Description and validation of the new data to determine a geoid model in Algeria

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Energy (2019) 000–000 254–260 EnergyProcedia Procedia157 00 (2017) www.elsevier.com/locate/procedia Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18, 19–21 September 2018, Athens, Greece Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18, 19–21 September 2018, Athens, Greece Description and validation of the new data to determine a geoid

model in Algeria DescriptionTheand of the new dataHeating to determine 15th validation International Symposium on District and Cooling a geoid inAHMED Algeria GHOUGALI MAMMAR a,*, model S.A. BEN DAHO b, HACINI Messaoud a Assessing the feasibility of using the heat demand-outdoor a,*laboratory of Sahara University of Ouargla- Algeria, b a Geology GHOUGALI MAMMAR , S.A. BEN AHMED DAHOheat , HACINI Messaoud temperature function for a long-term district demand forecast Centre des Techniques Spatiale, Arzew, Algeria a

b

a

Geology laboratory of Sahara University of Ouargla- Algeria,

a,b,c a b Algeria des Techniques Spatiale, Arzew, *, A. Pinaa,Centre P. Ferrão , J. Fournier ., B. Lacarrièrec, O. Le Correc Abstract I. Andrić b

a

Center Innovation, Technology and Policy Research - Instituto Técnico, Av. Rovisco 1, 1049-001 Lisbon, Portugalour SinceIN+ 2000, theforera of dedicated satellite gravity missions such Superior as CHAMP, GRACE andPais GOCE has revolutionized b Abstract Veoliafield Recherche Innovation, Avenue Daniel, 78520 Limay, France knowledge onc the Earth’s gravity and its&changes in 291 time. TheyDreyfous will be mapping the Earth’s gravity field with significantly Départementspatial Systèmes Énergétiques et Environnement - IMT Atlantique, 4Models rue Alfred Kastler, 44300 Nantes,lead France increasing resolution. Globalsuch Earth were released. to substantial Since 2000,accuracy the eraand of dedicated satellite Several gravity new missions as Gravity CHAMP, GRACE and GOCEThese has revolutionized our improvements of our knowledge of the long wavelength part of the Earth’s gravity field, and thereby of the long-wavelengths of knowledge on the Earth’s gravity field and its changes in time. They will be mapping the Earth’s gravity field with significantly the geoid. However, the up-to-date, accuracy of the global geoid modelling is a few decimetres and sometimes it may be increasing accuracy and spatial resolution. Several new Global Earth Gravity Models were released. These lead to substantial significantly higher areas lacking accurate gravity like Algeria, which isgravity not sufficient many of scientific and engineering improvements of ourinknowledge of the long wavelength part of the Earth’s field, andfor thereby the long-wavelengths of Abstract So, high resolution and accurate local geoid models are still necessary for the most practical purposes. Furthermore, applications. the geoid. However, the up-to-date, accuracy of the global geoid modelling is a few decimetres and sometimes it may be the SRTM has improved tremendously our knowledge of the topography fornot about 80 percent of thescientific Earth’s land surface and significantly higher in areas lacking accurate gravity like Algeria, which is sufficient for many and engineering District heating networks are commonly addressed in the asnecessary one of the effective solutions for decreasing the consequently, thehigh new high resolution SRTM global DEM wasliterature generated. applications. So, resolution and accurate local geoid models are still formost the most practical purposes. Furthermore, greenhouse gasimproved emissionstremendously from the building sector. These systems requirefor high investments which areEarth’s returnedland through theand heat the SRTM has our knowledge of the topography about 80 percent of the surface The computation of the local geoid model via remove-restore requires different of data: good quality gravimetric sales. Due to the changed climate conditions andDEM buildingtechnique renovation policies, heat types demand in the future could decrease, consequently, high resolution SRTM global generated. measurements,the annew optimum geopotential model, a high was resolution digital terrain model, and leveled GPS data. But before prolonging the investment return period. integrating them, wethe must describe and validate these data. technique requires different types of data: good quality gravimetric The model via feasibility remove-restore Thecomputation main scope of of thislocal papergeoid is to assess the of using the heat demand – outdoor temperature function for heat demand measurements, an optimum geopotential model, a high(Portugal), resolutionwas digital model, and The leveled GPSisdata. But before forecast. The district of Alvalade, located in Lisbon usedterrain as a case study. district consisted of 665 integrating we must describe and validate buildings them, that vary in both construction periodthese anddata. typology. Three weather scenarios (low, medium, high) and three district © 2018 The Authors. Published by Elsevier Ltd. scenariosPublished were developed (shallow, deep). To estimate the error, obtained heat demand values were ©renovation 2019 The Authors. by Elsevier Ltd. intermediate, This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) compared withaccess resultsarticle from aunder dynamic heatBY-NC-ND demand model, previously developed and validated by the authors. This is an open the CC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection andAuthors. peer-review underby responsibility of the scientific committee of Technologies and Materials for Renewable Energy, © 2018 The Published Elsevier The results that when weatherLtd. change considered, the margin of error could acceptable some applications Selection andshowed peer-review underonly responsibility of the isscientific committee of Technologies andbeMaterials forfor Renewable Energy, Environment and Sustainability, TMREES18. This an open access article under the CCthan BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) (theiserror in and annual demand was lower 20% for license all weather scenarios considered). However, after introducing renovation Environment Sustainability, TMREES18. Selection responsibility of the scientific on committee of Technologies andscenarios Materialscombination for Renewable Energy, scenarios,and thepeer-review error valueunder increased up to 59.5% (depending the weather and renovation considered). Keywords: geoid ; GPS ; EGM2008 ; geopotential model Environment and Sustainability, TMREES18. The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Keywords: ; GPS ; EGM2008 geopotential modelintercept increased for 7.8-12.7% per decade (depending on the renovation geoid scenarios considered). On the; other hand, function coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and * Corresponding author. Tel.: +213(0)661380490 improve the accuracy of heat demand estimations. E-mail address: [email protected] * Corresponding author. Tel.: +213(0)661380490

