^{1}

^{*}

^{1}

^{2}

^{2}

^{3}

This paper aims to contribute to the prevention of natural disasters and generate a complement to other similar studies. The Popocatépetl volcano has showed significant and constant activity since 1994. The Colorada and Quimichule canyons are located within its geologic structure; due to their topographic features, ejected volcanic material and torrential rains in the past recent years, they put nearby communities at risk. This work presents a geostatistical analysis to obtain the gravity acceleration, slope by the distance-elevation relation, height-gravity and the fluid force on the canyons. The conversion of UTM to geographical coordinates was made with the use of the program Traninv applying the ITRF2008 epoch 2010.0 Datum and the 14 Zone; the local gravity was calculated with the use of International Organization of Legal Metrology (OIML) and the statistical analysis was obtained with the use of the Geostatistical Environmental Assessment. The structural modeling was performed using Surfer , and the spending and force were calculated using hydrological models. The correlation analysis concluded that Quimichule has the greatest gravity and that it would transport lahars faster. Mapping, geomorphological and statistical techniques and models were applied in accordance with the study to obtain the results presented here.

The Popocatépetl volcano is located at 19˚17'N latitude - 98˚38'W longitude from the Greenwich Meridian. Its height is 5520 meters above sea level and it borders with the states of Puebla, Morelos and Mexico. In 1994, the Popocatépetl volcano began an important stage of activity presenting in 1994, an important stage of steam, ash and incandescent rock ejection, as well as seismic events. It has remained active presenting both high and low intensity periods ever since. Its constant activity, atypical torrential rains caused by climate change, existing melting glaciers and topography, favor landslides of mudflows of volcanic ash in the canyons such as Colorada and Quimichule. These are directly related to the gravity, slope, height and expense, which might put the surrounding communities at risk. Furthermore, the pressure changes generated by the activity within the magma chamber cause gravity deformations and variations on the surface of the volcano―which must be quantified periodically. A study named “Possible Mudflow in the possible mudflow on the east side of the Popocatépetl volcano” [

This paper aims to contribute to the prevention of natural disasters caused by volcanoes, specifically through the development of geostatistical methodologies. This information will be useful to determine which prevention actions to take in the event of volcanic activity created by thaw when a major volcanic activity exists. Currently, studies continue to be conducted in order to calculate other geomorphologic variables.

Studies on canyon stability have been carried out applying geotechnical methods and finite elements to determine tensions, deformations and shear strength [

The location of this volcano and its activity in recent years represent a risk structure to the nearby communities (

Regarding the work in this paper, there is no information on similar studies or research in the area of Popocatépetl. Still, it is important to know the possible scenarios that would arise in the case of a major eruption.

The UTM coordinates of the canyons’ profile were obtained through digital topographic maps of the volcano readings and are available to users on the website of the NATIONAL INSTITUTE OF STATISTICS AND GEOGRAPHY. Using these maps, we defined the points where the acceleration of gravity, distance-lift slope and gravity-height would be calculated. The UTM coordinates were converted to geographic coordinates using the Traninv program applying the ITRF2008 Datum and Zone 14. Currently, all the mapping and digital products produced by INEGI, subsequent to the date of December 2010 is based on the new Datum ITRF2008, also

releasing at the same time a software (Traninv) based on the mathematical algorithm for the transformation or conversion of coordinate ITRF92 to ITRF2008, which seeks a smooth transition to a new reference system. The acceleration of local gravity was calculated using the program on the National Metrology Center (Mexico) website, based on the OIML-N. 127 of 1992 newsletter.

The statistical analysis was carried out using the Geostatistical Environmental Assessment, and the structural modeling using the Surfer program. In addition, hydrological models were used to calculate the expense and force of a liquid.

Later, relations between gravity-height and gravity-slope were obtained, as well as their corresponding correlation coefficients. The correlation between the three studied variables is important because it defines the behavior of flows over the canyons, giving an idea location of the area of greatest risk in those geological structures.

