Simulation of DEM Based on ICESat-2 Data Using Openly Accessible Topographic Datasets ^†

Abstract

The digital elevation model (DEM) is a three-dimensional digital representation of the terrain or the Earth’s surface. For determining topography, DEMs are the most used and ideal method with (i.e., the digital surface model) or without the objects (i.e., the digital terrain model). Various techniques are used to create DEMs, including traditional surveying methods, photogrammetry, InSAR, lidar, clinometry, and radargrammetry. DEMs generated by LiDAR tend to be the most accurate except for the VHR datasets acquired from UAVs with spatial resolution of a few centimeters. In many parts of the region, LiDAR data are not available, which limits researchers’ access to high-resolution and accurate DEMs. With a beam footprint of 13 m and a pulse interval of 0.7 m, ICESat-2 promises high orbital precision and high accuracy. ICESat-2 can produce high-accuracy DEMs in complex topographies with an accuracy of a few centimeters. The Earth’s surface elevations are provided by discrete photon data from ICESat-2. It is difficult to justify the continuity of the topographical data using traditional interpolation techniques since they over-smooth the estimated space. Geospatial data can be analyzed with machine learning algorithms to extract patterns and spatial extents. To estimate a DEM from LiDAR point data from ICESat-2 using CartoDEM, machine learning regression algorithms are used in this study V3 R1. This study was conducted over a hilly terrain of the Dehradun region in the foothills of the Himalayas in India. The applicability and robustness of these algorithms has been tested for a plain region of Ghaziabad, India, in an earlier study. The interpolation of DEM from ICESat-2 data was analyzed using regression-based machine learning techniques. Interpolated DEMs were evaluated against the TANDEM-X DEM of the same region with RMSEs of 7.13 m, 7.01 m, 7.15 m, and 3.76 m respectively, using gradient boosting regressors, random forest regressors, decision tree regressors, and multi-layer perceptron (MLP) regressors. Based on the four algorithms tested, the MLP regressor shows the best performance in the previous study. The accuracy of the simulated ICESat-2 DEM using the MLP regressor was assessed in this study using the DGPS points over the Dehradun region. The RMSE was of the order of 6.58 m for the DGPS reference data.

1. Introduction

The digital elevation model is a visualization of the bare Earth’s surface elevations [1]. DEMs are generated from numerous sources including contour lines, topographic maps, stereo photogrammetry, SAR interferometry, DGPS points, etc. Amongst all the techniques to create DEMs, high-resolution laser altimetry (LiDAR) is proven to generate higher accuracy DEMs [2]. Various terrain-related studies including hydrological modelling, flood inundation mapping, monitoring volcanic activities, etc. use DEM as an integral input data. Therefore, the accuracy of the input DEMs for various applications is an important parameter to yield good quality results [3]. Systematic errors in DEM products are still possible due to equipment precision limitations, which is time consuming, costly and difficult to rectify [4]. To enhance the quality and accuracy of the available open-source DEMs various studies have been conducted [5].

An Earth Observation System satellite, the Ice, Cloud, and Land Elevation Satellite (ICESat-2), was launched by NASA. Highly accurate data from ICESat-2 provides extensive and sufficient reference data for quality analyzing different DEMs [6].

Interpolation is the process of estimating the value of attributes at unsampled sites from measurements made at point locations within the same area or region, but it often leads to over-smoothening [7]. Simulation technique can be defined as a statistical way to generate data, where unavailable, based on the statistical models like linear regression which correlates the input and output of the sample/training data and calculates the statistical relationship between the two and implements the same for other input points to generate their corresponding output. This study hence utilizes the CartoDEM and ICESat-2 LiDAR data to simulate a higher accuracy DEM using machine learning algorithms.

Various studies have shown that for the Indian region, good-quality and best accuracy terrain data are available via Cartosat-1 DEM [8]. This study focusses on simulating a higher accuracy spaceborne LiDAR DEM by correlating it with the CartoDEM measurements. The simulated DEM is then validated using DGPS data. The accuracy of the simulated output DEM is higher than the CartoDEM and closer to the LiDAR measurements.

2. Methods

2.1. Study Area

This study was conducted over the hilly terrain of the Dehradun region in the foothills of the Himalayas. The study area lies between latitudes 30°01′ N and 31°2′ N and longitudes 77°34′ E and 78°18′ E (Figure 1).

