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An infiltration characteristic model was developed by using the modified Kostiakov method for the Agricultural Engineering demonstration field of Bangladesh Agricultural Research Institute (BARI). The constant values a, α, and b of the equation for accumulated infiltration y = atα + b were 9.12, 0.683, and 0.145, respectively. The average value of percentage of error between the actual and calculated values by the model was only 0.134 and showed very good agreement between the model and the field values of accumulated infiltration. This model will be very helpful for making a good irrigation scheduling and best water management.

Infiltration may be defined as the intake of water into the soil profile. The rate and cumulative infiltration amount are necessary to calculate the total water requirement for efficient irrigation system [

- lack of awareness of measuring actual volume and rate of infiltration;

- lack of skill and knowledge of infiltration measurement and its role in water management practices.

Considering the importance and economic benefit of irrigation and water management practices, a mathematical model may be prepared and available for serving the assessment and quantifying the amount of water needed for actual water requirement of the crops [

Infiltration capacity is dependent on soil texture, soil structure, and soil cover. Also, infiltration is dependent on existing soil moisture content, soil hydraulic conductivity, soil porosity, existing soil swelling colloids and organic matters, irrigation or rainfall duration, and viscosity of water [

There are three methods for determining the infiltration characteristics for any irrigation system design and water management practices. They are: 1) cylindrical infiltrometer method, 2) Accumulation infiltration estimation from waterfront advance data, and 3) Depletion of free water surface measurement in a large basin.

Out of the above mentioned methods, cylindrical infiltrometer method is most commonly used. Cylindrical infiltrometer method offers the advantages over the other two avoiding the cumbersome procedure in collecting correct data from the field while estimating from waterfront advance data and there is necessity of considering the evaporation loss due to atmospheric influences on the large basin while measurement of water depletion is considered [

The material used for making these cylinders is of 2 mm rolled steel. The inner and the outer cylinders are both ponded with water. The outer cylinder is used as a buffer pond to avoid the lateral movement of water from and to the inner cylinder. Care should be taken against beveling of the cylinder bottoms. The cylinders are driven into the soil by a falling weight hammer striking on top of a wooden plank placing on top of the cylinders to avoid the damage at the edge of the cylinders.

The main objective of this study was to develop a model for infiltration characteristic by modified Kostiakov method and to calculate the accumulated infiltration and infiltration rate with specific focus on: 1) deriving the constant values of modified Kostiakov method for the soil under consideration, 2) judging the applicability of the model using the field data, and 3) find the percentage of error between the actual and the values calculated by the model.

This study was carried out in the Irrigation and Water Management demonstration field of BARI in 2012. This field is used for demonstration purposes and to exhibit different irrigation methods for training the farmers and agricultural extension officials. Sometimes, these plots are used for both exhibition and crop related research purposes too. The field was kept fallow at the time when the study was conducted. It was clay-loamy soil, without any tillage practices done and had common soil vegetation. Four infiltrometers were installed lengthwise with distances as shown in

The water levels of the inner cylinder were read by a needle type pointed hook gage whose sharp and pointed headend was just touching water level for initial water height reading and the tail end was set with a scale to read the difference after a predetermined time when a depletion of water height was there by adjusting the pointed head again touching the depleted water surface. The difference between initial and the final readings were the height of water that infiltrated during the predetermined time. This height divided by time is the one what is defined as the infiltration rate. Here times were recorded as minutes but they were converted into hours for calculation purposes and express the infiltration rate as cm/hr. After some period, there is no more depletion of water took place and the curve of accumulated infiltration (ordinate) vs. time (abscissa), is the constant infiltration rate the characteristic of this point and hereafter is called asymptote. At the initial stages, time vs. depletion of water recordings were taken frequently, refill of water were done as quickly as possible so that the pace of infiltration could be kept constant. Water levels in the inner and the outer cylinders were kept approximately same to keep up the water pressures same between the inner and outer cylinders and avoids the lateral water movement due to dissimilar height between the inner and the outer cylinders. The average values of accumulated infiltration y and average infiltration rate have been plotted against time t and shown in

The modified Kostiakov method [

to time t can be mathematically defined by the following equation, known as modified Kostiakov method:

where

y = accumulated infiltration at time t, (cm),

t = elapsed time, (min), and

a, α, and b are three characteristic constants.