For each canyon data, the data was obtained from the E14B42 topographic map, getting the UTM coordinates and then transforming them to geographical coordinates using the Traninv program where X = W and Y = N (

The data used for the processing each 500 m in length for both canyons is shown on

The acceleration of gravity is the act of universal attraction that propels bodies to the center of the Earth; it is a force that determines the weight of bodies [

The Equation (1) was used to confirm the results of gravity in different points of the canyon every 500 meters of distance, which can be calculated accurately in the 0.001% = 100 ppm order. Introduced data includes: altitude (m) and North latitude (˚). This program calculates the acceleration of local gravity by applying the Equation (1) (

where:

gl = acceleration of local gravity (m/s^{2}).

ge = 9.7803185 m/s^{2}, acceleration of gravity in the Equator (φ = 0).

Data | |||||
---|---|---|---|---|---|

Point | Latitude | Longitude | Z | W | N |

1 | 19˚1˚46.451˚ | 98˚37˚23.916˚ | 4880 | 539640.388 | 2104015.758 |

2 | 19˚1˚39.899˚ | 98˚37˚07.464˚ | 4580 | 540121.747 | 2103815.432 |

3 | 19˚1˚33.707˚ | 98˚36˚51.840˚ | 4280 | 540578.888 | 2103626.111 |

4 | 19˚1˚26.616˚ | 98˚36˚36.287˚ | 4040 | 540034.0525 | 2103409.175 |

5 | 19˚1˚21.071˚ | 98˚36˚20.015˚ | 3820 | 541510.084 | 2103239.814 |

6 | 19˚1˚14.628˚ | 98˚36˚03.888˚ | 3580 | 541981.976 | 2103042.855 |

7 | 19˚1˚08.400˚ | 98˚35˚48.119˚ | 3440 | 542443.398 | 2102852.492 |

8 | 19˚0˚01.668˚ | 98˚35˚31.236˚ | 3280 | 542937.432 | 2102646.725 |

9 | 19˚0˚54.404˚ | 98˚35˚15.396˚ | 3120 | 543401.024 | 2102424.549 |

10 | 19˚0˚49.14˚ | 98˚34˚59.628˚ | 3000 | 543862.377 | 2102263.849 |

11 | 19˚0˚44.280˚ | 98˚34˚47.460˚ | 2960 | 544218.462 | 2102115.326 |

Data | |||||
---|---|---|---|---|---|

Point | Latitude | Longitude | Z | W | N |

1 | 19˚4˚25.824˚ | 98˚36˚11.16˚ | 3400 | 541756.3216 | 2108918.483 |

2 | 19˚4˚14.087˚ | 98˚36˚21.995˚ | 3500 | 541440.2879 | 2108557.144 |

3 | 19˚4˚3.9˚ | 98˚36˚35.244˚ | 3587.872 | 541054.0718 | 2108243.504 |

4 | 19˚3˚52.055˚ | 98˚36˚46.835˚ | 3651.994 | 540715.6962 | 2107878.453 |

5 | 19˚3˚39.996˚ | 98˚36˚55.512˚ | 3738.675 | 540463.5108 | 2107507.299 |

6 | 19˚3˚24.66˚ | 98˚37˚0.804˚ | 3820.266 | 540309.7976 | 2107035.544 |

7 | 19˚3˚11.087˚ | 98˚37˚8.4˚ | 3881.08 | 540088.629 | 2106617.608 |

8 | 19˚2˚56.759˚ | 98˚37˚15.348˚ | 3978.361 | 539885.7634 | 2106177.386 |

9 | 19˚2˚41.64˚ | 98˚37˚17.436˚ | 4149.287 | 539826.3458 | 2105712.186 |

10 | 19˚2˚27.42˚ | 98˚37˚14.52˚ | 4291.082 | 539912.5866 | 2105275.253 |

11 | 19˚2˚11.327˚ | 98˚37˚14.808˚ | 4491.679 | 539904.7367 | 2104780.647 |

12 | 19˚1˚56.567˚ | 98˚37˚21.576˚ | 4760.342 | 539708.4806 | 2104326.534 |

13 | 19˚1˚46.74˚ | 98˚37˚22.835˚ | 4962.988 | 539672.0045 | 2104024.676 |

CALCULATION OF PARTIAL ACCELERATION OF GRAVITY | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Pnt. | COORDINATES | Altitude (Z) | Latitude ˚ | (Decimal) | sen^{2} | Sen^{2}2 | Local gravity acceleration (gl) | Constants to calculate the acceleration of gravity of a point with latitude different Ecuador (ge) | ||||

