Triangle Method for Estimating Soil Surface Wetness from Satellite Imagery in Allahabad District, Uttar Pradesh, India

Soil surface wetness is indispensable land surface parameter in agriculture, hydrology and environmental engineering. This paper explores the relationship between surface radiant temperature and fractional vegetation cover derived from satellite imagery to estimate soil surface wetness (triangle method) in Allahabad district. The pixel distributions create triangular shapes because the range of surface radiant temperature decreases as the amount of vegetation cover increases and sufficient number of pixels exists. A very weak correlation is found between the simulated soil surface wetness and ground measured soil moisture at deeper soil layers (R2 < 0.15) on all the dates under investigation. This is because the drying rates at the surface discontinue to be linearly correlated to that at lower levels (depths). The standing water pixels distort the shape of the triangle especially at lower left edge of the triangle. This distortion is removable. The spatial and temporal inhomogeneity of soil surface wetness is examined.

Regional Estimates of Evapotranspiration over Northern China Using a Remote-sensing-based Triangle Interpolation Method

Regional estimates of evapotranspiration （ET） are critical for a wide range of applications. Satellite remote sensing is a promising tool for obtaining reasonable ET spatial distribution data. However, there are at least two major problems that exist in the regional estimation of ET from remote sensing data. One is the conflicting requirements of simple data over a wide region, and accuracy of those data. The second is the lack of regional ET products that cover the entire region of northern China. In this study, we first retrieved the evaporative fraction （EF） by interpolating from the difference of day/night land surface temperature （AT） and the normalized difference vegetation index （NDVI） triangular-shaped scatter space. Then, ET was generated from EF and land surface meteorological data. The estimated eight-day EF and ET results were validated with 14 eddy covariance （EC） flux measurements in the growing season （July September） for the year 2008 over the study area. The estimated values agreed well with flux tower measurements, and this agreement was highly statistically significant for both EF and ET （p 〈0.01）, with the correlation coefficient for EF （R2=0.64） being relatively higher than for ET （R2---0.57）. Validation with EC-measured ET showed the mean RMSE and bias were 0.78 mm d-1 （22.03 W m-2） and 0.31 mm d-1 （8.86 W m-2）, respectively. The ET over the study area increased along a clear longitudinal gradient, which was probably controlled by the gradient of precipitation, green vegetation fractions, and the intensity of human activities. The satellite-based estimates adequately captured the spatial and seasonal structure of ET. Overall, our results demonstrate the potential of this simple but practical method for monitoring ET over regions with heterogeneous surface areas.

Zeno and the Wrong Understanding of Motion—A Philosophical-Mathematical Inquiry into the Concept of Finitude as a Peculiarity of Infinity

In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .

Average temperature calculation for straight single-row-piped frozen soil wall

The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil＇s mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin＇s analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin＇s analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.

Discrimination of Junctions in Line Drawing by Computer

For discrimination of the common W-junction and Y-junction in the labels of line drawing for a three-dimensional manifold plane surface with trihedral vertices, the existing algorithms are almost using angles between two adjacent lines and W-junction and Y- junction＇s definitions, and other complex methods. This passage gives four methods with their detailed mathematical inference processes in order to use these algorithms implemented by computer. The algorithms listed are Angle Summation method and Points to the Line method, Triangle methods which are the Triangle Area method and the Cross method. When the computer programs discriminate junctions, by comparison, the Angle Summation method and Points to the Line method are less efficacious than the Triangle method, and Cross method is more efficacious than the Triangle Area method in the Triangle method.