Improving the Accuracy of Open Source Digital Elevation Models with Multi-Scale Fusion and a Slope Position-Based Linear Regression Method

Round 1

Reviewer 1 Report

The manuscript Improving the Accuracy of Open Source Digital Elevation Models with Multi-scale Fusion and Slope Position-Based Linear Regression Method deals with some methods aim to use different sources of DEMs in order to get a more accuracy fused DEM. The issue of the manuscript matches with the scope of the Remote Sensing journal and it develops an interesting approach and well exposed study.

Some minor improvements are suggested:

A table indicating the horizontal and vertical accuracy for the DEM (AW3D30 and SRTM-1 DEM)used in the fusion and the test DEM (ICESat GLAH14) would facilitate the understood of the procedure accuracy achieved in this study and why ICESat GLAH14 is used as test dataset.

The introduction section would be more complete if the authors mention that the DEM accuracy could be studied not only from the elevation accuracy viewpoint but also to the horizontal accuracy viewpoint.

Carrara, A., Bitelli, G,. Carla, R. (1997). Comparison of techniques for generating digital terrain models from contour lines. International Journal of Geographical Information Science. 11(5): 451-473

Gao, J. (1997). Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. International Journal of Geographical Information Science. 11(2): 199-212.

Reinoso, J. F. (2011). An algorithm for automatically computing the horizontal shift between homologous contours from DTMs. ISPRS Journal of Photogrammetry and Remote Sensing, 66(3):272-286

Line 105 says …with a complex surface topology…  Is it possible the authors wanted to say topography? 

Red rectangles in Figure 7 almost are not visible, and green ones are difficult to see, please improve their thick lines.

Lines 422-424 the authors say …The Haar wavelet method has better performance than the Bior3.7 wavelet method in both sites, which proves indirectly that having many wavelet basis functions is advantageous for wavelet analysis… I think this assertion is not proved because the differences between values is very small, so a less categorical assertion should be expressed.

Lines 436-437 authors say …Hence, the fused DEM obtained by N-AMD, named DEMN, is chosen for further research… so that I understand its ME in table 2 is 3.173 but in table 4 the ME is 2.789. Please could you explain why do they have not the same value?

Author Response

Reviewer 1:
The manuscript Improving the Accuracy of Open Source Digital Elevation Models with Multi-scale Fusion and Slope Position-Based Linear Regression Method deals with some methods aim to use different sources of DEMs in order to get a more accuracy fused DEM. The issue of the manuscript matches with the scope of the Remote Sensing journal and it develops an interesting approach and well exposed study.

Response: We appreciate for your affirmation about our manuscript. Thanks for your valuable suggestions and comments. We have corrected our manuscript according to your comments. The corresponding revision can be found with tracked corrections in the updated manuscript.

Main Corrections:

1.         A table indicating the horizontal and vertical accuracy for the DEM (AW3D30 and SRTM-1 DEM)used in the fusion and the test DEM (ICESat GLAH14) would facilitate the understood of the procedure accuracy achieved in this study and why ICESat GLAH14 is used as test dataset.

Response: We have added it according to the comment which can be seen in the updated manuscript.

Table 1. The basic parameters of the SRTM-1, AW3D30 and ICESat global land surface altimetry product.

2.         The introduction section would be more complete if the authors mention that the DEM accuracy could be studied not only from the elevation accuracy viewpoint but also to the horizontal accuracy viewpoint.

Carrara, A., Bitelli, G,. Carla, R. (1997). Comparison of techniques for generating digital terrain models from contour lines. International Journal of Geographical Information Science. 11(5): 451-473

Gao, J. (1997). Resolution and accuracy of terrain representation by grid DEMs at a micro-scale. International Journal of Geographical Information Science. 11(2): 199-212.

Reinoso, J. F. (2011). An algorithm for automatically computing the horizontal shift between homologous contours from DTMs. ISPRS Journal of Photogrammetry and Remote Sensing, 66(3):272-286

Response: The introduction has been improved from the two viewpoints of horizontal accuracy and vertical accuracy according to the comment which can be seen in the updated manuscript.The references you provided have broaden our horizons, and we have quoted them in this article. Thank you very much for your guidance. The revised introduction is as follows.

DEMs are the fundamental tools of geo-analysis, and also the essential input variables for many models. They have been widely used in science and engineering fields such as water resource management [1–3], agriculture [4,5], and ecology [6–8]. DEMs can be derived not only from scanned/vectorized contour lines of existing topographic sheets obtained by field measurement [9], but also from remote sensing techniques. While the accuracy of the field measurement method is quite high, it is also time consuming and costly, especially in hard-to-reach areas [10,11]. Remote sensing has become the primary means of obtaining DEMs due to its near ideal characteristics in terms of coverage, and spatial and temporal resolution [12].

Owing to their high resolution (1 arc-second) and free access to download, the two most widely used quasi-global digital elevation models produced by remote sensing technology are the SRTM-1 DEM and the ASTER GDEM v2 [13]. The ASTER GDEM v2 is produced by optical stereoscopy [14], while the SRTM-1 DEM is based on the interferometric synthetic aperture radar technique, called InSAR [15]. They are widely applied in various fields because of their availability rather than their accuracy [16]. Unfortunately, all DEMs contain errors owing to the methods of collection and processing of the images that are used to produce them [17]. Their accuracy can lead to problems that are experienced in local and regional analyses [18].

