Zhengping Du

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.

A Multi-Grid Method of High Accuracy Surface Modeling and Its Validation

A method of high accuracy surface modeling (HASM) has been constructed to find a solution for error problems that had long troubled surface modeling in geographical information systems (GIS). It is found that when a preconditioned conjugate gradient (PCG) algorithm is used to solve the large sparse linear system, which HASM can be transferred into, HASM performs best in terms of simulation compared with all other algorithms. But its computing speed is not fast enough for all applications. A multi-grid method is introduced into HASM to try to shorten its computing time. Both numerical and real-world tests demonstrate that there is a range of stop error (SE). The multi-grid method of HASM (HASM-MG) greatly increases computing speed when SEs are within this range, compared with the PCG algorithm of HASM (HASM-PCG). HASM-MG is suitable for applications with a need for less accuracy and a shorter computing time. HASM-PCG is appropriate for issues needing higher accuracy. HASM-MG performs better than HASM-PCG in flat areas, while HASM-PCG does better in complex terrainm in terms of accuracy and computing time.

Development of a surface modeling method for mapping soil properties

High accuracy surface modeling (HASM) is a method which can be applied to soil property interpolation. In this paper, we present a method of HASM combined geographic information for soil property interpolation (HASM-SP) to improve the accuracy. Based on soil types, land use types and parent rocks, HASM-SP was applied to interpolate soil available P, Li, pH, alkali-hydrolyzable N, total K and Cr in a typical red soil hilly region. To evaluate the performance of HASM-SP, we compared its performance with that of ordinary kriging (OK), ordinary kriging combined geographic information (OK-Geo) and stratified kriging (SK). The results showed that the methods combined with geographic information including HASM-SP and OK-Geo obtained a lower estimation bias. HASM-SP also showed less MAEs and RMSEs when it was compared with the other three methods (OK-Geo, OK and SK). Much more details were presented in the HASM-SP maps for soil properties due to the combination of different types of geographic information which gave abrupt boundary for the spatial variation of soil properties. Therefore, HASM-SP can not only reduce prediction errors but also can be accordant with the distribution of geographic information, which make the spatial simulation of soil property more reasonable. HASM-SP has not only enriched the theory of high accuracy surface modeling of soil property, but also provided a scientific method for the application in resource management and environment planning.

Surface modeling of soil antibiotics

Large numbers of livestock and poultry feces are continuously applied into soils in intensive vegetable cultivation areas, and then some veterinary antibiotics are persistent existed in soils and cause health risk. For the spatial heterogeneity of antibiotic residues, developing a suitable technique to interpolate soil antibiotic residues is still a challenge. In this study, we developed an effective interpolator, high accuracy surface modeling (HASM) combined vegetable types, to predict the spatial patterns of soil antibiotics, using 100 surface soil samples collected from an intensive vegetable cultivation area located in east of China, and the fluoroquinolones (FQs), including ciprofloxacin (CFX), enrofloxacin (EFX) and norfloxacin (NFX), were analyzed as the target antibiotics. The results show that vegetable type is an effective factor to be combined to improve the interpolator performance. HASM achieves less mean absolute errors (MAEs) and root mean square errors (RMSEs) for total FQs (NFX+CFX+EFX), NFX, CFX and EFX than kriging with external drift (KED), stratified kriging (StK), ordinary kriging (OK) and inverse distance weighting (IDW). The MAE of HASM for FQs is 55.1 μg/kg, and the MAEs of KED, StK, OK and IDW are 99.0 μg/kg, 102.8 μg/kg, 106.3 μg/kg and 108.7 μg/kg, respectively. Further, RMSE simulated by HASM for FQs (CFX, EFX and NFX) are 106.2 μg/kg (88.6 μg/kg, 20.4 μg/kg and 39.2 μg/kg), and less 30% (27%, 22% and 36%), 33% (27%, 27% and 43%), 38% (34%, 23% and 41%) and 42% (32%, 35% and 51%) than the ones by KED, StK, OK and IDW, respectively. HASM also provides better maps with more details and more consistent maximum and minimum values of soil antibiotics compared with the measured data. The better performance can be concluded that HASM takes the vegetable type information as global approximate information, and takes local sampling data as its optimum control constraints.

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.

A review of recent developments in HASM

Ground observation is able to obtain highly accurate data with high temporal resolution at observation points, but these observation points are too sparsely to satisfy the application requirements at regional scale. Satellite remote sensing can frequently supply spatially continuous information on earth surface, which is impossible from ground-based investigations, but remote sensing description is not able to directly obtain process parameters. In fact, in terms of fundamental theorem of surfaces, a surface is uniquely defined by the first fundamental coefficients, about the details of the surface observed when we stay on the surface, and the second fundamental coefficients, the change of the surface observed from outside the surface. A method for high accuracy surface modeling (HASM) has been developed initiatively to find solutions for error problem and slow-speed problem of earth surface modeling since 1986. HASM takes global approximate information (e.g., remote sensing images or model simulation results) as its driving field and local accurate information (e.g., ground observation data and/or sampling data) as its optimum control constraints. Its output satisfies the iteration stopping criterion which is determined by application requirement for accuracy. This paper reviews problems to be solved in every development stage and applications of HASM.

