مـدل‌سـازی بـرآورد حجـم تپـه‌هـای بـرخـانی(مطالعه موردی: برخان-های منطقه چاه‌جام)

1. Introduction
Among sedimentary systems that are rich and poor in terms of sediment load, a different organization of the sand dunes can be seen. Barchan dunes are one of the accumulative landforms of wind that are considered from poor sedimentary systems in desert environments. The dunes are the crescent shape, and have two horns at the end. Along the horns the prevailing wind direction and the maximum of its speed is indicated. These crescent dunes are formed from tow side with different slope that slip face has the maximum slope via the collapse of sediment grains by shear velocity of wind and the gravity. The windward side with fewer slopes than slip face is separated from it by brink. The change in wind direction and the collision of barchan dunes with each other cause the instability in the size and shape of them.
The morphological characteristics of barchan are affected by various spatial and temporal factors. The volume of sediment is one of the most important features of barchan morphology that is the function of the three-dimensional form and morphometric parameters of barchan such as length, width, height and area. Barchan dunes which have the smaller three-dimensional form and less volume are more unstable, relatively. Therefore, barchan volume is important and fundamental parameter for estimation of movement rate and its control. Also, the barchan volume estimation, with regard to environmental management and planning according to systematic approach is a necessary condition to calculate the rate of input and output of material (sand grains) and energy (wind power) to the barchan system. Therefore, there is this possible to identify and study the function and behavior of barchan along its movement way.
The aim of this research is to achieve the appropriate models for estimating the sediment volume of barchan dunes. For this purpose, the sediment estimation models were determined using simple and multiple statistical relationships among various parameters of barchan, and the most suitable model was introduced according to the accuracy measurement factors. Therefore, this study tries to present the accurate models for estimation of barchan volume using its morphometric parameters such as length, width, height and area.
2. Study area
The study area in this research is barchan field of Chah Jam that is located in the southern part to south east of Damghan Basin and Haj Ali Gholi Playa. Damghan Basin is a rectangular region that with area of 18700 km2 is extended in the south and south eastern of Alborz Range. The maximum and minimum altitudes belong to Alborz Mountains (3908 m) and Haj Ali Gholi Playa (1060 m), respectively. In this region wind morphogenesis systems are dominant on others, because it has sparse vegetation and rare precipitation. The most common of geomorphic features in the area are Nebka, Barchan (longitudinal, transverse, symmetric and asymmetric), Seif and sand dunes that have been developed more in the Chah Jam region. This region, with an area of about 25260 hectares, is located at Eastern longitudes between 54° 40΄ and 55° 10΄ and at Northern latitudes between 35° 45΄ and 35° 50΄.

3. Materials and Methods
The first step in this research is the investigation, extent determination and recognition of environmental and geomorphological characteristics of study area using Google Earth images, topographic maps 1:50000 and field studies. The next step is the field visits to the region, positioning barchan dunes, sampling and measurement of their morphometric parameters via linear method. In order to cover the entire study area, some transects was considered using the GPS, and then, only barchan dunes coinciding with mentioned transects have been studied and measured. Totally, 52 barchans were measured and evaluated. The most important of barchan morphometric parameters that this study has more emphasis on them are the volume, length, height, width and area.
Eventually, the quantities of barchans morphometric parameters were determined, and a data matrix was prepared for modeling. The data sets were modeled using SPSS software and the regression analysis technique. For this purpose, first, simple and complex regression methods were examined. Then, the accuracy of models is determined through comparing their validity, and the most suitable was selected. The preference and selection indexes of models are based on the maximum R. Square, R., Adjusted R. Square, Sig. level and the minimum Std. Error of Estimate (α≤0.01).
In order to determine the relations type and intensity between volume and barchan morphometric parameters, simple and complex regression methods were examined, and among them the most suitable relationships were selected. The obtained results from the study of simple relationships between volume and height, width, length and area of barchan have been presented in tables (2) and (3). In this study, power equations gave the best results. Therefore, in first part, we have only mentioned power relationships. The results of multiple statistical modeling between volume and other parameters have been described in table (4).
Results of statistical modeling showed significant relationships between barchan volume and other morphometric parameters. In the simple relations, there is maximum significant power relationship between barchan volume and its area with 0.993 R. Square and 0.169 Std. Error of Estimate. Also complex nonlinear relationships indicate several models with preference value better than simple power models. Among them, there is maximum significant multiplier relationship between barchan volume with area and height parameters that has maximum of R. Square (0.999) and minimum of standard error.