To address these errors, a mass of relevant researches have been carried on by many scholars. Rawat et al. [19] assessed the horizontal accuracy of ASTER GDEM, SRTM and Castosat DEM with 20 GCPS and concluded that the three DEMs have different horizontal accuracy. Reinoso [20] provided an algorithm which automatically computed the horizontal shift for each contour set with same height between two DEMs. Further research by Reinoso et al. [21] estimated horizontal displacement between DEMs by means of particle image velocimetry techniques and pointed out that the largely ignored horizontal component beared a great influence on the positional accuracy of certain linear features, e.g., in hydrological features. In another study, a simple and robust co-registration method presented for DEM pairs using the elevation difference residuals and the elevation derivatives of slope and aspect [22]. The method represented the complete analytical solution of a 3-D shift vector between two DEMs.

The DEM accuracy can be studied from the horizintal accuracy viewpoint as well as the vertical accuracy viewpoint. There has been much research into improving the vertical accuracy of DEMs. Some studies have aimed to improve the accuracy of the DEM by filling voids and removing the vegetation canopy [23–25]. Some other studies utilized geostatistical conflation techniques to increase the performance of DEM using a set of accurate Ground Control Points [26,27]. The research objects of these studies were single-source DEMs, and the inherent errors of the DEMs (depending on the method of data acquisition) cannot be eliminated. Interferometric synthetic aperture radar technique has the advantages of strong penetration ability and weak weather influence, but there remain problems with radar shadow, specular reflection and phase unwrapping. This can lead to errors when the relief amplitude and surface roughness change abruptly (such as at peaks, cliffs, etc.). As for the DEM obtained by optical sensors, the data accuracies are affected by weather conditions such as cloud cover, mist occlusion, and so on [28]. The complementary error behaviors of optical stereoscopy and InSAR provide the possibility for DEM fusion [28]. Therefore, the integration of the two kinds of DEMs using data fusion can achieve this advantageous behavior and improve the accuracy of original DEMs.

To date, many methods of DEM fusion have been put forward. Fabris et al. [29] integrated bathymetric multibeam surveys with aerial photogrammetry and lidar surveys provided the first high resolution 3D terrestrial and marine morphological map of the Panarea volcano. An innovative method of weighted sum of data sources with geomorphologic enhancement was deveioped [30] to get a better DEM than any data source, which was visually and geomorphologically homogenous. In some other studies, scholars focus on the weighted average method of DEM fusion. Schultz et al. [31] implemented the fusion of multi-temporal DEMs, obtained by optical stereoscopy in the same region through self-consistency. Honikel [32] described the process of DEM fusion by weighting the values of two DEMs according to the estimation error, utilizing the advantages of InSAR and optical stereoscopy. Schindler [33] improved the precision of large scale DEM data by weighted fusion, and pointed out the importance of weight to the fusion result. These studies looked at the DEM data as a whole and used weighted averages to improve the accuracy of the fused DEM, ignoring the different characteristics of the DEM data in various frequency domain scales. In another study, the original DEMs were transformed into the frequency domain, then high-pass and low-pass filters were used to fuse it, which achieved good results [34]. Nevertheless, details and texture information might be lost in the filtering process, which affects the ability of the DEM to describe micro-topography.

In most of the reported studies, DEM fusion was based on SRTM and ASTER. With the development of modern imaging technology, new high-resolution DEM products have been produced and released in recent years, such as the AW3D30 DSM [35,36], which also uses optical stereoscopy (with a resolution of 1 arc-second). It is the most accurate of the open source DEMs according to accuracy assessments, so it can be regarded as an alternative to the ASTER GDEM v2 [35,37]. Existing studies have showed that the impact of DEM resolution on the accuracy of terrain representation and of the gradient determined [38]. The representation accuracy decreases sharply at coarse resolutions. Therefore, Further research is necessary to examine and apply DEM fusion techniques to newly-released high-resolution datasets such as the SRTM-1 and AW3D30. Besides, Honikel [39] suggested that the errors of the stereo optical DEMs and interferometric DEMs were shown in different frequency domains. Coincidentally, multi-scale analysis methods (e.g. the popular WT and BEMD) can decompose DEMs into different frequency domains. Thus, a rule-based fusion of DEMs based on multi-scale analysis methods makes sense.

This study aims at improving the overall accuracy of open source DEMs (the SRTM-1 and AW3D30) with complementary sensing technologies by multi-scale fusion. Due to the absence of reference DEM in the study area, the ICESat global land surface altimetry product, is used to assess the accuracy of the results. The basic parameters of the experimental data are shown in Table 1. Furthermore, the effectiveness of three multi-scale analysis methods (WT, BEMD and N-AMD) in fusing DEMs is examined, based on the fusion rule mentioned in Section 3.2. Among these, N-AMD - which was originally invented to remove the cycle from sunspots - has proven superior to existing methods (e.g. chaos-based and wavelet-based approaches) in noise removal and trend determination [40–42]. Thus, it is considered to have potential for DEM multi-scale fusion because of its good performance. Finally, it is known that DEM accuracy varies for different slopes [16,43]. This suggests a further extension is possible by using the local variations in errors for different slope positions and a slope position-based linear regression method is proposed to use this information for the further calibration of fused DEM.