2.2. Datasets

2.2.1. CartoDEM V3 R1

Using the CartoDEM V3 R1 product, the corresponding LiDAR DEM was generated to enhance the vertical accuracy of the CartoDEM. The Cartosat-1 satellite is the first Indian remote sensing satellite that can provide stereo visualization in orbit. A number of products derived from Cartosat-1 can be used for various geographical information system (GIS) applications, including digital elevation models (Figure 1), orthoimage products, and value-added products for GIS.

2.2.2. ICESat-2

In ICESat-2, the ATLAS instrument provides all of the topographic data through its advanced topographic laser altimetry system. A total of three relatively strong beams and three relatively weak beams are present [9]. In the context of the accurate analysis of different DEMs, it provides enough and high-quality reference data [10].

2.2.3. Ground Control Points (GCPs)

The Trimble R7 GNSS receivers and Leica 500 series receivers were used for the collection of the field data. A total of 16 GCPs were collected over the Dehradun region and utilized for the validation of the simulated DEM.

2.3. Methodology

The overall methodology followed for this study is depicted in Figure 2. Pancholi et al. has successfully generated DEM using the machine learning models of decision tree (DT), random forest, gradient boosting machine (GBM), and multi-layer perceptron (MLP) [11], out of which the MLP model gave minimal error output.

2.3.1. Machine Learning Models

This section describes the machine learning models used for this study.

• Decision Tree

The decision tree model, which finds a foundation in machine learning theory, is a potent tool for dealing with regression and classification challenges. In contrast to other classification approaches that use a group of features (or bands) together to complete classification/regression in a single decision step, it relies on a multilevel or hierarchical decision strategy or a tree-like structure. It consists of leaves, internal nodes, and the root node. Each decision tree node uses a top–down technique to perform binary classification, separating one or more classes from the others by progressing down the tree until the leaf node is reached. In essence, a complicated problem statement is divided into lesser problems by a decision tree, and the simpler decisions that follow lead to the complex conclusion. The decision tree model is chosen for the study because it effectively resolves problems involving both linear and non-linear interactions [12].

• Random Forest

The ensemble machine learning model random forest has two or more decision trees, which together form a “decision forest”. Finding the majority by voting on the individual decision tree outcomes yields the random forest model’s outcome. The design of each decision tree that makes up random forest affects how well it performs. There are two steps in this process that include random selection. The first step uses a bootstrap technique to randomly select about two-thirds of the training dataset before beginning to build each decision tree. Out-of-bag (OOB) data, which make up the final third of the dataset, are utilized for inner cross-validation to assess the precision of the mode [13].

• Gradient Boosting Machine

Gradient boosting is a unique ensemble machine learning approach that utilizes the predictive capability of boosting on a decision tree. It has several decision trees constructed sequentially, each of which is a “weak” learner. These following learners draw lessons from the preceding model’s errors to create the final model, which is a “strong” one. The first model is given some initial constant values that are calculated by averaging all of the target values. Residuals are the calculated differences between the anticipated value and the actual target values. The goal values for the following decision tree are these residuals r1, and the residuals r2 are computed from the anticipated value and r1. This carries on until every decision tree is trained [14].

• Artificial Neural Network

An artificial neural network (ANN) is a nonlinear nonparametric framework that uses neural network propagation across layers based on gradient learning techniques to simulate human brain receptors and information processing. The input layer, hidden layer, and output layer are the three layers that make it up. Through synapses, the input layer receives the input and transmits it to the hidden levels; likewise, the hidden layers transmit the data to the output layer. The weights that the synapses hold regulate how information moves from one layer to the next. Equation (1) mathematically describes a neuron in the hidden layer or output layer.

$$u={\sum }_{i=1}^n{w}_i{x}_i \mathrm{a}\mathrm{n}\mathrm{d}, \mathrm{y}=\phi (u+b)$$

(1)

where w denotes synaptic weights, x denotes the input to neurons, y denotes the output from neurons, u denotes a linear combiner of input signals, b denotes bias, and $\phi$() is the activation function used to restrict the input range.

2.3.2. Hyperparameters Used

Some variables must be put up in advance and cannot be changed while training. These variables or parameters are called hyperparameters. They are the factors that control how a learning algorithm learns and determine the final outcome of the models [15]. The goal of hyperparameter optimization is to find the optimal settings for hyperparameters to provide good results from data as rapidly as feasible. Hyperparameter optimization is performed as the parameters tuned during this process (

Table 1. Hyperparameters tuned for the regression models.

