-GCG and HASM-GPCG needed less computing time than other methods and HASM-PCG had the fastest convergent rate. This study could provide valuable suggestions for HASM users to make a wise choice of linear system solving method for different surface construction applications.

Speeding up the high-accuracy surface modelling method with GPU

In order to find a solution for accurate, topographic data-demanding applications, such as catchment hydrologic modeling and assessments of anthropic activities impact on environmental systems, high-accuracy surface modeling (HASM) method is developed. Although it can produce a digital elevation model (DEM) surface of higher accuracy than classical methods, e.g. inverse distance weighted, spline and kriging, HASM requires numerous iterations to solve large linear systems, which impede its applications in high-resolution and large-scale surface interpolation. This paper aims to demonstrate the utilization of graphics’ processing units (GPUs) device to accelerate HASM in constructing large-scale and high-resolution DEM surfaces. We parallelized the linear system algorithm for solving HASM with Compute Unified Device Architecture, a parallel programming model developed by NVIDIA. We designed a memory-saving strategy to enable the HASM algorithm to run on GPUs. The speedup ratio of GPU-based algorithm was tested and compared with CPU-based algorithm through simulations of both ideal Gaussian synthetic surface and real topographic surface in the loess plateau of Gansu province. The GPU-parallelized algorithm can attain an over 10× speedup ratio with the CPU-based algorithm as a reference. The speedup ratio increases with the scale and resolution of the dataset. The memory management strategy efficiently reduces the memory usage by more than eight times the grid cell number. Implementing HASM in the GPUs device enables modeling large-scale and high-resolution surfaces in a reasonable time period and implies the potential benefits from the use of GPUs as massive, parallel co-processors for arithmetic-intensive data-processing applications.

Change trend of monthly precipitation in China with an improved surface modeling method

In this paper, a combination of a novel interpolation method and a local regression method was employed to improve the estimation accuracy of monthly precipitation over China. After the normalized processing and Box-Cox transformation of the data, we used the geographically weighted regression (GWR) method to describe the spatial precipitation trend, and then interpolated the residual by using a modified high accuracy surface modeling method (HASM-PRE). A high quality database of monthly precipitation with a resolution of 1 km(2) was constructed based on the meteorological stations. Results showed that wet years and dry years appear alternatively, and trend analysis of precipitation data series from 1981 to 2010 showed that the probability of years with extreme precipitation has increased in recent years. Precipitation in winter is rather uncertain and more dynamic from year to year compared to precipitation in summer.

Sensitivity studies of a high accuracy surface modeling method

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling (HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951-2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.

An improved version of a high accuracy surface modeling method

A method of surface modeling, high accuracy surface modeling (HASM), which is based on the fundamental theorem of surface theory, is modified. The earlier version of HASM is theoretically incomplete and almost performs similar or slightly better than other methods being compared in the practical applications which definitely limit its promotion. According to the fundamental theorem of surface theory, we modify HASM by adding another important nonlinear equation to solve the low accuracy in some cases and make HASM have a complete and solid theory foundation. A numerical test and a real-world example are employed to comparatively validate the effectiveness of this modification. It is found that the accuracy of the simulation result has a great improvement. Another feature of the modified version of HASM is that it is theoretically perfect since it considers the third equation of the surface theory. The modified HASM will be useful with a wide range of spatial interpolation, particularly if the focus on simulation accuracy.

An Overview of High Accuracy Surface Modeling of Soil Properties

Abstract High accuracy surface modeling (HASM) of soil properties is regarded as an important topic for the fields of pedometrics and “digital soil”. The HASM method, constructed by Yue et al., is a spatial interpolation technique based on the fundamental theorem of surfaces. In this paper, we will give an overview of high accuracy surface modeling of soil properties. Soil properties for the interpolation were measured on 150 samples of topsoil (0–20 cm) in a red soil region of Jiangxi Province, China. Predicted and measured values were compared using the mean error (ME), mean absolute error (MAE) and root mean square error (RMSE). First, HASM has more accuracy than the classical interpolator including kriging, inverse distance weighting (IDW) and splines. Second, in order to improve the calculation speed for HASM applied in soil interpolation, multigrid has been combined in HASM (HASM-MG). HASM-MG can be considered as an accurate method for interpolating soil properties on the premise of improving the calculation speed, and it advances the practicability of HASM applied in soil property interpolation. Third, modified HASM method based on the incorporation of ancillary variables was developed for improving interpolation of soil properties (HASM-SP). To evaluate the performance of HASM-SP, it was compared with ordinary kriging (OK), ordinary kriging combined geographical information (OK-Geo) and stratified kriging (SK). HASM-SP not only showed less MAEs and RMSEs, but also presented much more details due to the abrupt boundary from spatial variation of geographical information. Therefore, HASM can be considered not only as an alternative, accurate and high speed method for interpolating soil properties, but also can make the map more consistent with the true geographical information.

Surface modelling of soil properties based on land use information

High accuracy surface modelling (HASM) is a spatial interpolation technique based on the fundamental theorem of surfaces. This study proposed a modified HASM method based on the incorporation of ancillary land use information (HASM_LU) for improved interpolation of soil properties. To assess its feasibility, a total of 150 samples were collected in different land use types (woodlands, croplands and grasslands) of a typical red soil region in the middle part of Jiangxi Province, China. Observations on soil pH, alkali-hydrolyzable N (AN), total C, N, K, Al, Ca, Mg and Zn were interpolated. To evaluate the performance of HASM_LU, it was compared with four other interpolators: HASM, ordinary kriging with land use information (OK_LU), stratified kriging (SK) and regression-kriging using a generalized linear model (RK_GLM). To do so, predicted and measured values were compared using the mean error (ME), mean absolute error (MAE), root mean square error (RMSE) and prediction efficiency (PE). The results have shown that HASM_LU generally performs better than HASM, OK_LU, SK and RK_GLM with a lower estimation bias, MAE and RMSE as well as greater PE. In particular, the RMSE of HASM_LU for AN was smaller than that of HASM by 33.4%; that of OK_LU, 1.6%; that of SK, 41.5%; and that of RK_GLM, 67.6%. The largest difference in PE occurred when comparing HASM_LU with HASM for N (57.95%), with OK_LU (7.18%) for K, with SK (125.16%) for Zn and with RK_GLM (100.21%) for AN. The HASM_LU maps of soil properties present more details and more accurate spatial patterns. The good performance of HASM_LU can be attributed to the adequate surface modelling ability of HASM, combined with incorporation of information on abrupt spatial boundaries introduced by land use.

High-accuracy surface modelling and its application to DEM generation

An innovative method, high-accuracy surface modelling (HASM), is presented, which is based on the fundamental theorem of surfaces. The fundamental theorem of surfaces makes sure that a surface is uniquely defined by the first and second fundamental coefficients. Numerical tests of a Gaussian synthetic surface show that the Root Mean Square Error of the HASM method is much less than the ones of classical methods, such as the Triangulated Irregular Network, Spline, Inverse Distance Weight and Kriging methods. The HASM method gives a solution to the error problem that has long troubled generations of digital elevation models. All the methods for surface modelling are used to simulate a Digital Elevation Map (DEM) of Qian-Yan-Zhou Experimental Station for Red Soil and Hilly Land, which has a great topographical variety. Shaded relief maps of the simulated DEMs are developed to represent the terrain relief of Qian-Yan-Zhou Experimental Station, which shows that simulation results of the HASM method are much better than the ones of classical methods.