Table 1. The basic parameters of the SRTM-1, AW3D30 and ICESat global land surface altimetry product.

3.         Line 105 says …with a complex surface topology…  Is it possible the authors wanted to say topography? 

Response: Yes, we want to say that the one of the study area is a typical mountainous area with a complex terrain.We have corrected it according to the comment which can be seen in the updated manuscript. The revised sentences are as follows.

“It is a typical mountainous area with a complex terrain.”

4.         Red rectangles in Figure 7 almost are not visible, and green ones are difficult to see, please improve their thick lines.

Response: We have corrected it according to the comment which can be seen in the updated manuscript. The revised figure is as follows.

Figure 7. The fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red and green rectangles are the areas selected in sites A and B that are enlarged in Figure 8.

5.         Lines 422-424 the authors say …The Haar wavelet method has better performance than the Bior3.7 wavelet method in both sites, which proves indirectly that having many wavelet basis functions is advantageous for wavelet analysis… I think this assertion is not proved because the differences between values is very small, so a less categorical assertion should be expressed.

Response: We have corrected it according to this comment which can be seen in the updated manuscript with tracked corrections. The revised sentences are as follows.

“The Haar wavelet method has better performance than the Bior3.7 wavelet method in both sites, which proves that different wavelet basis functions can obtain differing results. Consequently, better results can be obtained by selecting an appropriate wavelet basis function based on source data.”

6.         Lines 436-437 authors say …Hence, the fused DEM obtained by N-AMD, named DEMN, is chosen for further research… so that I understand its ME in table 2 is 3.173 but in table 4 the ME is 2.789. Please could you explain why do they have not the same value?

Response: Because the statistical results of ME in tables 2 and 4 are based on different parts of GLAH14 dataset. In our experiment, the GLAH14 set is divided into two parts: the test set and the validation set. The test set is used to assess the vertical accracy of original and fused DEMs, and the statistical results are listed in table 2. Linear equations for the test set and fused DEM in different slope position classes are then established upon linear regression analysis to get the calibrated DEM in Section 4.2. Finally, The validation set is utilized for evaluating the vertical accuracy of fused DEM before and after the calibration, and the statistical results are listed in table 4.

Author Response File: Author Response.pdf

Reviewer 2 Report

This study targets to compare the digital elevation models from different sources based on quantitative accuracy assessment. For that, authors processed the open source DEMs including, SRTM-1 and AW3D and also applied several multi-scale fusion techniques on them (i.e. WT, BEMD, and N-AMD). To my knowledge, the manuscript has written in a scientific way, while methods and results are logically described. Yet, there are some corrections that need to be implemented before publishing.

Comments for author File: Comments.pdf

Author Response

Reviewer 2:
This study targets to compare the digital elevation models from different sources based on quantitative accuracy assessment. For that, authors processed the open source DEMs including, SRTM-1 and AW3D and also applied several multi-scale fusion techniques on them (i.e. WT, BEMD, and N-AMD). To my knowledge, the manuscript has written in a scientific way, while methods and results are logically described. Yet, there are some corrections that need to be implemented before publishing.

Response: We appreciate for your affirmation about our manuscript. Thanks for your valuable suggestions and comments. We have corrected our manuscript according to your comments. The corresponding revision can be found with tracked corrections in the updated manuscript.

Main Corrections:

General comment:

1.        What is the author’s motivation to resample the AW3D that has 5-meter DEM resolution to AW3D30? It is strange to me to shrink down an open source satellite image and then try to increase the accuracy by fusing it with other sources. In other words, when can use AW3D with 5-meter resolution, a fusion of two 30 meter dataset is not an option for surface analysis like deriving slope, aspect, etc.

Response: We feel sorry for our expression that has caused your confusion. The 5m version of AW3D is commercial data for a fee. The version we can download for free is AW3D30, which is obtained by AW3D resampling.

Specific comments:

1.       In abstract the motivation of this study was not highlighted

Response: We have improved the abstract according to the comment which can be seen in the updated manuscript. The revised abstract is as follows.

The growing need to monitor changes in the surface of the Earth requires a high-quality, accessible Digital Elevation Model (DEM) dataset, whose development has become a challenge in the field of Earth-related research. The purpose of this paper is to improve the overall accuracy of public domain DEMs by data fusion. Multi-scale decomposition is an important analytical method in data fusion. Three multi-scale decomposition methods – the wavelet transform (WT), bidimensional empirical mode decomposition (BEMD) and nonlinear adaptive multi-scale decomposition (N-AMD) - are applied to the 1-arc-second Shuttle Radar Topography Mission Global digital elevation model (SRTM-1 DEM) and the Advanced Land Observing Satellite World 3D – 30 m digital surface model (AW3D30 DSM) in China. Of these, the WT and BEMD are popular image fusion methods. A new approach for DEM fusion is developed using N-AMD (which is originally invented to remove the cycle from sunspots). Subsequently, a window-based rule is proposed for the fusion of corresponding frequency components obtained by these methods. Quantitative results show that N-AMD is more suitable for multi-scale fusion of multi-source DEMs, taking the Ice Cloud and Land Elevation Satellite (ICESat) global land surface altimetry data as a reference. The fused DEMs offer significant improvements of 29.6% and 19.3% in RMSE at a mountainous site, and 27.4% and 15.5% over a low-relief region, compared to the SRTM-1 and AW3D30 respectively. Furthermore, a slope position-based linear regression method is developed to calibrate the fused DEM for different slope position classes, by investigating the distribution of the fused DEM error with topography. The results indicate that the accuracy of the DEM calibrated by this method is improved by 16% and 13.6%, compared to the fused DEM in the mountainous region and low-relief region respectively, proving that it is a practical and simple means of further increasing the accuracy of the fused DEM.