Values of a, α, and b can be calculated by the method suggested by Davis [

1) plot the values of y and t;

2) select a pair of points of (t_{1}, y_{1}) and (t_{2}, y_{2}) from this plot, selection of the points on the plotted line should be near the extremities of the line to cover a wide range of interpolated values;

3) calculate a third value for time t_{3} using the values of t_{1} and t_{2} from the procedure followed in the previous step. The equation for calculating t_{3} is as follows:

Values of t_{1} and t_{2 }are available from the plotted line and that has been described in step 2.The corresponding value of accumulated infiltration y_{3} = 5.9 cm when t_{3} = 25.5 minutes. Value of b can be calculated by formula used in regression analysis. The formula can be shown as follows (refer to

Equation (1) can be rearranged and written as

Taking log both sides

Equation (3) yields the following equations when the values of b and t are substituted:

Infiltrometer No. 1 | Infiltrometer No. 2 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Height of water surface from reference | Infiltration during elapsed time | Height of water surface from reference | Infiltration during elapsed time | |||||||

Time (min) | Before filling (cm) | After filling (cm) | Depth (cm) | Rate of infiltration (cm/hr) | Accumulated infiltration (cm) | Before filling (cm) | After filling (cm) | Depth (cm) | Rate of infiltration (cm/hr) | Accumulated infiltration (cm) |

0 | 0 | 11.5 | 0 | 0 | 0 | 0 | 11.5 | 0 | 0 | 0 |

5 | 9.7 | 11.5 | 1.8 | 21.6 | 1.8 | 9.6 | 11.5 | 1.9 | 22.8 | 1.9 |

10 | 10.3 | 11.5 | 1.2 | 14.4 | 3.0 | 9.8 | 11.5 | 1.7 | 20.4 | 3.6 |

15 | 9.7 | 11.5 | 1.8 | 21.6 | 4.8 | 10.2 | 11.5 | 1.3 | 15.6 | 4.9 |

25 | 9.9 | 11.5 | 1.6 | 9.6 | 6.4 | 9.7 | 11.5 | 1.8 | 10.8 | 6.7 |

45 | 9.7 | 11.5 | 1.8 | 5.4 | 8.2 | 9.7 | 11.5 | 1.8 | 5.4 | 8.5 |

60 | 9.7 | 11.5 | 1.8 | 7.2 | 10.0 | 9.5 | 11.5 | 2.0 | 8.0 | 10.5 |

75 | 9.7 | 11.5 | 1.8 | 7.2 | 11.8 | 9.5 | 11.5 | 2.0 | 8.0 | 12.5 |

90 | 9.7 | 11.5 | 1.8 | 7.2 | 13.6 | 9.3 | 11.5 | 2.2 | 8.8 | 14.7 |

110 | 9.3 | 11.5 | 2.2 | 6.6 | 15.8 | 9.3 | 11.5 | 2.2 | 6.6 | 16.9 |

130 | 9.3 | 11.5 | 2.2 | 6.6 | 18.0 | 9.0 | 11.5 | 2.5 | 7.5 | 19.4 |

Infiltrometer No. 3 | Infiltrometer No. 4 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Height of water surface from reference | Infiltration during elapsed time | Height of water surface from reference | Infiltration during elapsed time | |||||||

Time (min) | Before filling (cm) | After filling (cm) | Depth (cm) | Rate of infiltration (cm/hr) | Accumulated infiltration (cm) | Before filling (cm) | After filling (cm) | Depth (cm) | Rate of infiltration (cm/hr) | Accumulated infiltration (cm) |

