High Accuracy Surface Modeling Research Articles

Dynamic changes and impacts of accumulated temperature on the Tibetan plateau from 1980 to 2018 based on the fusion of simulation and observation data

In the context of global warming, the thermal conditions of the Tibetan Plateau have changed significantly in recent decades. In the present study, we analysed the spatiotemporal variation in T ≥ 0 °C accumulated temperature (AT0) on the Tibetan Plateau from 1980 to 2018 and its effect on normalized difference vegetation index (NDVI) changes by fusing climate model outputs and ground observations using the High Accuracy Surface Modeling (HASM). Cross-validation revealed that the root mean square error (RMSE) and R2 of the fused data from HASM were 1.593 °C and 0.719, respectively, which were greater than the 5.864 °C and 0.385, respectively, before fusion, indicating that HASM fusion improved the accuracy and that a more accurate AT0 could be obtained. Over the past 39 years, AT0 on the Tibetan Plateau had increased at a rate of 7.53 °C/year. The growth period was extended by 0.46 days/year, while the start and end of the growth period were 0.27 days/year earlier and 0.18 days/year later, respectively. Analysis of the decadal change in AT0 revealed that the areas with AT0 < 500 °C decreased by 5 % and that the areas with AT0 > 2000 °C increased by 6.2 %. However, a slower warming trend appeared after 2010 because of the decreasing rate of the daily mean temperature increase during the growth period. Increasing AT0 also promoted vegetation growth, especially in parts of the southern and eastern plateau regions, with a Pearson's correlation coefficient of 0.46 on the entire plateau between AT0 and the average NDVI during the growth periods. However, there was a significant negative correlation with a coefficient lower than −0.4 in the Qaidam Basin, and partial correlation analysis showed that the extension of the growth period was the main factor influencing the decrease in the NDVI in the Qaidam Basin.

Spatiotemporal analysis of global atmospheric XCO2 concentrations before and after COVID-19 using HASM data fusion method

The COVID-19 outbreak that began in 2020 has changed human activities and thus reduced anthropogenic carbon emissions in most parts of the world. To accurately study the impact of the COVID-19 pandemic on changes in atmospheric XCO2 concentrations, a data fusion method called High Accuracy Surface Modeling (HASM) is applied using the CO2 simulation from GEOS-Chem as the driving field and GOSAT XCO2 observations as the accuracy control conditions to obtain continuous spatiotemporal global XCO2 concentrations. Cross-validation shows that using High Accuracy Surface Modeling greatly improves the mean absolute error and root mean square error of the XCO2 data compared with those for GEOS-Chem simulation data before fusion, and the R2 is also increased from 0.54 to 0.79 after fusion. Moreover, OCO-2/OCO-3 XCO2 observational data verify that the fused XCO2 data achieve a lower MAE and RMSE. Spatiotemporal analysis shows that the global XCO2 concentration exhibited no obvious trend before or after the COVID-19 outbreak, but the growth of global and terrestrial atmospheric XCO2 in 2020 can reflect the impact of the COVID-19 pandemic; that is, the rapid growth in terrestrial atmospheric XCO2 observed before 2019 slowed, and high-speed growth resumed in 2021. Finally, obvious differences in the pattern of XCO2 growth are found on different continents.

Estimation and Mapping of Actual and Potential Grassland Root Carbon Storage: A Case Study in the Altay Region, China

The actual root carbon storage (ARCS) and potential root carbon storage (PRCS) of grasslands play an important role in the global carbon balance and carbon neutralization. However, estimation of these indicators is difficult. In addition, their spatial patterns and crucial driving factors also require clarification. In this study, an approach for accurate estimation of ARCS and PRCS was developed incorporating a support vector machine model and high-accuracy surface modeling. Based on field data collected from Altay Prefecture in 2015, the estimation accuracy (R2) of root biomass in the 0–10, 10–20, and 20–30 cm soil layers of grassland were 0.73, 0.63, and 0.60, respectively. In addition, the spatial patterns of actual root carbon density (ARCD) and potential root carbon density (PRCD) were analyzed. The ARCD increased with the increase in elevation. High PRCD was located on hillsides with a gentle slope. The dominant interaction factors for the ARCD spatial pattern were temperature and precipitation, whereas the main interaction factors for the PRCD pattern were temperature and slope. The grassland ARCS and PRCS in Altay Prefecture were estimated to be 48.52 and 22.69 Tg C, respectively. We suggest there is considerable capacity to increase grassland ARCS in the study area.