2.         Why did the authors use WT, BEMD and N-AMS fusion methods while there are many high performed fusion techniques are subjected by others?

Response: First of all, the original DEMs chosen in this article are the newly-released AW3D30 and SRTM-1 because of their fine resolution and accuracy. The method of data acquisition of AW3D30 and SRTM-1 are different, resulting in their inherent errors being distributed in different frequency domains. However, most of the existing studies of DEM fusion neglected this importance characteristic and regarded the original DEM as a whole. Fortunately, the multi-scale decomposition method can transform the DEMs into different frequency domains, and the advantages of the two DEMs can be synthesized by fusing the corresponding frequency domains. Secondly,the WT and BEMD are widely used multi-scale decomposition method in the field of RGB image fusion, but few literatures have studied their application in DEM fusion. As for the N-AMD, we found that it reduced the noise of time series data more effectively than the linear filters, wavelet shrinkage and chaos-based noise reduction scheme. The DEMs can be regarded as a two-dimensional nonlinear surface. Therefore, we tried to extend the N-AMD to two-dimensional for DEM multiscale decomposition, compared with the WT and BEMD methods.

3.       Line 181 what is “10 fJ”? Please define it.

Response: The “fJ”is an energy unit, and its full name is femtojoule. Generally, the signal energy value of GLAS facula received from the surface without cloud interference is 10-15 fJ. Therefore, this paper take 10 fJ as threshold as one of the basic filterring criteria for GLAS data.

4.         The computational flowchart should be improved to reflect the entire process in detail. The current format is not so informative for readers.

Response: We have re-plotted the flowchart according to the comment which can be seen in the updated manuscript. The revised flowchart is as follows.

Figure 3. Schematic flowchart of the multi-scale fusion of the SRTM-1 and AW3D30.

5.        Equations are not consistently written. Normally, scalar variables and functions as single italic letters (with or without superscripts/subscripts) [exceptions are well-established multi-letter variables, e.g. ‘NDVI’, but these should be shown as roman and in their own parentheses when on the right of the equals sign in equations, with any superscripts/subscripts outside the parentheses]. Vector quantities as single bold italic letters (with or without superscripts/subscripts). Matrices and tensors as single bold roman letters (with or without superscripts/subscripts). Sets and subsets as roman.

Response: We have corrected it according to the comment which can be seen in the updated manuscript. However, we are sorry that we can't understand your meaning well. For example, we modified (1) into (2). Is that what you want to say?

                       (1)

                      (2)

6.       I suggested adding a horizontal accuracy assessment to compare the fused results horizontally.

Response: The study area selected in this paper lacks high-precision reference DEM and accurate ground control points, so we use ICESat/GLAH14 as reference data to evaluate the vertical accuracy of original and fused DEMs. Besides, The diameter of GLAH14 ground spot is 70m. Thus, we can’t effectively evaluate the horizontal accuracy of the fusion results. Nevertheless, the accurate co-registration of the original data before DEM fusion can greatly eliminate the horizontal errors and ensure the accuracy of the fusion results.

7.         I could not see any significant improvement in fused DEM among original DEM, according to Table 2.

Response: As we can see in Table 2, the fused DEMs obtained by N-AMD offer significant improvements of 29.6% and 19.3% in RMSE at a mountainous site, and 27.4% and 15.5% over a low-relief region, compared to the SRTM-1 and AW3D30 respectively. Combined with the improvement using slope position-based linear regression method, the accuracy of the fused DEM can be significantly improved by about 40% compared with the original SRTM-1 in both study areas. We hope you will be satisfied with our answer.

Table 2. Accuracy statistics of original DEMs and fused DEMs

8.         Among original DEMs, the AW3D30 is more accurate according to the RMSE, while SRTM-1 is more accurate on the basis of the ME assessment, Why?

Response: Because the AW3D30 was photogrammetrically derived from visible-band, 2.5-m resolution stereo images. The image pixel size is 2.5 m, but the DEM was produced at a 5 m resolution which is distributed for a fee. Although the free version is resampled to 30m, it still the most accurate one in all open source DEMs according to the vertical accuracy evaluation of many literatures. So the RMSE of AW3D30 is lower than that of SRTM-1. As for the ME, we think this may be caused by that the AW3D30 is more susceptible to weather conditions such as cloud cover, mist occlusion than SRTM-1. In addition, the SRTM-1 produced by C-band radar signal can partially penetrate the vegetation canopy, while the AW3D30 produced by optical stereoscopy is not able to penetrate the canopy. This may also contribute to a larger ME of AW3D30 than SRTM-1.

