Exploring landslide erosion volume-area scaling relationships by slip depth using changes in DTMs for basin sediment volume estimation

Landslides produce large quantities of sediment deposits and reduce reservoir life. This study investigated landslides at the Shihmen Reservoir basin in Taiwan that were induced by Typhoon Sinlaku and Typhoon Jangmi in 2008. We formulate scaling relationships between landslide erosion volume and area and conclude that sediment budget can be estimated based on the easier-todetermine landslide erosion area. The methodologies applied for the investigation were geomorphological analysis through 5 m × 5 m digital terrain models(DTMs) of the basin created before and after the landslide events and spatial analysis through a geographic information system. The erosion area and volume of landslides were measured through the subtraction of DTMs produced before and after the events. Statistical analysis revealed that the landslide erosion frequency–magnitude distribution exhibited power-law behaviors with a scaling exponent of 2.15 for the frequency–area distribution and 1.66 for the frequency–volume distribution. This paper proposes different scaling relationships for different moving depths, and landslide erosion volumes were estimated on the basis of depth; thus, landslides of different scales can be distinguished to avoid errors in volume estimation. Two different scaling exponents are proposed: 1.21 for landslide erosions with depths of less than 2 m and 1.01 for landslide erosions with depths of more than 2 m. The proposed scaling relationships are practical for landslide erosion volume estimation by different depths according to the landslide area, and they can provide preliminary results for sediment budget planning in a reservoir basin.

Assessment of glacier stored water in Karakoram Himalaya using satellite remote sensing and field investigation

Karakoram Himalaya(KH) has continental climatic conditions and possesses largest concentration of glaciers outside the polar regions. The melt water from these glaciers is a major contributor to the Indus river. In this study, various methods have been used to estimate the ice volume in the Karakoram Range of glaciers such as Coregistration of Optically Sensed Images and Correlation(COSI-Corr) method and Area-Volume relations. Landsat 8 satellite data has been used to generate the ice displacement, velocity and thickness map. Our study for 558 Karakoram glaciers revealed that the average ice thickness in Karakoram is 90 m. Ground Penetrating Radar(GPR) survey has been conducted in one of the KH glacier i.e. Saser La glacier and the collected GPR data is used for the validation of satellite derived thickness map. GPR measured glacier thickness values are found comparable with satellite estimated values with RMSE of 4.3 m. The total ice volume of the Karakoram glaciers is estimated to be 1607±19 km3(1473±17 Gt), which is equivalent to 1473±17 km3 of water equivalent. Present study also covers the analysis of glacier surface displacement, velocity and ice thickness values with reference to glacier mean slope.

Ratio of In-Sphere Volume to Polyhedron Volume of the Great Pyramid Compared to Selected Convex Polyhedral Solids

The architecture of the Great Pyramid at Giza is based on fascinating golden mean geometry. Recently the ratio of the in-sphere volume to the pyramid volume was calculated. One yields as result RV = π ⋅ φ5, where is the golden mean. It is important that the number φ5 is a fundamental constant of nature describing phase transition from microscopic to cosmic scale. In this contribution the relatively small volume ratio of the Great Pyramid was compared to that of selected convex polyhedral solids such as the Platonic solids respectively the face-rich truncated icosahedron (bucky ball) as one of Archimedes’ solids leading to effective filling of the polyhedron by its in-sphere and therefore the highest volume ratio of the selected examples. The smallest ratio was found for the Great Pyramid. A regression analysis delivers the highly reliable volume ratio relation , where nF represents the number of polyhedron faces and b approximates the silver mean. For less-symmetrical solids with a unique axis (tetragonal pyramids) the in-sphere can be replaced by a biaxial ellipsoid of maximum volume to adjust the RV relation more reliably.

Estimation of glacier ice storage in western China constrained by field ground-penetrating Radar surveys

Recent decades have witnessed the accelerated retreat of alpine glaciers,which likely portends a decline in the glacial ice melt on which large downstream populations rely for freshwater.Thus,estimating water storage in alpine glaciers is critical for predicting the trend of glacier melting.This study compiled a rich set of ice thickness observations for glaciers of varying sizes in western China.We here presented a first-order assessment of the various errors involved in interpreting ice thickness from ground-penetrating radar(GPR)observations.An empirical Bayesian kriging(EBK)method was used for ice thickness interpolation and volume estimation.We then established a new volume-scaling law specific to western China glaciers based on these 36 volume-area pairs.And together with the Second Chinese Glacier Inventory(SCGI),we obtain a regional volume estimate of 4451±298 km^(3).By comparison,we believed that this result is the most reliable estimate of the total ice storage in western China and more reliably predicts gross glacier melting.However,our results show that the method of glacier division can strongly affect the total volume estimation,which previous studies ignored.This emphasizes the need for more surveyed glaciers data and more accurate glacier inventory to improve the evaluation of the climate impact on glacier melting water resources and to help ensure the future survival of these alpine glaciers.