A comparative mapping of plant species diversity using ensemble learning algorithms combined with high accuracy surface modeling

Plant species diversity (PSD) has always been an essential component of biodiversity and plays an important role in ecosystem functions and services. However, it is still a huge challenge to simulate the spatial distribution of PSD due to the difficulties of data acquisition and unsatisfactory performance of predicting algorithms over large areas. A surge in the number of remote sensing imagery, along with the great success of machine learning, opens new opportunities for the mapping of PSD. Therefore, different machine learning algorithms combined with high-accuracy surface modeling (HASM) were firstly proposed to predict the PSD in the Xinghai, northeastern Qinghai-Tibetan Plateau, China. Spectral reflectance and vegetation indices, generated from Landsat 8 images, and environmental variables were taken as the potential explanatory factors of machine learning models including least absolute shrinkage and selection operator (Lasso), ridge regression (Ridge), eXtreme Gradient Boosting (XGBoost), and Random Forest (RF). The prediction generated from these machine learning methods and in situ observation data were integrated by using HASM for the high-accuracy mapping of PSD including three species diversity indices. The results showed that PSD was closely associated with vegetation indices, followed by spectral reflectance and environmental factors. XGBoost combined with HASM (HASM-XGBoost) showed the best performance with the lowest MAE and RMSE. Our results suggested that the fusion of heterogeneous data and the ensemble of heterogeneous models may revolutionize our ability to predict the PSD over large areas, especially in some places limited by sparse field samples.

Application of a combinatorial approach for soil organic carbon mapping in hills

Accurate mapping of soil organic carbon (SOC) is critical to improve C management and develop sustainable management policies. However, it is constrained by local variations of the model parameters under complex topography, especially in hills. This study applied a methodological framework to optimize the spatial prediction of SOC in the hilly areas during 1981–2012 by quantifying the relative importance of environmental factors, which include both qualitative factors and quantitative variables. Results showed that SOC increased twofold with a moderate spatial dependence during the past 32 years. During this period, land use patterns, soil groups, topographic factors, and vegetation coverage had significant impacts on the SOC changes (p < 0.01). Specifically, the impact of land use patterns has exceeded the impact of soil groups and became the dominant factor affecting SOC changes. Meanwhile, impacts from the topographic factors and vegetation coverage have substantially declined. Based on those results, a combinatorial approach (LS_RBF_HASM) was developed to map SOC using radial basis function neural network (RBF) and high accuracy surface modelling (HASM), and to generate more detailed spatial mapping relationships between SOC and the affecting factors. Compared with ordinary kriging (OK), land use-soil group units (LS) and HASM combined (LS_HASM), multiple linear regression (MLR) and HASM combined with LS (LS_MLR_HASM); LS_RBF_HASM showed a better performance with a decline of 6.3%–37.7% prediction errors and more accurate spatial patterns due to the quantitative combination of auxiliary environmental variables and more information on the SOC variations within local factors captured by RBF and HASM. Additionally, MLR may partially undermine the relationship of the internal spatial structure due to the highly nonlinear relation between SOC and environmental variables. This methodological framework highlights the optimization of more environmental factors and the calculation of spatial variability within local factors and provides a more accurate approach for SOC mapping in hills.

Incorporation of high accuracy surface modeling into machine learning to improve soil organic matter mapping