W | N | ˚ | ' | " | ||||||||

1 | 539640.388 | 2104015.758 | 4880 | 19 | 01 | 46.451 | 19.02956972 | 0.10631257 | 0.380041 | 9.770750 | ge = 9.7803185 m/s² | |

2 | 540121.747 | 2103815.432 | 4580 | 19 | 01 | 39.899 | 19.02774972 | 0.10629299 | 0.379979 | 9.771675 | f′ 0.0053024 | |

3 | 540578.888 | 2103626.111 | 4280 | 19 | 01 | 33.707 | 19.02602972 | 0.10627448 | 0.379921 | 9.772600 | f_{4} = 0.0000059 | |

4 | 540034.0525 | 2103409.175 | 4040 | 19 | 01 | 26.616 | 19.02406 | 0.10625329 | 0.379854 | 9.773339 | Dg 0.000003086 | |

5 | 541510.084 | 2103239.814 | 3820 | 19 | 01 | 21.071 | 19.02251972 | 0.10623673 | 0.379802 | 9.774017 | ||

6 | 541981.976 | 2103042.855 | 3580 | 19 | 01 | 14.628 | 19.02073 | 0.10621748 | 0.379741 | 9.774757 | h = (altitude) | |

7 | 542443.398 | 2102852.492 | 3440 | 19 | 01 | 8.400 | 19.019 | 0.10619887 | 0.379683 | 9.775188 | f XX" | |

8 | 542937.432 | 2102646.725 | 3280 | 19 | 01 | 1.668 | 19.01713 | 0.10617876 | 0.379619 | 9.775681 | (latitude) | |

9 | 543401.024 | 2102424.549 | 3120 | 19 | 00 | 54.404 | 19.01511222 | 0.10615706 | 0.379551 | 9.776173 | Local Gravity Acceleration (gl) | |

10 | 543862.377 | 2102263.849 | 3000 | 19 | 00 | 49.140 | 19.01365 | 0.10614134 | 0.379501 | 9.776543 | ||

11 | 544218.462 | 2102115.326 | 2960 | 19 | 00 | 44.280 | 19.0123 | 0.10612683 | 0.379456 | 9.776666 | ||

∑gl = 107.517389928 | Data | |||||||||||

11 | ||||||||||||

Average Gravity Canyon: | ||||||||||||

9.774308 |

CALCULATION OF PARTIAL ACCELERATION OF GRAVITY | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Pnt. | COORDINATES | Altitude (Z) | Latitude ˚ | (Decimal) | sen^{2} | Sen^{2}2 | Local gravity acceleration (gl) | Constants to calculate the acceleration of gravity of a point with latitude different Ecuador (ge) | ||||

W | N | ˚ | ' | " | ||||||||

1 | 541756.3216 | 2108918.483 | 3400 | 19 | 4 | 25.824 | 19.07384 | 0.10678937 | 0.381542 | 9.775342 | ge = 9.7803185 m/s² | |

2 | 541440.2879 | 2108557.144 | 3500 | 19 | 4 | 14.087 | 19.07057972 | 0.10675422 | 0.381431 | 9.775032 | f' 0.0053024 | |

3 | 541054.0718 | 2108243.504 | 3587.872 | 19 | 4 | 3.900 | 19.06775 | 0.10672372 | 0.381335 | 9.774759 | f_{4} = 0.0000059 | |

4 | 540715.6962 | 2107878.453 | 3651.994 | 19 | 3 | 52.055 | 19.06445972 | 0.10668826 | 0.381224 | 9.774559 | Dg 0.000003086 | |

5 | 540463.5108 | 2107507.299 | 3738.675 | 19 | 3 | 39.990 | 19.06110833 | 0.10665215 | 0.38111 | 9.774290 | ||

6 | 540309.7976 | 2107035.544 | 3820.266 | 19 | 3 | 24.660 | 19.05685 | 0.10660627 | 0.380965 | 9.774036 | h = (altitude) | |

7 | 540088.629 | 2106617.608 | 3881.08 | 19 | 3 | 11.087 | 19.05307972 | 0.10656566 | 0.380838 | 9.773846 | f XX" | |