9.       In a line of 433 “In site B, the RMSE is 1.892 m”??

Response: We have corrected it according to the comment which can be seen in the updated manuscript. The revised sentence is as follows.

“In site B, the RMSE is 1.902 m”

Author Response File: Author Response.pdf

Reviewer 3 Report

Brief Summary:

The proposed paper proposes a fusion (integration) method applying three decomposition methods, wavelet transformation (WT), bidimensional empirical mode decomposition (BEMD), and nonlinear adaptive multi-scale decomposition (N-AMD). These methods were applied to the SRTM-1 and the AW3D30 and tested for two topographically different regions in China. Since the

N-AMD was successful in the fusion process, the calibrated method was proposed, with the classification of the study areas according to the TPI and SDE and alignment with linear regression. This brought a little bit better results.

Broad comments:

The article in general clearly and systematically describes the studied problem. However, I miss a short Discussion section, where the results would be compared with the other solutions, as well as the results using different approaches. For example, could you indicate/explain the reasons why the N-AMD was successful in your approach, while the WT and BEMID were not? Is this result because the specific topographic areas were chosen, or could be different in some other conditions, especially in the flat areas?

Please increase visual presentations (maps).

Somewhere the north arrow is used, somewhere not, similar is with the geographic coordinates (e.g., Figures 1 and 2 vs. Figures 9 and 11). Apply the same style to all maps.

Change “Km” to km” according to the SI standards.

Specific comments:

l. 28, 32 and in the text: It is not correct to write that the vertical accuracy was improved by 29.6% or by 19.3% since behind this information is only a particular measure. It is correct to write about the improvement of the accuracy according to the particular measure (write which one).

l. 73: I do not agree with you that the DEM fusion is mainly based on the weighted average method. First of all, the DEM “fusion” methods could be find also as “integration” or “conflation”. Moreover, they use many other methods, e.g. (1) Felgueiras C.A, Ortiz J.O., Camargo E.C.G. 2014: Application of Geostatistical Conflation Techniques to Improve the Accuracy of Digital Elevation Models; (2) Paredes-Hernandéz C.U., Tate N.J., Tansey K.J, Fisher P.F. 2010: Increasing the accuracy of digital elevation models by means of geostatistical conflation.

They are also applied to different number of data sources, e.g. (1) Podobnikar T. 2005: Production of integrated digital terrain model from multiple datasets of different quality; (2) Fabris M., Baldi P., Anzidei M., Pesci A., Bortoluzzi G., Aliani S. 2010: High resolution topographic model of panarea island by fusion of photogrammetric, lidar and bathymetric digital terrain models … etc.

I suggest reconsidering this part using these or other references.

l. 111, 188: I suggest adding some hillshading, in order to make the presentation of the relief visually better for understanding the data.

l. 296: You proposed the “window-based fusion rule”, but in the reference [58] it is not possible to find this term. Could you please clarify this?

l. 202, 203: Repeated title.

l. 393, 397: It is impossible to distinguish visually between the results. I suggest combining presentation of elevations and hillshading. The ellipses need to be more emphasized.

l. 406: You mentioned that you used the ArcGIS software here. You probably used other software, in order to process the results. I suggest to move this information and better explain in section 2.

l. 481: Have you tried to improve the result applying a linear regression also for the entire tested areas (not classified)?

Author Response

Reviewer: 3
The proposed paper proposes a fusion (integration) method applying three decomposition methods, wavelet transformation (WT), bidimensional empirical mode decomposition (BEMD), and nonlinear adaptive multi-scale decomposition (N-AMD). These methods were applied to the SRTM-1 and the AW3D30 and tested for two topographically different regions in China. Since the N-AMD was successful in the fusion process, the calibrated method was proposed, with the classification of the study areas according to the TPI and SDE and alignment with linear regression. This brought a little bit better results.

Response: We appreciate for your affirmation about our manuscript. Thanks for your valuable suggestions and comments. We have corrected our manuscript according to your comments. The corresponding revision can be found with tracked corrections in the updated manuscript.

Main Corrections:

Broad comments:

1.      The article in general clearly and systematically describes the studied problem. However, I miss a short Discussion section, where the results would be compared with the other solutions, as well as the results using different approaches. For example, could you indicate/explain the reasons why the N-AMD was successful in your approach, while the WT and BEMID were not?

Response: A brief analysis and discussion of the BEMD method is mentioned in the Results and analysis section (Line 478-488).

The fused DEMs, obtained by the BEMD method at sites A and B, correspond to Figure 8(c) and (g), respectively. It is clear that both contain irregular patches in the ridge and valley regions (the red rectangles in Figure 8), which means that the detail information of the fused DEM is lost or distorted locally. Obviously, it does not meet the requirements for the application of the DEM. The reason is that the terrain of these two regions is irregular and complex. The irregularity of the extremum distribution causes improper fitting of the interpolation method in the BEMD. This results in patches appearing in the decomposition components, leading to local mutation of the fused DEMs.

Figure 8. Enlarged images of the fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red shapes indicate irregular patches.

We have added a analysis of N-AMD method at Line 534 according to the comment which can be seen in the updated manuscript.