Digital soil mapping approaches related to soil organic matter (SOM) are crucial to quantify the process of the carbon cycle in terrestrial ecosystems and thus, can better manage soil fertility. Recently, many studies have compared machine learning (ML) models with traditional statistical models in digital soil mapping. However, few studies focused on the application of hybrid models that combine ML with statistical models to map SOM content, especially in loess areas, which have a complicated geomorphologic landscape. In this study, the trend prediction used two ML models, i.e., gradient boosting modeling and random forest (RF), and a traditional stepwise multiple linear regression plus interpolated residuals generated from two classic geostatistical models, i.e., ordinary kriging and inverse distance weighting, and a high accuracy surface modeling (HASM) were implemented to map SOM content in the Dongzhi Loess Tableland area of China. A total of 145 topsoil samples and heterogeneous environmental variables were collected to develop the hybrid models. Results showed that 18 variables related to soil properties, climate variables, terrain attributes, vegetation indices, and location attributes played an important role in SOM mapping. The models that incorporate ML algorithms and interpolated residuals to predict SOM variation were found to have a better ability to handle complex environment relationships. The HASM model outperformed traditional geostatistical models in interpolating the residuals. In contrast, RF combined with HASM residuals (RF_HASM) gave the best performance, with the lowest mean absolute error (1.69 g/kg), root mean square error (2.30 g/kg), and the highest coefficient of determination (0.57) and concordance correlation coefficient (0.69) values. Moreover, the spatial distribution pattern obtained with RF_HASM yielded a spatial distribution of SOM that better fit the actual distribution pattern of the study area. In conclusion, these results suggest that RF_HASM is particularly capable of improving the mapping accuracy of SOM content at the regional scale.

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.

Remote sensing inversion of grassland aboveground biomass based on high accuracy surface modeling

Accurate and effective accounting of grassland aboveground biomass (AGB) is essential for grassland carbon storage accounting and pastoral agriculture sustainability. In this study, we combined AGB field survey data and remote sensing data to build a suitable model to estimate the grassland AGB in the Three-River Source Region (TRSR) of China. Three machine learning models were used to simulate the grassland AGB from 2001 to 2019, including support vector machine (SVM), random forest (RF), and high accuracy surface modeling (HASM). The results show that (1) the HASM achieved better results than the RF and SVM models (R2 = 0.8459 > 0.72 > 0.5858; RMSE = 29 < 41 < 56), and the HASM results reproduce the spatial distribution characteristics of the biomass well. The subsequent spatiotemporal analysis of the AGB conducted in this study was based on the results of the HASM. (2) The highest AGB was located in the eastern and central-southern parts of the TRSR, and the lowest AGB was distributed in the western region. (3) The overall change in the AGB revealed that the percentage of the area that experienced a significant increase in AGB (21%) was larger than that of the area that experienced a significant decrease (13%), and the stable areas accounted for 66% of the total area. The grassland AGB increased by 1 g/m2/yr during 2001–2019. (4) The factors driving the changes in the AGB were analyzed. Overall, the warm and wet climate conditions promoted grass growth in most regions of the TRSR. (5) However, the biomass decreased in some regions with warm and wet conditions. For example, overgrazing and increased populations of grazing led to significant biomass decreases in the towns of Ziketang and Heka in Xinghai County. In this study, the grassland AGB was simulated based on the HASM model, with a high accuracy and a spatial resolution of 500 m. The results of this study provide a scientific basis for grassland resource protection and the highly effective implementation of grassland restoration projects in China.

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.

A fundamental theorem for eco-environmental surface modelling and its applications

We propose a fundamental theorem for eco-environmental surface modelling (FTEEM) in order to apply it into the fields of ecology and environmental science more easily after the fundamental theorem for Earth’s surface system modeling (FTESM). The Beijing-Tianjin-Hebei (BTH) region is taken as a case area to conduct empirical studies of algorithms for spatial upscaling, spatial downscaling, spatial interpolation, data fusion and model-data assimilation, which are based on high accuracy surface modelling (HASM), corresponding with corollaries of FTEEM. The case studies demonstrate how eco-environmental surface modelling is substantially improved when both extrinsic and intrinsic information are used along with an appropriate method of HASM. Compared with classic algorithms, the HASM-based algorithm for spatial upscaling reduced the root-mean-square error of the BTH elevation surface by 9 m. The HASM-based algorithm for spatial downscaling reduced the relative error of future scenarios of annual mean temperature by 16%. The HASM-based algorithm for spatial interpolation reduced the relative error of change trend of annual mean precipitation by 0.2%. The HASM-based algorithm for data fusion reduced the relative error of change trend of annual mean temperature by 70%. The HASM-based algorithm for model-data assimilation reduced the relative error of carbon stocks by 40%. We propose five theoretical challenges and three application problems of HASM that need to be addressed to improve FTEEM.