8 | 539885.7634 | 2106177.386 | 3978.361 | 19 | 2 | 56.759 | 19.04909972 | 0.10652279 | 0.380703 | 9.773543 | (latitude) | |

9 | 539826.3458 | 2105712.186 | 4149.287 | 19 | 2 | 41.640 | 19.0449 | 0.10647757 | 0.38056 | 9.773014 | Local Gravity Acceleration (gl) | |

10 | 539912.5866 | 2105275.253 | 4291.082 | 19 | 2 | 27.420 | 19.04095 | 0.10643505 | 0.380427 | 9.772574 | ||

11 | 539904.7367 | 2104780.647 | 4491.679 | 19 | 2 | 11.327 | 19.03647972 | 0.10638693 | 0.380275 | 9.771952 | ||

12 | 539708.4806 | 2104326.534 | 4760.342 | 19 | 1 | 56.567 | 19.03237972 | 0.10634281 | 0.380136 | 9.771121 | ||

13 | 539672.0045 | 2104024.676 | 4962.988 | 19 | 1 | 46.740 | 19.02965 | 0.10631343 | 0.380044 | 9.770494 | ∑gl = 127.054561911 | Data |

13 | ||||||||||||

Average Gravity Canyon: | ||||||||||||

9.773427839 |

f′ = 0.0053024 (gravitational collapse)

ϕ = Latitude, in degrees, minutes, seconds (00˚00'00")

h = Height above mean sea level (m)

F_{4} = 0.0000059

Dg = 0.000003086

The slope is the existing relation between the elevation and horizontal distance on a plane, which is equal to the tangent of the angle that forms the line to measure with the X axis. See Equation (2)

Using the contour lines on the topographic map and applying the interpolation method, the slope of the canyons was determined taking readings every 500 meters along the channel. The arithmetic average was also calculated for the points in each canyon [

Through the use of the Geoeas program, which creates weighted normal probability graphics of the forcing variables (gravity and height), the statistical behavior of dispersion was obtained with the linear regression model of the matrix of the analyzed variables, which coefficient for each processed canyon is close to −1 (

Slope of the Canyon | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Pnt. | COORDINATES | Altitude | Distance | ||||||||

W | N | ||||||||||

1 | 539640.388 | 2104015.758 | 4880 | ∑m_{1} + m_{2} = −3.840000000 | |||||||

2 | 540121.747 | 2103815.432 | 4580 | 500 | −0.60000 | ||||||

3 | 540578.888 | 2103626.111 | 4280 | 500 | −0.60000 | ||||||

4 | 540034.0525 | 2103409.175 | 4040 | 500 | −0.48000 | Average slope | |||||

5 | 541510.084 | 2103239.814 | 3820 | 500 | −0.44000 | ||||||

6 | 541981.976 | 2103042.855 | 3580 | 500 | −0.48000 | −0.349090909 | |||||

7 | 542443.398 | 2102852.492 | 3440 | 500 | −0.28000 | ||||||

8 | 5422937.432 | 2102646.725 | 3280 | 500 | −0.32000 | High point | |||||

9 | 543401.024 | 2102424.549 | 3120 | 500 | −0.32000 | 4880 | |||||

10 | 543862.377 | 2102263.849 | 3000 | 500 | −0.24000 | Low point | |||||

11 | 544218.462 | 2102115.326 | 2960 | 500 | −0.08000 | 2960 | |||||

Distance | |||||||||||

5000 | |||||||||||

Slope between points | |||||||||||

−0.384000000 | |||||||||||

Slope of the canyon | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Pnt. | COORDINATES | Altitude | Distance | ||||||||