Exploring itscauses, the N-AMD method is based on Taylor series expansion, and its fitting of the trend of the original signal is optimal or near optimal. Therefore, when using N-AMD method to decompose AWAD30 and SRTM-1 respectively, the noise of two DEMs can be detected effectively and the consistency of trend signals can be ensured. Combining with the window-based fusion rule, the noise caused by weather conditions such as cloud cover, mist occlusion and the abrupt change of surface roughness can be minimized.

2.         Is this result because the specific topographic areas were chosen, or could be different in some other conditions, especially in the flat areas?

Response: Owing to the limit of scale, the texture and detail information of the fused DEMs are not obvious in Figure 7. Hence, a small area is selected in each of sites A and B (defined by the red and green rectangles) to get a better visual effect, as shown in Figure 8. However, this does not affect the final fusion results, because we use ICESat/GLAH14 data as reference data in the quantitative evaluation of fused DEM, and its distribution is shown in Figure 2. It is distributed throughout the study area.

Figure 2. Distribution of the GLAH14 points (red) in (a) the mountainous site, and (b) the low-relief site.

3.       Please increase visual presentations (maps).

Somewhere the north arrow is used, somewhere not, similar is with the geographic coordinates (e.g., Figures 1 and 2 vs. Figures 9 and 11). Apply the same style to all maps.

Change “Km” to km” according to the SI standards.

Response: We have corrected it according to the comment which can be seen in the updated manuscript.

Specific comments:

1.         28, 32 and in the text: It is not correct to write that the vertical accuracy was improved by 29.6% or by 19.3% since behind this information is only a particular measure. It is correct to write about the improvement of the accuracy according to the particular measure (write which one).

Response: We have corrected it according to the comment which can be seen in the updated manuscript. The revised sentence is as follows

The fused DEMs offer significant improvements of 29.6% and 19.3% in RMSE at a mountainous site, and 27.4% and 15.5% over a low-relief region, compared to the SRTM-1 and AW3D30 respectively.

2.         73: I do not agree with you that the DEM fusion is mainly based on the weighted average method. First of all, the DEM “fusion” methods could be find also as “integration” or “conflation”. Moreover, they use many other methods, e.g. (1) Felgueiras C.A, Ortiz J.O., Camargo E.C.G. 2014: Application of Geostatistical Conflation Techniques to Improve the Accuracy of Digital Elevation Models; (2) Paredes-Hernandéz C.U., Tate N.J., Tansey K.J, Fisher P.F. 2010: Increasing the accuracy of digital elevation models by means of geostatistical conflation.

They are also applied to different number of data sources, e.g. (1) Podobnikar T. 2005: Production of integrated digital terrain model from multiple datasets of different quality; (2) Fabris M., Baldi P., Anzidei M., Pesci A., Bortoluzzi G., Aliani S. 2010: High resolution topographic model of panarea island by fusion of photogrammetric, lidar and bathymetric digital terrain models … etc.

I suggest reconsidering this part using these or other references.

Response: We have improved the introduction of the DEM fusion method according to the comment which can be seen in the updated manuscript. The references you provided have broaden our horizons. We have quoted them in this article. Thank you very much for your guidance. The revised introduction is as follows.

DEMs are the fundamental tools of geo-analysis, and also the essential input variables for many models. They have been widely used in science and engineering fields such as water resource management [1–3], agriculture [4,5], and ecology [6–8]. DEMs can be derived not only from scanned/vectorized contour lines of existing topographic sheets obtained by field measurement [9], but also from remote sensing techniques. While the accuracy of the field measurement method is quite high, it is also time consuming and costly, especially in hard-to-reach areas [10,11]. Remote sensing has become the primary means of obtaining DEMs due to its near ideal characteristics in terms of coverage, and spatial and temporal resolution [12].

Owing to their high resolution (1 arc-second) and free access to download, the two most widely used quasi-global digital elevation models produced by remote sensing technology are the SRTM-1 DEM and the ASTER GDEM v2 [13]. The ASTER GDEM v2 is produced by optical stereoscopy [14], while the SRTM-1 DEM is based on the interferometric synthetic aperture radar technique, called InSAR [15]. They are widely applied in various fields because of their availability rather than their accuracy [16]. Unfortunately, all DEMs contain errors owing to the methods of collection and processing of the images that are used to produce them [17]. Their accuracy can lead to problems that are experienced in local and regional analyses [18].

To address these errors, a mass of relevant researches have been carried on by many scholars. Rawat et al. [19] assessed the horizontal accuracy of ASTER GDEM, SRTM and Castosat DEM with 20 GCPS and concluded that the three DEMs have different horizontal accuracy. Reinoso [20] provided an algorithm which automatically computed the horizontal shift for each contour set with same height between two DEMs. Further research by Reinoso et al. [21] estimated horizontal displacement between DEMs by means of particle image velocimetry techniques and pointed out that the largely ignored horizontal component beared a great influence on the positional accuracy of certain linear features, e.g., in hydrological features. In another study, a simple and robust co-registration method presented for DEM pairs using the elevation difference residuals and the elevation derivatives of slope and aspect [22]. The method represented the complete analytical solution of a 3-D shift vector between two DEMs.