Optimized free-form surface modeling of point clouds from laser-based measurement

Freeform parameterizations to reproduce structure deformation are increasingly important topics in laser-scanner-based deformation analyses. High-accuracy assurance of free-form surface approximation is extremely critical for reliable deformation analysis. One main challenge in this field is the model selection. Improper model complexity could result in under-fitting the real object shape or overfitting data noises, and thus a failure of deformation analysis. A multi-sensor system could integrate advantages of different sensors and improve the quality of mission completed. This paper combines terrestrial laser scanning (TLS) and laser tracker (LT) technologies, to enhance high-accuracy surface modeling in deformation analysis. A surface-based B-spline approximation and a multi-sensor system are investigated, the latter of which focuses mainly on the combination of TLS and LT technologies. The innovation of this paper is that the surface-based B-spline approximation is validated and optimized with LT corner cube reflectors. Hypothesis testing is adopted to select the best parameter setting by judging most consistency of TLS and LT in various epochs. In the B-spline surface modeling, both instrumental and numerical uncertainties are considered. We use the instrumental uncertainty model based on intensity value, as well as numerical uncertainty based on adjustment theories. A sampling strategy is proposed to avoid data gaps and obtain even distributed data points.

Surface modelling of forest aboveground biomass based on remote sensing and forest inventory data

An accurate estimation of forest aboveground biomass (AGB) is important for carbon accounting. In this study, six methods, including partial least squares regression, regression kriging, k-nearest neighbour, support vector machines, random forest and high accuracy surface modelling (HASM), were used to simulate forest AGB. Forest AGB was mapped by combining Geoscience Laser Altimeter System data, optical imagery and field inventory data. The Normalized Difference Vegetation Index (NDVI) and Wide Dynamic Range Vegetation Index (WDRVI0.2) of September and October, which had a stronger correlation with forest AGB than that of the peak growing season, were selected as predictor variables, along with tree cover percentage and three GLAS-derived parameters. The results of the different methods were evaluated. The HASM model had the best modelling accuracy (small MAE, RMSE, NRMSE, RMSV and NMSE and large R 2). A forest AGB map of the study area was generated using the optimal model.

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.

Temperature changes in the Heihe River Basin based on high accuracy surface modelling

AbstractIn the context of global warming, significant differences in temperature changes occur in different regions. Obtaining a more accurate temperature distribution is important for studying regional climate change. A high accuracy surface modeling (HASM) was introduced using the air temperature output from the weather research and forecasting (WRF) model as the driving field, and observation data from meteorological stations as the accuracy control conditions to obtain 30 years of high accuracy temperature fields in the Heihe River Basin. Verified by ground‐based observations, the WRF model has a limited ability to simulate temperature conditions and performs worse in low altitude areas and in winter. The fusion results of the HASM decrease the mean absolute error from 2.21 to 0.9°C and decrease the root mean square error from 2.58 to 1.16°C, thus significantly increasing the accuracy compared with the original simulation from the WRF model and resulting in a more reasonable temperature analysis. The Mann–Kendall test shows clear warming in the Heihe River Basin, but there is a mutation year of 1998 in winter and annual average. The space–time distributions of and variations in the temperature from the HASM results are also analysed by dividing the study period into three subperiods. The analysis shows consistent warming except for the winter 2001–2010 period compared with the winter 1991–2000 period, in which the northeast area of the lower reaches of the Heihe River Basin was cool. Temperature changes in the Heihe River Basin also show that the sparsely populated Gobi Desert in the north and the southern high mountains show extreme sensitivity to climate change.

Methods for simulating climate scenarios with improved spatiotemporal specificity and less uncertainty