0 | 0 | 11.5 | 0 | 0 | 0 | 0 | 11.5 | 0 | 0 | 0 |

5 | 9.5 | 11.5 | 2 | 24 | 2.0 | 9.8 | 11.5 | 1.7 | 20.4 | 1.7 |

10 | 10.1 | 11.5 | 1.4 | 16.8 | 3.4 | 10.0 | 11.5 | 1.5 | 18.0 | 3.2 |

15 | 10.3 | 11.5 | 1.2 | 14.4 | 4.6 | 10.1 | 11.5 | 1.4 | 16.8 | 4.6 |

25 | 10.2 | 11.5 | 1.3 | 7.8 | 5.9 | 9.6 | 11.5 | 1.9 | 11.4 | 6.5 |

45 | 9.7 | 11.5 | 1.8 | 5.4 | 7.7 | 9.6 | 11.5 | 1.9 | 5.7 | 8.4 |

60 | 9.7 | 11.5 | 1.8 | 7.2 | 9.5 | 9.5 | 11.5 | 2.0 | 8.0 | 10.4 |

75 | 9.3 | 11.5 | 2.2 | 8.8 | 11.7 | 9.5 | 11.5 | 2.0 | 8.0 | 12.4 |

90 | 9.3 | 11.5 | 2.2 | 8.8 | 13.9 | 9.3 | 11.5 | 2.2 | 8.8 | 14.6 |

110 | 9.2 | 11.5 | 2.3 | 6.9 | 16.2 | 9.0 | 11.5 | 2.5 | 7.5 | 17.1 |

130 | 9.2 | 11.5 | 2.3 | 6.9 | 18.5 | 9.0 | 11.5 | 2.5 | 7.5 | 19.6 |

Adding Equations (4) to (8)

Adding Equations (9) to (13)

Solving Equations (14) and (15), the value of α becomes 0.683

The value of

Now substituting the values of a, b, and α in equation for individual elapsed times

At t = 5 min,

At t = 10 min,

At t = 15 min,

At t = 25 min,

At t = 40 min,

At t = 60 min,

At t = 75 min,

At t = 90 min,

At t = 110 min,

At t = 130 min,

The percentage of error was calculated by the following equation:

where,

Time (min) | Average | |
---|---|---|

Rate of infiltration (cm/hr) | Accumulated infiltration (cm) | |

0 | 0 | 0 |

5 | 21.60 | 1.80 |

10 | 19.20 | 3.40 |

15 | 16.20 | 4.75 |

25 | 11.10 | 6.60 |

45 | 5.55 | 8.45 |

60 | 8.00 | 10.45 |

75 | 8.00 | 12.45 |

90 | 8.80 | 14.65 |

110 | 7.05 | 17.00 |

130 | 7.50 | 19.50 |

Time (min) | Observed accumulated infiltration (cm)^{*} | Calculated accumulated infiltration (cm)^{**} | Percent of error (%) |
---|---|---|---|

Observed | Calculated | ||

5 | 1.80 | 2.137 | 18.72 |

10 | 3.40 | 3.344 | −1.65 |

15 | 4.75 | 4.365 | −8.11 |

25 | 6.60 | 6.126 | −7.18 |

40 | 8.45 | 8.39 | −0.71 |

60 | 10.45 | 11.021 | 5.46 |

75 | 12.45 | 12.812 | 2.91 |

90 | 14.65 | 14.492 | −1.08 |

110 | 17.00 | 16.599 | −2.36 |

130 | 19.50 | 18.588 | −4.68 |

Average error | 0.134 |

^{*}Average of 1 to 4 infiltrometer reading; ^{**}Equations (16) to (25).

0.145, respectively, which are below 1 and follows and maintains the requirement of the modified Kostiakov method [

This model is developed to estimate the rate and accumulated infiltration of water in agricultural land is using

modified Kostiakov method. Values for a, α, and b of modified Kostiakov equation are calculated to be 0.178, 0.683, and 0.145, respectively, which are below 1. This condition follows the principle of modified Kostiakov method [

The authors would like acknowledge Prof. Rao Mentreddy and Prof. Michael Ayokanmbi of Alabama Agricultural and Mechanical University for reviewing this manuscript and making valuable suggestion.

MahbubHasan,TamaraChowdhury,MebougnaDrabo,AschalewKassu,ChanceGlenn, (2015) Modeling of Infiltration Characteristics by Modified Kostiakov Method. Journal of Water Resource and Protection,07,1309-1317. doi: 10.4236/jwarp.2015.716106