The DEM accuracy can be studied from the horizintal accuracy viewpoint as well as the vertical accuracy viewpoint. There has been much research into improving the vertical accuracy of DEMs. Some studies have aimed to improve the accuracy of the DEM by filling voids and removing the vegetation canopy [23–25]. Some other studies utilized geostatistical conflation techniques to increase the performance of DEM using a set of accurate Ground Control Points [26,27]. The research objects of these studies were single-source DEMs, and the inherent errors of the DEMs (depending on the method of data acquisition) cannot be eliminated. Interferometric synthetic aperture radar technique has the advantages of strong penetration ability and weak weather influence, but there remain problems with radar shadow, specular reflection and phase unwrapping. This can lead to errors when the relief amplitude and surface roughness change abruptly (such as at peaks, cliffs, etc.). As for the DEM obtained by optical sensors, the data accuracies are affected by weather conditions such as cloud cover, mist occlusion, and so on [28]. The complementary error behaviors of optical stereoscopy and InSAR provide the possibility for DEM fusion [28]. Therefore, the integration of the two kinds of DEMs using data fusion can achieve this advantageous behavior and improve the accuracy of original DEMs.

To date, many methods of DEM fusion have been put forward. Fabris et al. [29] integrated bathymetric multibeam surveys with aerial photogrammetry and lidar surveys provided the first high resolution 3D terrestrial and marine morphological map of the Panarea volcano. An innovative method of weighted sum of data sources with geomorphologic enhancement was deveioped [30] to get a better DEM than any data source, which was visually and geomorphologically homogenous. In some other studies, scholars focus on the weighted average method of DEM fusion. Schultz et al. [31] implemented the fusion of multi-temporal DEMs, obtained by optical stereoscopy in the same region through self-consistency. Honikel [32] described the process of DEM fusion by weighting the values of two DEMs according to the estimation error, utilizing the advantages of InSAR and optical stereoscopy. Schindler [33] improved the precision of large scale DEM data by weighted fusion, and pointed out the importance of weight to the fusion result. These studies looked at the DEM data as a whole and used weighted averages to improve the accuracy of the fused DEM, ignoring the different characteristics of the DEM data in various frequency domain scales. In another study, the original DEMs were transformed into the frequency domain, then high-pass and low-pass filters were used to fuse it, which achieved good results [34]. Nevertheless, details and texture information might be lost in the filtering process, which affects the ability of the DEM to describe micro-topography.

In most of the reported studies, DEM fusion was based on SRTM and ASTER. With the development of modern imaging technology, new high-resolution DEM products have been produced and released in recent years, such as the AW3D30 DSM [35,36], which also uses optical stereoscopy (with a resolution of 1 arc-second). It is the most accurate of the open source DEMs according to accuracy assessments, so it can be regarded as an alternative to the ASTER GDEM v2 [35,37]. Existing studies have showed that the impact of DEM resolution on the accuracy of terrain representation and of the gradient determined [38]. The representation accuracy decreases sharply at coarse resolutions. Therefore, Further research is necessary to examine and apply DEM fusion techniques to newly-released high-resolution datasets such as the SRTM-1 and AW3D30. Besides, Honikel [39] suggested that the errors of the stereo optical DEMs and interferometric DEMs were shown in different frequency domains. Coincidentally, multi-scale analysis methods (e.g. the popular WT and BEMD) can decompose DEMs into different frequency domains. Thus, a rule-based fusion of DEMs based on multi-scale analysis methods makes sense.

This study aims at improving the overall accuracy of open source DEMs (the SRTM-1 and AW3D30) with complementary sensing technologies by multi-scale fusion. Due to the absence of reference DEM in the study area, the ICESat global land surface altimetry product, is used to assess the accuracy of the results. The basic parameters of the experimental data are shown in Table 1. Furthermore, the effectiveness of three multi-scale analysis methods (WT, BEMD and N-AMD) in fusing DEMs is examined, based on the fusion rule mentioned in Section 3.2. Among these, N-AMD - which was originally invented to remove the cycle from sunspots - has proven superior to existing methods (e.g. chaos-based and wavelet-based approaches) in noise removal and trend determination [40–42]. Thus, it is considered to have potential for DEM multi-scale fusion because of its good performance. Finally, it is known that DEM accuracy varies for different slopes [16,43]. This suggests a further extension is possible by using the local variations in errors for different slope positions and a slope position-based linear regression method is proposed to use this information for the further calibration of fused DEM.

Table 1. The basic parameters of the SRTM-1, AW3D30 and ICESat global land surface altimetry product.

3.         111, 188: I suggest adding some hillshading, in order to make the presentation of the relief visually better for understanding the data.

Response: We have corrected it according to the comment which can be seen in the updated manuscript. The revised figures are as follows.

Figure 1. Locations of (a) the mountainous site and (b) the low-relief site.

Figure 2. Distribution of the GLAH14 points (red) in (a) the mountainous site, and (b) the low-relief site.

4.         296: You proposed the “window-based fusion rule”, but in the reference [58] it is not possible to find this term. Could you please clarify this?

Response: We're sorry to have misquoted the author's literature, and we've corrected it to the following literature. The correct reference is as follows.

Burt, P. J.; Kolczynski, R. J. Enhanced image capture through fusion. In 1993 (4th) International Conference on Computer Vision; 1993; pp. 173–182.