© E-mail 2017 The Authors. Published by Elsevier Ltd. address: [email protected] Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 2018 The Authors. Published by Elsevier Ltd. 1876-6102©

This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: demand;under Forecast; Climate change Selection andHeat peer-review responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment 1876-6102© 2018 The Authors. Published by Elsevier Ltd. and Sustainability, TMREES18. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 10.1016/j.egypro.2018.11.188

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1- Introduction New developments and advances in gravity field determination from satellite tracking have taken place in the last few years. The most recent models are released from satellite gravity missions CHAMP, GRACE and GOCE. They will be mapping the Earth’s gravity field with significantly increasing accuracy and spatial resolution. The GOCE mission is expected to achieve an accuracy of 1mGal for gravity anomalies and 2cm for the geoid at length scales down to 100km which corresponds to a spherical harmonic expansion up to degree and order 180. However, the comparisons these global geoid models with a set of the GPS/Levelling data have shown that these models do not have the required accuracy to be able to transform a GPS ellipsoidal height to an orthometric height. Their accuracy is a few decimetres and sometimes it may be significantly higher in areas lacking accurate gravity like Algeria, which is not sufficient in practice for many scientific and engineering applications. So, high resolution and accurate local geoid models are still indispensable for the most practical purposes. The precise model of the geoid not only enable us to transform satellite-derived heights to physically meaningful heights based on the Earth’s gravity field, but also plays an important role in geophysics, oceanography and in navigation. In general, the gravimetric geoid solution is carried out using the remove-restore technique in which the gravity signal is split into three components the low, medium and high frequency represented by Global geopotential model, local gravity information and digital terrain model, respectively. The main purpose of this paper is to describe and validate all data will be used in Algerian gravimetric geoid computation. 2- Description and validation of the data used 2-1) Gravimetric data: In this work, we used two types of gravity data. A set consisting of 12472 land gravity data and 52714 altimetry-derived gravity anomalies covering a part of the Mediterranean Sea between the limits [35 ° to 39 °] in latitude and [-11 ° to 14 °] in longitude. 2-1-1) Terrestrial gravimetric data: The Land gravity anomalies used in this work, and composed of 12472 land data covering the territory of Algeria, were supplied by the B.G.I. (Bureau Gravimétrique International). These measurements were collected for exploration geophysical, rather than physical-geodetic purposes. These measurements with an initial precision of 2mGal were expressed in the Geodetic Reference System GRS67. All gravity measurements were transformed from the GRS67 to the GRS80 system. Moreover, we applied an atmospheric correction recommended by the International Association of Geodesy (IAG, 1971) in order to eliminate the influence of the atmospheric masses. 2-1-2) Marine gravimetric data: In all previous geoid solutions for Algeria, no satellite-altimeter derived gravity anomalies were used. This factor has considerably affected the quality of the geoid model in the in coastal regions on land, which stretches over a distance of 1,200 km and contains important industrial and port infrastructures, and requires a reliable geoid model of good quality. For reasons of availability, we used the KMS02 model with a resolution of 0.033 ° (2 minutes). This grid consisting of 52714 values covers a part of the Mediterranean between the limits [35 ° to 39 °] in latitude and [-11 ° to 14 °] in longitude. The geographical distribution of the gravity anomaly values provided by KMS and BGI is shown in Figure 01. From this figure, it becomes clear that the coverage with gravity observations is not sufficient for some land areas particularly in the south of the Algeria and new measurements are needed to accomplish a homogeneous coverage.