Abstract The General Circulation Models and Coupled Model Intercomparison Project Phase 5 (CMIP5) datasets used for the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) painted future opportunities and challenges afforded by climate change with broad strokes. The model outputs incorporate substantial uncertainty due to the relatively coarse spatial scales and the complexity of the processes incorporated in these models and as a consequence, it is difficult to predict future trends and infrastructure needs in large countries like China at local and regional scales over the next century. The work reported in this article describes several statistical transfer functions that were used to downscale CMIP5 climate predictions in China. The original and new downscaled CMIP5 predictions are compared with observations from 735 meteorological stations scattered across China for the period 2006–2015 to show the various improvements achieved with downscaling. Comparing the three RCP scenarios (2.6, 4.5 and 8.5) during the period 2006–2015 with observations from 735 meteorological stations indicates that MAEs of mean annual temperature were 1.9 °C for China on average and that the actual temperature was under-estimated at 87% of the meteorological stations under all three scenarios. After the downscaling process using a High Accuracy Surface Modeling (HASM)-based method, the MAEs for mean annual temperature under the three scenarios were reduced to 0.62 °C for China on average. The MAEs of annual mean precipitation were 317.29, 315.24 and 315.49 mm under the RCP2.6, RCP4.5, and RCP8.5 scenarios, respectively for China on average and the actual precipitation was over-estimated by all three scenarios at approximately 75% of the meteorological stations. The HASM-based downscaling process meant that the MAEs for the three scenarios were reduced to 80–85 mm for China on average. The downscaled predictions are used to show how temperature and precipitation are likely to vary by region in China from 2011 to 2100. The downscaled results suggest that most of China will become warmer and wetter on average under all three scenarios over the next 30 years and provide improved information to guide the investments and actions that will be needed to improve climate change resilience across China's varied landscapes in the 21st century.

Fusion of Simulated and Observational Temperature Data in the Beijing-Tianjin-Hebei Region Based on High-Accuracy Surface Modeling

Temperature changes have a major impact on all aspects of human society and have attracted global attention. The scarcity of observation data and the inaccuracy of the models make obtaining accurate temperature distributions a challenge. This study introduces high-accuracy surface modeling (HASM) combined with temperature simulations from the Weather Research and Forecasting (WRF) model and temperature records from observation stations to investigate the spatiotemporal characteristics of temperature in the Beijing-Tianjin-Hebei region during the period of 1956–2005. Leave-one-out cross-validation is applied to verify the temperature fields before and after the fusion of the models. The results indicate that the WRF model has a limited ability to simulate temperature conditions, but the overall deviation across the region is relatively large. The fusion results of the HASM decrease the mean absolute error (MAE) and the root-mean-square error (RMSE) by half in most instances, and the correlation between the fusion data and observation data is approximately 0.01–0.03 higher than that with the WRF simulation data. Based on the fusion data, obvious warming trends are observed during 1976–2005. In general, temperatures in spring, summer, and autumn increase rapidly from 1996 to 2005 but from 1976 to 1995 in winter. The substantial fluctuations in the interannual temperature during 1996–2005 in summer, autumn, and winter may be related to the frequent occurrence of extreme weather. The spatial distribution of temperature change differs in each season during 1956–1995. A dramatic increase in temperature occurs in the western part of the study area during 1996–2005 but with no seasonal difference.

Simulation and analysis of XCO2 in North China based on high accuracy surface modeling

As an important cause of global warming, CO2 concentrations and their changes have aroused worldwide concern. Establishing explicit understanding of the spatial and temporal distributions of CO2 concentrations at regional scale is a crucial technical problem for climate change research. High accuracy surface modeling (HASM) is employed in this paper using the output of the CO2 concentrations from weather research and forecasting-chemistry (WRF-CHEM) as the driving fields, and the greenhouse gases observing satellite (GOSAT) retrieval XCO2 data as the accuracy control conditions to obtain high accuracy XCO2 fields. WRF-CHEM is an atmospheric chemical transport model designed for regional studies of CO2 concentrations. Verified by ground- and space-based observations, WRF-CHEM has a limited ability to simulate the conditions of CO2 concentrations. After conducting HASM, we obtain a higher accuracy distribution of the CO2 in North China than those calculated using the classical Kriging and inverse distance weighted (IDW) interpolation methods, which were often used in past studies. The cross-validation also shows that the averaging mean absolute error (MAE) of the results from HASM is 1.12 ppmv, and the averaging root mean square error (RMSE) is 1.41 ppmv, both of which are lower than those of the Kriging and IDW methods. This study also analyses the space-time distributions and variations of the XCO2 from the HASM results. This analysis shows that in February and March, there was the high value zone in the southern region of study area relating to heating in the winter and the dense population. The XCO2 concentration decreased by the end of the heating period and during the growing period of April and May, and only some relatively high value zones continued to exist.

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.

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.