Allometric Analysis of Barchans Morphometric Parameters in Southeast Part of Haj Ali Gholi Playa

Introduction
Management principles predominated on the development and evolution stages of the geomorphic landscapes are different. This is because of variability in landscape evolution, its relationship with other system components and its response to environmental changes and feedback. One of the most important methods of management of geomorphic landscape is the study and evaluation of morphometric parameters and allometric measurements. Allometric measurement is the investigation of relative changes between system components. It also represents the development of a system component compared with that of the entire system or other components.  Therefore, the study and evaluation of barchan morphometric parameters and allometric relations between them will help managers and environmental planners achieve the unified and accurate recognition from landscape, in one hand. On the other hand, it may be effective in the determination of stability, equilibrium and thresholds of barchan system.
One of the most important problems of management in arid and semi-arid regions is the identification and application of environmental principles governing on the behavior of Barchan dunes. Barchans are one of the aerial depositional features formed in regions by sand and prevailing uni-directional wind.
The aims of this study are to determine the most important morphometric parameters of Barchan dunes in the southeast part of Haj Ali Gholi Playa and also to recognize relationships, the ratio and allometric properties between them. These are conducted to identify the management principles governing on the Barchan dunes.
 
Materials and Methods
The study area in the research is the barchan field located in the southeast area of Haj Ali Gholi Playa. With about 25260 hectares in area, the field is one of the most important ergs of Haj Ali Gholi playa. It is located irregularly along northeastern - southwestern edge of playa with 10 to 12 km long. This region is located at Eastern longitudes between 55^° and 55^°, 10΄ and at Northern latitudes between 35^°, 45΄ and 35^°, 50΄.
At first, the study area is recognized via topography maps and Google Earth images. Then, barchans morphometric parameters are measured along 10 transects covering entire extent of the erg.
We define for each barchan dunes, the lengths La, Lb and the widths Wa, Wb independently. Furthermore, this study introduces the length of the slip face Ls and the length Lo from the dune’s toe on the windward side to the brink. Finally, the height of the slip face H is defined at the highest point of the brink. This is the intersection of the brink and the longitudinal centerline of the dune. The total width (W) of a barchan is the sum of the widths Wa and Wb. The overall length (L) of a barchan is the sum of the length (Lo) from the windward foot of the dune to its crest, the length of the slip face (Ls), and the average of the horn lengths [(La + Lb)/ 2].
From measurement and determination of morphometric parameters, for recognition of the type and intensity of relationships between them, we have reexamined these relationships using SPSS software and regression analysis technique. Finally, with analysis and evaluation of the obtained relationships using mathematical tests, the ratio and the allometric state of morphometric parameters have been defined and determined for the studied barchans.
 
Results and Discussion 
In the study area, several barchans can be observed that they have the same form and shape, generally. The barchan dunes of the southeast Haj Ali Goli playa are 1.2 and 17.9 m high, between 19.5 and 307.9 m long, and between 6.3 and 165.6 m, wide.
The results obtained from statistical modeling by the regression analysis are presented. Models Summary indicates the correlation index, determination index, adjusted determination index and standard deviation of estimation error. The values of model parameters (coefficient and line slope), t value and their significant level are also demonstrated. Totally, the most important and the most suitable relationships are following from simple linear relationships, in this study. Therefore, in the results part, only, these relationships are presented.
Comparative evaluation of similar studies reveals the application of different equations in other regions. Quantitative researches of the morphology studied by other researchers show the specific relationship between barchan morphometric parameters in their study area.
As mentioned previously, allometric analysis is the investigation of relative changes among system components. It also represents development of a system component compared with development of entire system or other components. In the study, to determine the ratio between morphometric parameters of the studied barchan and identification of allometric relationships between them was first attempted to determine the types of their relationship and, then, find the ratio from them.
 
Conclusion
The results show that the obtained relationships between morphometric parameters of the studied barchan represent the maximum significant linear relationship in barchan length and height, with determination index of 0.945 and standard error estimate of 0.889.The obtained relationships and allometric analysis among barchan morphometric parameters are statistical and mathematical models reported in this study. The mentioned models provide the possibility of rapid and accurate calculation of barchan morphometric parameters, and illustrate the allometric relationships among them.
The recognition of morphometric parameters of barchan dunes and their allometric analysis can serve as an index to determine the condition of barchan system and also shed light on their trends. Furthermore, recognition and estimation of these indices is a consequence from rate of threat and distribution.  This can provide environmental managers with the required information and help their investigation determine the states in different regions from the view point of environmental management.