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Figure 01 : Geographical distribution of used land and marine gravity data 2-1-3) Gravimetric Data Validation Procedure: Validation is an extremely strict procedure that guarantees quality and integrity of the gravity data bank. It is applied systematically to all sets of data before being integrated into the data bank. The principle consists of comparing the observed value and the predicted one estimated by a powerful technique. The validation was applied to the reduced free-air anomalies of the EGM2008 geopotential reference model using the least squares collocation method in which the Gauss-Markov model with its adjusted parameters was adopted as local covariance model to express the correlation between the data used and the signals to be estimated. Reduced data ( gred = g OBS  g EGM 2008 ) have been divided into two disjoint sets A and B which

have no common observations, but have the same distribution. To do this, a sampling with a step of 5 '(~ 10 km) on these data was carried out (it is not about average values). g pred is the predicted anomaly by the collocation method from a set of reduced values. This value is given by

(Moritz, 80): (01)

g pred  C g .C 1 .g red Where matrix

is the covariance vector between prediction and observed values, C is the sum of the covariance C g of the

g red quantities and the variance covariance matrix of the noise associated with the data.

Then, we have the prediction error,

 2 ( g red  g pred )  C 0  C g .C 1 .C Tg C0

(02)

is the variance of gravity anomalies.

Then a gross error is detected if

1

gred  gpred > k.( (gred  gpred)  g )2 2

where K is a constant generally having the value 3 and

2

2g is the error

(03)

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In our case, if the difference between

g obs and g pred

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was greater than 20 mGals, the observation was rejected.

The statistics of 12318 validated data on 12472 measurements provided by the BGI, are summarized in Table 01.

Minimum

Maximum

Average

Standard deviation

g r ed

-44.837

26.590

-0.550

5.319

g pred

-29.120

26.360

-0.440

3.948

Difference

-19.792

19.772

-0.109

4.222

Table 01 : Statistics of BGI validated gravity data [Unit: mGals] 2-2) Digital Terrain Model (DTM) Due to the lack of any high resolution photogrammetric based DEM in the Algeria region, a new MNE of resolution 15" (~450 m) covering the region limited by 17°    42° et -12°    14° was generated from of recent 3 second (~100 m) high resolution SRTM. In the Mediterranean Sea, this model was completed using the ETOPO2 bathymetric model and compared it with the above BGI gravity data points. In addition, we included in this evaluation the ETOPO30 model used in previous gravimetric geoid computations in Algeria. The differences between the tested Digital Elevation Models (DEMs) and BGI gravity heights data are summarized in Table 02 and show that most deviations are less than 10 meters. There are very few stations where really large differences occur. Usually they are located in areas where there is a SRTM data lack nearby or in the mountainous regions and in the south of the country. σ

Minimum

Maximum

Average

SRTM – Altitudes BGI

-320.844

474.712

-0.079

21.726

GTOPO – Altitudes BGI

-324.233

495.921

-0.242

22.060

Difference

Table 02 : Statistics of the differences between BGI heights and tested DEM (Unit: [m]). These differences for the two models tested can be summarized as follows (The values in parentheses correspond to ETOPO30): (Unit: [m]) • 46.6% (45.1%) of the differences are in the range [-5 to 5], • 71.1% (69.4%) of the differences are in the range [-10 to 10], • 83.7% (82.9%) of the differences are in the range [-16 to 16] (accuracy given with a confidence level of 90%), • 93% (92.2%) of the differences are in the range [-30 to 30]

