Quantitative and Morphological Analysis of Longitudinal Profile of Northern Alborz Rivers in Mazandaran Province

Introduction
The longitudinal profile of river is one of the main components of the fluvial system. It is result from the interaction between lithology, tectonics, fluvial incision and base level change. The longitudinal profile of the rivers that are in a Equilibrium state have concave form, but several factors cause changes to the longitudinal profile of the river, including lowering base level, rock resistance, structural control, sediment input, non-fluvial processes, bed load effects, and human changes. Alborz Mountains are considered as one of the geomorphological zone of Iran, which geological, climatological and vegetation characteristics have created a special geographic landscape. In this study, longitudinal profiles of the northern Alborz rivers (Mazandaran province), as part of the Caspian Sea basin, have been investigated in this research. The aim of this research is to make a quantitative analysis of the longitudinal profile of the rivers in the region.
Methods and material  
The longitudinal profiles of 15 rivers in the northern Alborz were investigated by quantitative measures. The drainage network was extracted by the 12.5-m DEM and longitudinal profiles of the fifteen trunk channels were extracted using the ArcGIS 10.3. Geological maps were used to interpret lithology and fault distribution. The form of longitudinal profiles was measured by the concavity index (CI) and SLK index. The longitudinal gradient index (SL) was also calculated for each segment of the profiles. The concavity index was computed based on deviations from a straight line profile (Philips and Lutz, 2008). The SL Index analysis was performed with Hack's (1973) method. The SLK index for the longitudinal profile of the river was calculated by normalizing the distances in the horizontal axis and the elevation in the vertical axis.
To normalize the values ​​(SLK), in the horizontal axis of the graph, the normalized distances are represented as (d / D), where d is the distance between the specific points along the longitudinal profile and D is the total length of the profile. In the vertical axis of normalized height (e / E) the e is the elevation of specific points along the longitudinal profile and E is the elevation difference between the beginning and the end of the longitudinal profile (Vojtco et al., 2012). The maximum amount of concavity along the SLK profile was determined as Z_max.
Results and discussion
The northern Alborz Rivers do not have smooth concave profiles and there are numerous knickpoints in their longitudinal profiles. In all cases, the best fit (R²) of regression has been matched with polynomial equations of degrees 2, 3 and 4.  The coefficient of determination of these regression equations was very high (>0.96). Some of the rivers such as Kheyrood, Kojur and Noor have a convex profile with concavity index of -4, -4, and -11, respectively. A number of other rivers such as Tajen, Babol, Sardabrood and Chalakrood with CI 8, 7.5, 9 and 8, respectively, have more concavity than other rivers.
Based on the relative concavity index (CI_rel), 20% of the longitudinal profile of the North Alborz in the convex form (CIrel <0), 53% had a relatively straight or very low concavity (0 <CIrel <0.2), 27% moderate concavity. No river has a very high relative concavity index (more than 0.5). The results obtained from the Z _max of SLK index show that khojour and Noor Rivers have a convex longitudinal profile with negative coefficients. Other rivers also have a Z _max between 0.2 and 0.3 and Babolrod has the highest value of 0.7 compared with other rivers. In each of the longitudinal profiles of the rivers, SL values ​​were calculated in different segments. The highest and lowest mean values ​​of SL are related to the rivers of Kojur and Babol, respectively. Changes in SL values ​​and Knickpoints were investigated based on three factors of tectonic, lithology and human. A total of 98 faults crossed the rivers in the study area have only caused 20 knickpoints, which 70% are located in the western part and 30% in the eastern part of the northern Alborz. Lithology factor in 53% of the cases has changed the longitudinal gradient and the SL values, which is 33 percent in the western part and 20 percent in the eastern part of the northern Alborz.
Given the good correlation coefficient (0.73) between the SLK index and the CI index, the SLK index is used for clustering. The studied rivers were classified into three groups based on concavity of longitudinal profile and the position of maximum concavity. The first group includes rivers with a concavity of between 0.13 and 0.47 and the maximum concavity is in the second quartile of the profile. In this group, 80% of the North Alborz Rivers are located in the state and they are all in the transverse valleys. In the second group, the value of concavity index of longitudinal profile was negative, that is, they have a convex shape and maximum convexity is in the third quartile. The rivers in the longitudinal valley are in this group in which the concavity is less than 0.1 and the maximum concavity is in the second quartile of the profile. The analysis of longitudinal gradient index (SL) in the northern Alborz Rivers shows that 53% of knickpoints are due to lithologic changes, 45% due to the activity of faults and 2% due to dam construction. In the 98 fault lines that crossing rivers, only 20% of them have broken the longitudinal profile. The effects of lithology on longitudinal profile were analyzed by statistical test. The results show that the sig value is less than 0.05 and the hypothesis is rejected zero for Safarood, Cheshmeh Kileh, Sardabrood, Chalous, Noor, Heraz, Talar and Neka catchments. The type of lithology has a significant difference in longitudinal profile formation. The effect of faults in the longitudinal profile of the rivers in west and east parts of Mazandaran province was 70% and 30%, respectively.
Conclusion
In the longitudinal valleys, the rivers have a convex profile, where uplift (active tectonics) is dominant. In these valleys, the rate of uplift is greater than the amount of river incision and the river can not create an equilibrium profile.The longitudinal profile of the rivers in the transverse valleys is concave–convex with erosion steps that indicate long-term predominance of erosional processes. Their profile is due to the high altitude difference, short distance to the base level (Caspian Sea) and lithological resistance. It seems that river icision has overcome the tectonics and the lithological factor has more effect on the longitudinal profile of the Northen Alborz Rivers.