Model	Parameter	Selected Value
DT	Maximum depth	None
	Criterion	Mean absolute error
RF	Number of trees	100
	Maximum depth	None
GBM	Loss	Squared error
	Number of estimators	100
ANN	Learning rate	0.001
	Maximum number of iteration	200
	Activation	ReLU

) are not optimized by the models during training and has to be provided to the models before the training actually begins.

2.3.3. Accuracy Assessment

Utilizing the coefficient of determination (R2), root mean square error (RMSE), and mean absolute error (MAE) in comparison to the simulated DEM and DGPS data, the machine learning model was statistically evaluated for the Dehradun region. The regression model performance is often evaluated using the R2 and RMSE of the predicted and actual values. For estimating accuracy metrics over an area’s elevation values, a higher R2 and lower MAE and RMSE are correlated with higher precision and accuracy, respectively. To obtain a clearer result, the LE90 value was also calculated for the simulated DEM using the MLP regressor model. The formula extensively used for LE90 is given in Equation (2) [16,17].

$$LE90=1.6449\ast RMSE$$

(2)

3. Results and Discussion

In this study, an implementation of machine learning models was conducted to simulate a higher accuracy DEM providing elevation values closer to the ICEsat-2. The accuracy of the simulation was evaluated primarily using the 20% testing data that is unseen by the model and is shown in

Table 2. Accuracy metrics of machine learning models.

	DT	RF	GBM	MLP
R2	0.99	0.99	0.99	0.99
RMSE	3.61	3.41	3.42	3.12
MAE	2.28	2.21	2.25	2.20

.

The ANN model displayed the best results in terms of RMSE and MAE followed by RF, GBM, and DT. Figure 3 shows the simulated DEM using the four models. The validation of the simulated output using MLP was conducted using DGPS GCPs (shown in Figure 4). The accuracy of the simulated DEM using DGPS yielded an RMSE of 6.58 m which is very promising, on a hilly terrain in the foothills of the Himalayas, for the simulated DEM product. The LE90 score for the simulated DEM was 10.82 m, signifying the confidence that a minimum of 90% of the vertical error falls within the limit of 10.82 m. The variation in the RMSE while comparing the RMSE derived from ICESat-2 and DGPS can be attributed to the lower uncertainty of DGPS on collecting the elevation data when compared to ICESat-2 points, which need the filtering of footprints (elevation values) based on the deviations. Furthermore, ICESat-2 footprints are not evenly distributed throughout the study area and are more concentrated in plane areas and less concentrated in hilly areas.

The highest values of elevation are 1950.87 m, 1975 m, 1964.77 m, and 1967.78 m for DT, GBM, RF, and MLP machine learning models, whereas the highest elevation value in the ICESat-2 footprint is 1976.87 m. This is a realistic representation of elevation with respect to the training data used in the model. However, since the ICESat-2 data points are not densely distributed in the study area and very sparsely distributed in the high elevation zones, there are possibilities of the under-representation of elevation in zones higher than 1976.87 m.

An even distribution of ICESat-2 data in plane and hilly terrains while training the model can potentially improve the accuracy of the models. Including ICESat-2 points in the hilly terrain of a nearby area for training the models or using the same for developing a deeper neural network based on the transfer learning approach can evenly balance training data in all elevation ranges and improve the results of the model.

4. Conclusions

The current study attempted to simulate an ICESat-2 DEM over a 388 km² area in the hilly terrain of Dehradun located in the foothills of the Himalayas. Four machine learning algorithms, DT, RF, GBM, and MLP, were used for the simulation using CartoDEM and ICESat-2 data and produced promising results with MLP performing the best. The accuracy assessment was initially conducted using ICESat-2 points and validated using DGPS GCPs. The study concluded that although DGPS points provide a planned way of validating DEMs, the collection of a large number of DGPS points is time consuming and a costly issue, whereas the ICESat-2 dataset not only provide a large number of high accuracy elevation points for the simulation. Further investigations must be carried out to improve the accuracy of the DEM at the centimeter scale. Increasing the number of training points in all elevation zones and land use or land cover areas, the transfer learning ML approach is suggested for future improvements.