W | N | ||||||||||

1 | 541756.3216 | 2108918.483 | 3400 | ∑m_{1} + m_{2} = 3.125976000 | |||||||

2 | 541440.2879 | 2108557.144 | 3500 | 500 | 0.20000 | ||||||

3 | 541054.0718 | 2108243.504 | 3587.872 | 500 | 0.17574 | ||||||

4 | 540715.6962 | 2107878.453 | 3651.994 | 500 | 0.12824 | Average slope | |||||

5 | 540463.5108 | 2107507.299 | 3738.675 | 500 | 0.17336 | ||||||

6 | 540309.7976 | 2107035.544 | 3820.266 | 500 | 0.16318 | 0.240459692 | |||||

7 | 540088.629 | 2106617.608 | 3881.08 | 500 | 0.12163 | ||||||

8 | 539885.7634 | 2106177.386 | 3978.361 | 500 | 0.19456 | ||||||

9 | 539826.3458 | 2105712.186 | 4149.287 | 500 | 0.34185 | High point | |||||

10 | 539912.5866 | 2105275.253 | 4291.082 | 500 | 0.28359 | 4963 | |||||

11 | 539904.7367 | 2104780.647 | 4491.679 | 500 | 0.40119 | Low point | |||||

12 | 539708.4806 | 2104326.534 | 4760.342 | 500 | 0.53733 | 3400 | |||||

13 | 539672.0045 | 2104024.676 | 4962.988 | 500 | 0.40529 | Distance | |||||

500 | |||||||||||

Slope between points | |||||||||||

−3.125976000 | |||||||||||

With an overlay of the surfer model and the statistical representation deployed, the match between the processed and modeled data can be observed. There were also graphics created to show the behavior of each one of the considered variables [

Geostatistical analysis of the canyons was carried out, calculating the standard deviation for determining the arithmetic average of fluctuation of data from its mean or center point and the covariance, a joint dispersion measure of two statistics variables for each of the canyons [

The analysis of the statistical variables between height and gravity was obtained by applying the Surfer program [

The 2D and 3D structural modeling was made using Surfer, which was useful to identify the canyons of study and their vector behavior [

The variogram is a tool that allows analysis of the spatial behavior of a variable over a defined area [

In the case of the canyons, the variogram of the height was created against the local calculated gravity (

Colorada Canyon

The force of water is the amount of thrust that this liquid exerts on the slope direction; the water density is 1 gr/cm^{3} or 1000 Kg/m^{3}. The calculations done using the mathematical model or Equation (3) showed that the force increases proportionally to the inclination of the slope.

The water channel was subdivided in an equidistance of 500 m [

The waste is the volume of a substance, which passes per unit of time. In this case, the waste of each of the can-

Pto. | Altitude (m) | Local gravity acceleration (m/s^{2}) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 4200 | 796.1538 | 633860.947 | 9.772851 | −0.002458 | 6.0394E−06 | −1.956560877 | |||||

2 | 4055 | 651.1538 | 424001.331 | 9.773300 | −0.002009 | 4.0373E−06 | −1.308367578 | |||||

3 | 3940 | 536.1538 | 287460.947 | 9.773655 | −0.00165 | 2.736E−06 | −0.886845767 | |||||

4 | 3800 | 396.1538 | 156937.870 | 9.774088 | −0.001221 | 1.4916E−06 | −0.48382825 | |||||

5 | 3640 | 236.1538 | 55768.639 | 9.774582 | −0.000727 | 5.2901E−07 | −0.171762177 | |||||

6 | 3440 | 36.1538 | 1307.101 | 9.775199 | −0.000110 | 1.2057E−08 | −0.003969814 | |||||

7 | 3315 | −88.8462 | 7893.639 | 9.775585 | 0.000276 | 7.6147E−08 | −0.024516798 | |||||

8 | 3195 | −208.8462 | 43616.716 | 9.775954 | 0.000645 | 4.1625E−07 | −0.134741456 | |||||

9 | 3065 | −338.8462 | 114816.716 | 9.776355 | 0.001046 | 1.0945E−06 | −0.354493546 | |||||

10 | 2985 | −418.8462 | 175432.101 | 9.776601 | 0.001292 | 1.6699E−06 | −0.541259438 | |||||

11 | 2920 | −483.8462 | 234107.101 | 9.776801 | 0.001492 | 2.2259E−06 | −0.721869941 | |||||

12 | 2855 | −548.8462 | 301232.101 | 9.777000 | 0.001691 | 2.8591E−06 | −0.928044829 | |||||

13 | 2840 | −563.8462 | 317922.485 | Standard deviation | 9.777046 | 0.001737 | 3.017E−06 | Standard deviation | −0.979377112 | |||