5.         202, 203: Repeated title.

Response: We have corrected it according to the comment which can be seen in the updated manuscript.

6.         393, 397: It is impossible to distinguish visually between the results. I suggest combining presentation of elevations and hillshading. The ellipses need to be more emphasized.

Response: We have re-plotted the figures according to the comment which can be seen in the updated manuscript. The revised figures are as follows.

Figure 7. The fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red and green rectangles are the areas selected in sites A and B that are enlarged in Figure 8.

Figure 8. Enlarged images of the fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red shapes indicate irregular patches.

7.         406: You mentioned that you used the ArcGIS software here. You probably used other software, in order to process the results. I suggest to move this information and better explain in section 2.

Response: Thank you very much for your suggestion. We have removed this explanation from 406. Besides, we preprocess the DEMs and GLAH14 in section 2 by programming, and the process have been described in detail.Thus, we think it is not necessary to explain the use of software. Beg for your understanding.

8.         481: Have you tried to improve the result applying a linear regression also for the entire tested areas (not classified)?

Response: We have added it in Table 5 according to the comment which can be seen in the updated manuscript.

Table 5. Performance of the adjusted DEM in comparison with the DEM_N at study sites A and B.

DEM_w represents the result of linear correction for DEM_N without slope position classification. It can be seen from the table that the linear correction effect on the DEM_N of the whole area is not obvious due to the difference of errors distribution between various slope position classes.

Author Response File: Author Response.pdf

Reviewer 4 Report

The paper studies the behavior of different algorithms to merge digital elevation model. The paper is in general well written I have only a couple of comments regarding figures.

1)      Figure 5: please add the legend also in sub-figure (a) and add units on  sub-figure (c).

2)      Figure 7 and 8 These two figures are quite difficult to be read. I suggest to plot just a reference DTM and then the difference between the reference dtm and the others.   Would it be possible to plot these differences with colors? In case you can mark the two rectangles with black solid line.

3)      In order to evaluate the goodness of the fusion algorithm I guess it would be of interest to use a synthetic dataset instead of a real one. For instance the authors can try (in a future work) to simulate the error of two digital elevation models, maybe also using the results obtained in this study, thus creating simulated observations to which the different proposed algorithms can be applied. This would allow to assess the performances of the different algorithms by comparing the results with an error-free reference digital elevation model.

Author Response

Reviewer: 4
The paper studies the behavior of different algorithms to merge digital elevation model. The paper is in general well written I have only a couple of comments regarding figures.

Response: We appreciate for your affirmation about our manuscript. Thanks for your valuable suggestions and comments. We have corrected our manuscript according to your comments. The corresponding revision can be found with tracked corrections in the updated manuscript.

Main Corrections:

1.        Figure 5: please add the legend also in sub-figure (a) and add units on sub-figure (c).

Response: The legend has been added in sub-figure (a) according to the comment which can be seen in the updated manuscript. Since our demo data is a random number generated by programming, and it has no units. So we can’t add units on sub-figure (c). Beg for your understanding.

Figure 5. Schematic of data decomposition using N-AMD: (a) three 2nd order polynomial fitted lines, (b) the fitted trend with window sizes of 21 and 121, and (c) different frequency components of the original data using various window sizes, where Residue is the fitted trend of original data with a window size of 121, level₂ is the fitted trend of (original data - Residue) with a window size of 21, and level₁ is the remaining part that satisfies the relationship: original data = (level)₁ + (level)₂+ (Residue).

2.         Figure 7 and 8 These two figures are quite difficult to be read. I suggest to plot just a reference DTM and then the difference between the reference dtm and the others. Would it be possible to plot these differences with colors? In case you can mark the two rectangles with black solid line.

Response: Thank you for your suggestions. We are sorry that we did not plot the figures well. We use the ICESat GLAH14 as reference data in this article, which is a point dataset. So we can't plot the difference between the reference DTM and the others. In order to make the graphics better read, we re-plotted Figures 7 and 8. We have changed their color matching and added some hillshading. The revised figure is shown below. Although limited by scale, the texture and detail information of the fused DEMs are not obvious in Figure 7, the difference can be clearly seen in its local enlarged Figure 8. We hope you will be satisfied with this revision.

Figure 7. The fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red and green rectangles are the areas selected in sites A and B that are enlarged in Figure 8.

Figure 8. Enlarged images of the fused DEMs obtained using the Bior3.7 wavelet, Haar wavelet, BEMD and N-AMD methods at (a)-(d) site A, and (e)-(h) site B. The red shapes indicate irregular patches.

3.         In order to evaluate the goodness of the fusion algorithm I guess it would be of interest to use a synthetic dataset instead of a real one. For instance the authors can try (in a future work) to simulate the error of two digital elevation models, maybe also using the results obtained in this study, thus creating simulated observations to which the different proposed algorithms can be applied. This would allow to assess the performances of the different algorithms by comparing the results with an error-free reference digital elevation model.

Response: We appreciate for your valuable suggestions. Your suggestions show us the direction of future research. We have added your comments in the article as a prospect for future work which can be seen in the updated manuscript. We would like to express our sincere thanks to you.

Author Response File: Author Response.pdf