5. Discussion and Conclusion
Barchan dunes are one of the aeolian landforms that originate from reciprocal interaction between wind and sand bed. These features have been formed from quicksand, and migration is one of the most important of their characteristics. The volume of dune is a principle parameter for prediction of barchan behavior, because it is an effective factor in the explaining its movement in different spatial and temporal situations. Therefore, estimation of dune volume can act as an index in order to determine the condition of barchan system and its trends. Also, barchans displacement is a consequence from its volume that indicates the threat and destruction rate of human infrastructures in arid and semi-arid regions.
In this research, we have used simple and multiple regression methods to model the barchan volume. As a result, we have presented several models that can be used to estimate the volume of barchan dunes (equations 6 to 15). Some models have one independent variable and some models have two independent variables. The latest models have better preference value than previous ones. The results of this study provide the possibility of exact and rapid estimation of barchan volume using its morphometric parameters. According to results of the research, comparative analysis of simple and complex models shows the importance of modeling approaches and presenting various models.

Keywords
Barchan Volume, Chah Jam, Statistical Analysis, Modeling, Morphometric Parameter.

6- References
- Ahmadi, H., 2004, Applied Geomorphology (Desert-Wind Erosion), 2nd Volume, Tehran, University of Tehran Press, 3rd Edition, Pp. 328.
- Anthonsen, K.L., Clemmensen, L.B., Jensen, J.H., 1996, Evolution of a dune from crescentic to parabolic form in response to short-term climatic changes — Rabjerg- Mile, Skagen-Odde, Denmark, Journal of Geomorphology, No. 17, Pp. 63–77.
- Anton, D., Vincent, P., 1986, Parabolic dunes of the Jafurah Desert, Eastern Province, Saudi Arabia. Journal of Arid Environments, No. 11, Pp. 187–198.
- Bagnold, R.A., 1941, The Physics of Blown Sand and Desert Dunes, Methuen, London. Pp. 90-189.
- Barclay, W. S., 1917, Sand dunes in the Peruvian Desert. Geogr. J. 49, Pp. 53–56.
- Bonham, C.D., 1989, Measurement for Terrestrial Vegetation, John wiley & Sons, Inc.
- Daniell, J., Hughes, M., 2007, The morphology of barchan-shaped sand banks from western Torres Strait, northern Australia, Journal of Sedimentary Geology, No. 202, Pp. 638-652.
- Douglass, A. E., 1909, The crescentic dunes of Peru. Appalachia 12, Pp. 34–45.
- El belrhiti, H., Douady, S., 2010, Equilibrium versus disequilibrium of barchan dunes, Journal of Geomorphology, 03416, Pp. 1-11.
- Finkel, H.J., 1959, The barchans of southern Peru, Journal of Geology, No. 67, Pp.614–647.
- Forman, S.L., Pierson, J., 2003, Formation oflinear and parabolic dunes on the eastern Snake River Plain, Idaho in the nineteenth century. Geomorphology 56: Pp. 189–200.
- Gay, S.P., 1999. Observations regarding the movement of barchan sand dunes in the Nazca to Tanaca area of southern Peru. Journal of Geomorphology, No. 27, Pp. 279–293.
- Havholm, K.G., Running, IV, G.L., 2005, Stratigraphy, sediment logy and environmental significance of late mid-Holocene dunes, Lauder Sand Hills, glacial lake Hind Basin, southwestern Manitoba. Canadian Journal of Earth Sciences, 42, Pp. 847–863.
- Herrmann, H.J., Sauerman, G., 2000, The shape of dunes, Journal of Physical A, No. 283, Pp. 24–30.
- Hersen, P., 2004, On the crescentic shape of barchan dunes, The European Physical Journal B, No. 37, Pp. 507–514.
- Hesp, P., Hastings, K., 1998, Width, height and slope relationships and aerodynamic maintenance of barchans, Journal of Geomorphology, No. 22, Pp. 193–204.