3403.846154 | 211873.669 | 460.2973698 | 9.775309 | 2.0157E−06 | 0.001419758 | −0.653510583 | ||||||

Correlation coefficient | Covariance | |||||||||||

−0.999999554 | ||||||||||||

Pto. | Altitude (m) | Local gravity acceleration (m/s^{2}) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 3920 | 750 | 562500.0000 | 9.773706 | −0.002312 | 5.3435E−06 | −1.733698657 | |||||

2 | 3680 | 510 | 260100.0000 | 9.774448 | −0.001570 | 2.4656E−06 | −0.800811723 | |||||

3 | 3500 | 330 | 108900.0000 | 9.775002 | −0.001016 | 1.0323E−06 | −0.335282639 | |||||

4 | 3360 | 190 | 36100.0000 | 9.775434 | −0.000584 | 3.414E−07 | −0.111015158 | |||||

5 | 3250 | 80 | 6400.0000 | 9.775773 | −0.000245 | 6.0108E−08 | −0.019613542 | |||||

6 | 3150 | −20 | 400.0000 | 9.776081 | 0.000063 | 3.9834E−09 | −0.00126228 | |||||

7 | 3080 | −90 | 8100.0000 | 9.776297 | 0.000279 | 7.7683E−08 | −0.025084539 | |||||

8 | 3030 | −140 | 19600.0000 | 9.776451 | 0.000433 | 1.8754E−07 | −0.060628639 | |||||

9 | 2990 | −180 | 32400.0000 | 9.776574 | 0.000556 | 3.0938E−07 | −0.100119271 | |||||

10 | 2900 | −270 | 72900.0000 | 9.776850 | 0.000832 | 6.9193E−07 | −0.224592674 | |||||

11 | 2840 | −330 | 108900.0000 | 9.777033 | 0.001015 | 1.0307E−06 | −0.335033064 | |||||

12 | 2780 | −390 | 152100.0000 | 9.777216 | 0.001198 | 1.4359E−06 | −0.467330943 | |||||

13 | 2730 | −440 | 193600.0000 | Standard deviation | 9.777369 | 0.001351 | 1.8247E−06 | Standard deviation | −0.594357709 | |||

3170 | 120153.8462 | 346.6321482 | 9.776018 | 1.1388E−06 | 0.001067156 | −0.369910064 | ||||||

Correlation coefficient | Covariance | |||||||||||

−0.999998549 | ||||||||||||

Univariate Statistics | |||
---|---|---|---|

X | Y | Z | |

Minimum: | 2840 | 9.772851392 | 9.772851392 |

25%-tile: | 2985 | 9.774087594 | 9.774087594 |

Median: | 3315 | 9.775584855 | 9.775584855 |

75%-tile: | 3800 | 9.776601172 | 9.776601172 |

Maximum: | 4200 | 9.777045867 | 9.777045867 |

Midrange: | 3520 | 9.7749486295 | 9.7749486295 |

Range: | 1360 | 0.0041944750000003 | 0.0041944750000003 |

Interquartile Range: | 815 | 0.0025135780000003 | 0.0025135780000003 |

Median Abs. Deviation | 395 | 0.0012159950000008 | 0.0012159950000008 |

Mean: | 3403.8461538462 | 9.7753089084615 | 9.7753089084615 |

Trim Mean (10%): | 3382.7272727273 | 9.7753744137273 | 9.7753744137273 |

Standard Deviation: | 460.29736979376 | 0.0014197582068528 | 0.0014197582068528 |

Variance: | 211873.66863905 | 2.015713365926E−006 | 2.015713365926E−006 |

Coef. of Variation | 0.00014523921649411 | ||

Coef. of Skewness | −0.34133729589633 |

Univariate Statistics | |||
---|---|---|---|

X | Y | Z | |

Minimum: | 2730 | 9.773706207 | 9.773706207 |

25%-tile: | 2900 | 9.775433515 | 9.775433515 |

Median: | 3080 | 9.776296522 | 9.776296522 |

75%-tile: | 3360 | 9.77684963 | 9.77684963 |

Maximum: | 3920 | 9.777638618 | 9.777368618 |

Midrange: | 3325 | 9.7755374125 | 9.7755374125 |

Range: | 1190 | 0.0036624110000005 | 0.0036624110000005 |

Interquartile Range: | 460 | 0.0014161149999996 | 0.0014161149999996 |

Median Abs. Deviation | 240 | 0.00073653499999971 | 0.00073653499999971 |

Mean: | 3170 | 9.7760178050769 | 9.7760178050769 |

Trim Mean (10%): | 3141.8181818182 | 9.7761051491818 | 9.7761051491818 |

Standard Deviation: | 346.63214818283 | 0.0010671560113215 | 0.0010671560113215 |