Modelling of XCO2 Surfaces Based on Flight Tests of TanSat Instruments

The TanSat carbon satellite is to be launched at the end of 2016. In order to verify the performance of its instruments, a flight test of TanSat instruments was conducted in Jilin Province in September, 2015. The flight test area covered a total area of about 11,000 km2 and the underlying surface cover included several lakes, forest land, grassland, wetland, farmland, a thermal power plant and numerous cities and villages. We modeled the column-average dry-air mole fraction of atmospheric carbon dioxide (XCO2) surface based on flight test data which measured the near- and short-wave infrared (NIR) reflected solar radiation in the absorption bands at around 760 and 1610 nm. However, it is difficult to directly analyze the spatial distribution of XCO2 in the flight area using the limited flight test data and the approximate surface of XCO2, which was obtained by regression modeling, which is not very accurate either. We therefore used the high accuracy surface modeling (HASM) platform to fill the gaps where there is no information on XCO2 in the flight test area, which takes the approximate surface of XCO2 as its driving field and the XCO2 observations retrieved from the flight test as its optimum control constraints. High accuracy surfaces of XCO2 were constructed with HASM based on the flight’s observations. The results showed that the mean XCO2 in the flight test area is about 400 ppm and that XCO2 over urban areas is much higher than in other places. Compared with OCO-2’s XCO2, the mean difference is 0.7 ppm and the standard deviation is 0.95 ppm. Therefore, the modelling of the XCO2 surface based on the flight test of the TanSat instruments fell within an expected and acceptable range.

DEM Construction from Contour Lines Based on Regional Optimum Control

Digital Elevation Model (DEM) data are widely used in many research areas such as Geographical Information System (GIS), hydrological analysis and soil erosion models. By minimizing the equations of HASM (High Accuracy Surface Modeling), subjected to equality constraints from discretizing vector contour lines and to boundary constraints from regional points between contour lines, a method called HASMROC(Regional Optimum Control) for constructing DEM from contour lines is presented. A case study is given on converting Gauss synthesis surfaces contour lines into DEM and the derived contour lines from simulated DEM is compared with the original ones. Information contained in between original contour lines can be most used by HASMROC, while it cannot be used by HASM and by the other DEM construction methods, so HASMROC can produce a more reliable result from contour lines. Much more kinds of original data sources and data sources of different qualities can be handled by HASMROC method in the future through regional optimum control.

Uncertainty of forest biomass carbon patterns simulation on provincial scale: A case study in Jiangxi Province, China

Forest vegetation carbon patterns are significant for evaluating carbon emission and accumulation. Many methods were used to simulate patterns of forest vegetation carbon stock in previous studies, however, uncertainty apparently existed between results of different methods, even estimates of same method in different studies. Three previous methods, including Atmosphere-vegetation interaction model 2 (AVIM2), Kriging, Satellite-data Based Approach (SBA), and a new method, High Accuracy Surface Modeling (HASM), were used to simulate forest vegetation carbon stock patterns in Jiangxi Province in China. Cross-validation was used to evaluate methods. The uncertainty and applicability of the four methods on provincial scale were analyzed and discussed. The results showed that HASM had the highest accuracy, which improved by 50.66%, 33.37% and 28.58%, compared with AVIM2, Kriging and SBA, respectively. Uncertainty of simulation of forest biomass carbon stock was mainly derived from modeling error, sampling error and statistical error of forest area. Total forest carbon stock, carbon density and forest area of Jiangxi were 288.62 Tg, 3.06 kg/m2 and 94.32×109 m2 simulated by HASM, respectively.

Simulation of vertical wind profile under neutral conditions

After analysing formulations of the horizontal wind velocity above a non‐uniform underlying surface, it is found that the mean height of roughness elements, fractional vegetation cover and leaf area index are the most essential parameters of vertical wind profile under neutral conditions. By using Landsat‐5 data, every‐10‐days observed data in the field, the every‐10‐days Normalized Difference Vegetation Index (NDVI) data from NOAA‐14 meteorological satellite, 1 : 10 000 land‐use data, and 1 : 10 000 topographical data, the mean height, leaf area index and fractional vegetation cover of wheat at Yucheng Integrated Agricultural Experiment Station are simulated as functions of NDVI. Then, hourly horizontal wind velocity at a height of 4 m during the period from 21:05 on 5 March 2000 to 7:05 on 24 May 2000 is calculated, for which hourly observed horizontal wind velocity at a height of 2 m is first used to simulate the wheat parameter of the dimensionless constant. The results show that the simulated velocity is almost identical to the observation velocity at a height of 4 m.