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2-3) Choice of an optimal geopotential model in Algeria The choice of the best geopotential model to reduce geodetic data is one of the critical steps in computing the geoid. Several studies have shown that the geopotential models tailored to regional or local gravity data are best suited for high precision geoid computations. In this paper, a new investigation was carried out to define the geopotential model, which fits best the gravity field in Algeria. Seven global potential models have been used, namely: EIGEN-GRACE02S (purely satellite solution from the GRACE satellite) and GGM02C combined solution, EIGEN-CG01C (combined CHAMP and GRACE model), EIGEN-GL04C (solution combined GRACE and LAGEOS), OSU91A, EGM96 and the new and revolutionary gravitational model EGM2008 For these comparisons, we used, in addition of BGI free air gravity anomalies and a set of the leveled GPS benchmarks, a pre-processed 5’x 5’ grid of the free air anomalies covering the area bounded by the limits 16°    40° and -10°    14°. The free air gravity anomalies from BGI and GETECH are compared with corresponding values computed from the tested geopotential models, and the smallest residuals (neglecting the effect of the zero-order term) imply the best fitting gravity anomalies, hence, GGM. So and before comparing them and in order to make a fair comparison and taking into account the EGM’s omission error, all tested geopotential models were truncated to degree and order 150 that represents the current limit for the new GRACE satellite-only EIGEN-GRACE02S. BGI and GETECH free air gravity anomalies are low-pass filtered using the high degree geopotential model EGM96 from degree 151 to degree 360, i.e. free air gravity information in this spectral range is subtracted from the BGI and GETECH free-gravity anomalies data sets before they are compared to the corresponding quantities obtained from the tested EGM (Gruber, 2004). The results, in mGals, for these comparisons are summarised for BGI free air gravity anomalies in Table 03, and for GETECH gravity data in Table 04. All the original data are referred to GRS80. The computations were carried out using the FORTRAN program harmonic_synth_v02 that was provided by the NGA/US EGM development team. We can see that the free air gravity anomalies computed from EGM2008 Gravity Field models have been significantly improved as compared to other tested geopotential models and that all models give almost the same results in terms of the standard deviation. This is because no new gravity data have been used in this region for the determination of the tested GGM models compared to OSU91A model.

Geopotential Models OSU91A EGM96 EIGENCG01C EIGENGL04C GGM02C EIGENGRACE02S EGM2008

Minimum

Maximum

Average

σ

-97.035 (-106.680) -100.959 (-101.977) -98.959 (-103.739) -99.362 (-104.522) -93.885 (-104.938) -90.684 (-106.680) -104.094 (-104.094)

125.561 (68.215) 112.026 (56.941) 110.187 (58.515) 112.031 (58.750) 123.040 (57.294) 144.810 (68.215) 55.925 (55.925)

0.300 (1.308) -2.170 (-0.942) -2.103 (-0.704) -1.924 (-0.531) -1.123 (-0.566) -1.136 (1.308) -0.610 (-0.610)

13.164 (6.534) 13.542 (6.683) 14.056 (6.649) 14.029 (6.659) 14.910 (6.345) 17.196 (8.413) 6.119 (6.119)

Table 03 : Statistics of the reduced data between the BGI gravity data and the geopotential models (with and without filtering (in brackets )) (Unit: [mGals]).

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GHOUGALI MAMMAR / Energy 00 (2018)157 000–000 Ghougali Mammar et al. Procedia / Energy Procedia (2019) 254–260

Geopotential Models

OSU91A EGM96 EIGENCG01C EIGENGL04C GGM02C EIGENGRACE02S EGM2008

Minimum

Maximum

Average

σ

-122.11 (-261.27) -143.06 (-269.45) -133.90 (-270.82) -133.85 (-269.63) -139.58 (-271.64) -142.36 (-283.99) -271.94 (-271.94)

190.57 (108.86) 167.09 (113.80) 170.06 (111.68) 170.78 (114.37) 183.38 (113.27) 215.04 (121.03) 110.91 (110.91)

-2.25 (-2.24) -2.57 (-2.56) -2.62 (-2.60) -2.60 (-2.58) -2.57 (-2.58) -2.60 (-2.62) -2.60 (-2.58)

14.82 (15.27) 15.51 (15.50) 15.66 (15.50) 15.66 (15.50) 17.65 (15.42) 19.69 (16.75) 15.35 (15.35)

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Table 04 : Statistics of the reduced data between the GETECH gravity data and the geopotential models (with and without filtering (in brackets)) (Unit: [mGals]).