Variance: | 120153.84615385 | 1.1388219524997E−006 | 1.1388219524997E−006 |

Coef. of Variation | 0.00010916060430734 | ||

Coef. of Skewness | −0.72181350474623 |

yons was obtained by applying the equation of the rational method (4) (

Strength calculation of water | ||||||||
---|---|---|---|---|---|---|---|---|

Pto. | Altitude | Density of water | Cosine of the slope (Cos m) | Acceleration gravity local (gl) | Partial forces | |||

F_{i}_{ }= (d*cosm) (gl) | ||||||||

Channel slope | ||||||||

1 | 4200 | ∑F_{i} = 1173.00206330 | ||||||

2 | 4055 | 1000 | −0.416168 | 0.999974 | 9.773300 | 97.730418 | ||

3 | 3940 | 1000 | −0.414141 | 0.999974 | 9.773655 | 97.733995 | ||

4 | 3800 | 1000 | 0.398168 | 0.999976 | 9.774088 | 97.738516 | Data | |

5 | 3640 | 1000 | −0.114741 | 0.999998 | 9.774582 | 97.745620 | ||

6 | 3440 | 1000 | −0.417382 | 0.999973 | 9.775199 | 97.749397 | 12 | |

7 | 3315 | 1000 | −0.412557 | 0.999974 | 9.775585 | 97.753314 | ||

8 | 3195 | 1000 | −0.000042 | 1.000000 | 9.775954 | 97.759541 | ||

9 | 3065 | 1000 | 0.000046 | 1.000000 | 9.776355 | 97.763551 | ||

10 | 2985 | 1000 | −0.348323 | 0.999982 | 9.776601 | 97.764205 | ||

11 | 2920 | 1000 | −0.417100 | 0.999974 | 9.776801 | 97.765418 | ||

12 | 2855 | 1000 | 0.582900 | 0.999948 | 9.777000 | 97.764936 | 97.75017194 N | |

13 | 2840 | 1000 | 1.582900 | 0.999618 | 9.777046 | 97.733150 | ||

Strength calculation of water | |||||||||
---|---|---|---|---|---|---|---|---|---|

Pto. | Altitude | Density of water | Cosine of the slope (Cos m) | Acceleration gravity local (gl) | Partial forces | ||||

F_{i} = (d*cosm) (gl) | |||||||||

Channel slope | |||||||||

1 | 3920 | ∑F_{i} = 1173.08566882 | |||||||

2 | 3680 | 1000 | −0.416168 | 0.999974 | 9.774448 | 97.741897 | |||

3 | 3500 | 1000 | −0.414141 | 0.999974 | 9.775002 | 97.747464 | |||

4 | 3360 | 1000 | 0.398168 | 0.999976 | 9.775434 | 97.751975 | Data | ||

5 | 3250 | 1000 | −0.114741 | 0.999998 | 9.775773 | 97.757530 | |||

6 | 3150 | 1000 | −0.417382 | 0.999973 | 9.776081 | 97.768215 | 12 | ||

7 | 3080 | 1000 | −0.412557 | 0.999974 | 9.776297 | 97.760431 | |||

8 | 3030 | 1000 | −0.000042 | 1.000000 | 9.776451 | 97.764509 | |||

9 | 2990 | 1000 | 0.000046 | 1.000000 | 9.776574 | 97.765740 | |||

10 | 2900 | 1000 | −0.348323 | 0.999982 | 9.776850 | 97.766690 | |||

11 | 2840 | 1000 | −0.417100 | 0.999974 | 9.777033 | 97.767740 | |||

12 | 2780 | 1000 | 0.582900 | 0.999948 | 9.777216 | 97.767101 | 97.75713907 N | ||

13 | 2730 | 1000 | 1.582900 | 0.999618 | 9.777369 | 97.736376 | |||