- Hesse, R., 2008, Do swarms of migrating barchan dunes record pale environmental changes? A case study spanning the middle to late Holocene in the Pampa de Jaguay, southern Peru, Journal of Geomorphology, 02747, Pp. 1 – 6.
- Howard, A.D., Morton, J.B., Gad-El-H& M., Pierce, D.B., 1978. Sand transport model of barchan dune equilibrium. Journal of Sedimentology, No. 25, Pp. 307-338.
- Hugenholtz, C.H., et al., 2008, Spatial and temporal patterns of aeolian sediment transport on an inland parabolic dune, Bigstick Sand Hills, Saskatchewan, Canada, Journal of Geomorphology: 02707, Pp. 1- 13.
- Klinsley, D.B., 2002, The Deserts of Iran and Geomorphological Features and its Paleoclimatology, Translated by Abbas Pashaei, Tehran, National Geographical Organization Publication, 1st Edition, Pp. 72-83.
- Lima, A.R., Sauermann, G., Herrmann, H.J., Kroy, K., 2002, Modeling a dune field. Journal of Physical A, 310, Pp. 487 – 500.
- Mahmoudi, F.A., 2000, Dynamic Geomorphology, Tehran, University of Payam-Noor Publication, 2nd Edition, P. 261.
- Mahmoudi, Sh., 2005, Investigation of physical variations of sand dunes in the East Jask (Monitoring of sand dunes using RS and GIS in the time period (1990-2004)), Isfahan, M.A. Thesis, University of Isfahan, Faculty of Literature and Humanities.
- Mohammad Rezaei, Sh., 2003, Systematic approach to analyzing the Ecosystems, Tehran, Environmental Protection Organization Publication, 1st Edition, P. 16.
- Mousavi, S.H., 2009, The assessment of effectiveness Barchan morphometry on stabilities (Case study: Erg Chah Jam), M.A. Thesis, Isfahan, University of Isfahan, Faculty of Literature and Humanities, Pp 1-120.
- Mousavi, S.H., Dorgouie, M., Vali, A.A., Pourkhosravani, M., & Arab Ameri A.R., 2010, Statistical Modeling of Morphological Parameters of Barchan Dunes (Case Study: Chah Jam Erg in South of Haj Ali GHoli Playa, in Central Part of Semnan Province, IRAN), Journal of Geography and Geology, Vol. 2, No. 1 Pp. 98-113.
- Mousavi, S.H., Moayeri, M., Vali, A.A., 2010, The combination of mathematical and statistical modeling of Barchan dunes (Case study: Chah Jam Erg), Iranian Journal of Physical Geography Research Quarterly, No. 73, Pp. 83-96.
- Mousavi, S.H., Vali, A.A., Moayeri, M., 2010, The effectiveness of Barchan morphometric parameters on its movement rate (Case study: Chah Jam Erg), Iranian Journal of Geography and Environmental Planning, No. 38 (2), Pp. 101-118.
- Negaresh, H., Latifi, L., 2008, Geomorphologic analysis of the advancing trend of sand dunes in East Sistan Plain in recent droughts, Iranian Journal of Geography and Development, No. 12, Pp. 43-60.
- Ramesht, M.H., 2002, Symbols and Images in Geomorphology, Tehran, Samt Publication, 1st Edition, Pp. 70-85.
- Sauermann, G., Andrade, J. S., Maia, L. P., Costa, U. M. S., Araujo, A. D., Herrmann, H.J., 2003. Wind velocity and sand transport on a barchan dune. Journal of Geomorphology, No. 54, Pp. 245 – 255.
- Sauermann, G., Rognon, P., Poliakov, A., Herrmann, H.J., 2000, The shape of the barchan dunes of Southern Morocco, Journal of Geomorphology, No. 36, Pp. 47–62.
- Valle, H.F.del., Rostagon, F.R, C.M., Coronato, F.R., Bouza, P.J., Blanceo, P.D., 2008, Sand dune activity in north-eastern Patagonia, Journal of arid Environment, No. 72, Pp. 411-422.

- Wang, T.Z., Chen Tao, S., Wen Xie, Y., Hui Dong, G., 2007, Barchans of Minqin: Morphometry, Journal of Geomorphology, No. 89, Pp. 405-411.
- Wippermann, F.K., Gross, G., 1986. The wind-induced shaping and migration of an isolated dune: A numerical experiment, Journal of Boundary-Layer Meteorol, No. 36, Pp. 319–334.