The same procedure described above was been applied to GPS leveled data. The global geopotential models discussed above were also compared with a number of GPS/Levelling data set available in the north part of Algeria. For this study, 51 leveled GPS stations were used, of which about ten points are benchmarks of the first order leveling network and the others belong to the second order levelling network. All of these points are located in the north of Algeria, were collected from TYRGEONET projects (TYRhenian GEOdynamical NETwork), ALGEONET (ALGerian GEOdynamical NETwork), and some local networks. The ellipsoidal heights obtained from different points of the network refer to the WGS84 system and their standard deviation does not exceed 3cm. However, and in order to make it possible to estimate the geoid height at these points, all of these stations have been connected to the NGA national leveling network through traditional leveling. The accuracy of the altitudes obtained by the leveling is of the order of 6cm on average and which remains dependent on the connection mode used to level the GPS points whose points are located in mountainous regions where the technique of precision leveling remains impracticable and expensive from a financial point of view. The geographic distribution of leveled GPS stations is shown in Figure 02. Table 05 summarises the statistics of the differences between the tested geopotential models and GPS/Levelling undulations in benchmarks. We can see that the Gravity Field Model EGM2008 model fits best the observed values in both cases (with and without filtering). The geoid undulations computed from this model have been significantly improved as compared to other tested models.

36

34

32

30

28

26

24

22

20 -8

-6

-4

-2

0

2

4

6

8

10

12

Figure 02 : Geographical distribution of leveled GPS points

Ghougali Mammar et al. / Energy Procedia 157 (2019) 254–260 Author name / EnergyProcedia 00 (2018) 000–000

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Geopotential Models OSU91A EGM96 EIGENCG01C EIGENGL04C GGM02C EIGENGRACE02S EGM2008

Minimum

Maximum

Average

σ

-3.705 (-3.502) -1.596 (-1.379) -1.280 (-1.106) -1.173 (-1.079) -1.687 (-1.065) -2.357 (-1.528) -0.967 (-0.967)

1.046 (1.262) -0.130 (-0.179) 0.053 (-0.407) 0.009 (-0.488) 0.129 (-0.567) 0.828 (-0.042) -0.589 (-0.589)

0.514 (-0.870) -0.751 (-0.943) -0.579 (0.749 -0.581 (-0.756) -0.457 (-0.771) -0.034 (-0.412) -0.773 (-0.773)

1.222 (0.998) 0.319 (0.242) 0.350 (0.134) 0.321 (0.120) 0.462 (0.104) 0.780 (0.407) 0.094 (0.094)

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Table 05 : Statistics of the differences between the tested geopotential models and GPS/Levelling undulations in benchmarks (with and without filtering (in brackets)) (Unit: [m]). Conclusion: - The new geoid model EGM2008 optimally adjusts the leveled GPS data compared to the other solutions used in this study. - The error rate detected using the cross validation method is of the order of 1.23% and it confirms that the data provided by the BGI are of good quality, and therefore they can be used for the determination of the Algerian geoid model. - The statistics of the differences between the BGI altitudes and the DEM derived from the SRTM mission show that they are of good quality compared to the GTOPO model. Recommendation: We recommend using the airborne technique to fill the gaps in gravity coverage, mainly in the mountainous regions and in the south of the country. REFERENCES BIBLIOGRAPHIQUES Benahmed Daho S. A., Fairhead J.D., 2004. A new quasi-geoid computation from gravity and GPS data in Algeria – Newton’s Bulletin N° 2, A joint Bulletin of the Bureau Gravimétrique International and of the International Geoid Service – Journal of the International Association of Geodesy and International Gravity Field Service - [pp 52-59] – ISSN 1810-8547 – Décembre 2004. Benahmed Daho S.A., 2000. The new gravimetric geoid in Algeria - Bulletin N°10 de l’International Geoid Service IGeS – ISSN 1128-3955 – [pp 78-84] - May 2000 Benahmed Daho S.A., Kahlouche S., 2000. Geopotential models comparison in Algeria - Bulletin N°10 de l’International Geoid Service IGeS – ISSN 1128-3955 – [pp 85-90] - May 2000 Beutler, G., Bock, H., Brockmann, E., Dach, R., Fridez, P., Gurtner, W., Hugentobler, U., Ineichen, D., Johnson, J., Meindl, M., Mervart, L., Rothacher, M., Schaer, S., Springer, T., Weber, R., 2001. Bernese GPS software version 4.2 manual, edited by U. Hugentobler, S. Schaer, and P. Fridez, 418 pp., Astron. Inst., University of Bern, Bern. Forsberg R., 1994. Terrain Effects in Geoid Computations, In International School for the Determination of the Geoid, Lecture Notes, Milan, Italy, Oct. 10-15, pp. 101-134. Gruber T., (2004). Validation Concepts for Gravity Field Models from Satellite Missions; Proceedings of Second International GOCE User Workshop "GOCE, The Geoid and Oceanography", ESA-ESRIN, Frascati, 8.-10. March 200. Moritz H., 1980: Advanced Physical Geodesy, H. Wichmann-Abazcus Press, Karlsruhe-Tundridge Wells.