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The areal distribution of soil moisture under sprinkler irrigation
Agricultural watermanagement ELSEVIER
Agricultural Water Management 32 (1996) 29-36
The area1 distribution of soil moisture under sprinkler irrigation Jiusheng Li aT*, Hiroshi Kawano b aDepartment of Hydraulic Engineering, Tsinghua University, Beijing 100084, Chinu b Faculty of Agriculture, Kagawa University, Kagawa 761-07, Japan
Accepted 29 April 1996
Abstract The area1 distributions of soil water content under varying uniformities of sprinkler water application were observed on two different soil types, to quantify the relationship between the subsurface distribution of soil moisture and water application on the ground surface. Field experimental results showed evidence of the importance of redistribution of the unevenly applied surface water. The water within the soil is more uniformly distributed than that applied through a sprinkler irrigation system. The extent of water redistribution within the soil profile depends mainly on the uniformity of initial soil water content and the total applied water. The distribution of water in the soil under a wide range of water application uniformities can be represented by a
normal distribution function. The analyses for the influence of the number of samples on observation accuracy of soil moisture uniformity indicated that the number should not be less than nine. Keywords: Sprinkler irrigation; Uniformity; Soil water content
1. Introduction Sprinkler irrigation tests commonly intercept the falling water with catch-cans on a horizontal surface, such as the ground. The mean application and the uniformity coefficient are computed for the area1 distribution of water. Extensive research has been made on the surface distribution of water from sprinklers (Christiansen, 1941; Hart, 1961; Elliot et al., 1980; Warrick, 1983; Marek et al., 1986; Heermann et al., 1992). However, the yield response of the crop is affected by the water within its root zone.
* Corresponding author. Fax: (10)259-5699. 0378-3774/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO378-3774(96)01261-9
30
J. Li, H. Kawano/Agriculturul
Water Management 32 (1996) 29-36
Therefore, the distribution of water within the soil is more important than its distribution on the soil surface. As early as 1963, Davis had indicated that the measured surface distribution is not a good indicator of yield (Davis, 1963). Hart (1972) studied the subsurface distribution of nonuniformly applied surface waters using a transient model and found that the water within the soil is more uniformly distributed than indicated by the initial surface-measured distribution. However, no field experiments were accompanied with his simulation. The objectives of this study were to quantify the relationship between the area1 distribution of soil moisture and the uniformity of water application, and to investigate the relative importance on the redistribution of water within the soil of the irrigation variables including initial water content and its uniformity, uniformity of water application, total applied water and soil type, by field experiments.
2. Field experiments The experiments were conducted on a volcanic ash soil (referred to as Soil A) with a bulk density of 0.74 g cmw3 and a saturated water content of 0.64 + 0.02 cm3 cmm3 (mean f standard deviation). The soil has a considerably high water holding capacity (Fig. 1). Shoji et al. (1993) fully described the properties of this soil type. For Soil A, four medium sprinklers were arranged in a 12 m by 12 m square spacings. The area enclosed by the four sprinklers was divided into 2 m square grids. A catch-can with 20 cm inside diameter was placed at the center of each grid to measure water application depth and uniformity. Soil water content for each grid was measured at a 10 cm depth and 20 cm apart from the can by an electrical resistance (gypsum block) method (Kutilek and Nielsen, 1994). Three replications were used for each measurement. The depth of 10 cm from the surface may represent the middle position of wetted depth for a normal irrigation amount in humid regions, such as Japan. The humid conditions would avoid salt accumulation by the substantial drainage at various times of the year because a rainfall event could usually be expected. In order to determine the initial soil water content and its distribution, water content for each grid was measured by the gypsum block method before the beginning of water application. Water content for each grid was
_. 0.0
0.2
0.4
0.6
Water content (cm3 / cm3) Fig.
I. Soil moisture characteristic
curves for Soils A and B.
J. Li, H. Kawano/Agricultural Table 1 A summary
of the experimental
conditions
Wuter Management 32 (1996) 29-36
and uniformity
coefficients
of water applications
AR (mm hh’)
No.
Soil A Al A2 A3 A4 A5 * A6 * A7 Soil B Bl B2 B3 B4 * B5
31
WC km3 cm- 3>
5.4 5.8 8.2 8.0 8.0
5.4 5.0 24.6 8.0 8.0 13.9 51.6
61 72 85 90 91 98 98
96 96 97 91 96 91 96
0.45 0.45 0.45 0.46 0.46 0.48 0.45
15.0 11.3 12.2 11.5
10.0 13.2 7.0 17.0 21.0
53 60 61 69 98
96 94 92 95 94
0.29 0.32 0.25 0.34 0.35
* Water was applied by rainfall events, others by sprinkler irrigation. AR: average application rate; TW: total water application; CU,,: initial uniformity of soil water content; and WC: initial soil water content.
also measured at different times after water application ceased, to investigate the redistribution of water within the soil. Seven experiments with the Christiansen uniformity coefficient (CU) from 61 to 98% (including two rainfall events) were conducted on Soil A. Field experiments were also conducted on a different texture of soil from Soil A. The soil was classified as a sandy loam (referred to as Soil B) according to the international classification standard (Hillel, 1971). The bulk density was 1.20 g cmm3 and the saturated water content was 0.40 + 0.03 cm3 cm-3 (mean f standard deviation). Fig. 1 also shows the soil moisture characteristic curve for Soil B. The arrangement and procedures for experiments conducted on Soil B were the same as those for Soil A except for sprinkler spacing and measuring method of soil water content. The sprinkler spacings were 6 m by 14 m and water content for each grid was sampled around the center of the grid by a 100 cm3 ring (a gravimetric method) at the depth of 7.5 to 12.5 cm (average 10 cm). Five experiments with CU ranging from 53 to 98% (including one rainfall event) were conducted (Table 1). All of the experiments were conducted on bare fields. The experimental conditions and the corresponding uniformities of water application are summarized in Table 1.
3. Results
and discussion
3.1. Uniformity
of soil water redistribution
The Christiansen
uniformity
coefficient
of soil water content (CU,)
is defined as:
(1)
J. Li, H. Kuwano/Agricultural
32
cu,=
[I- (;)t+,Nij]x
Water Management 32 (1996) 29-36
(2)
loo
where ei is the observed soil water content for the ith point, 8 is the mean of Bi, and N is the number of points. Fig. 2a and b present the uniformity of soil water content (CU,) as a function of time after water application ceased, for varying water application uniformities on Soils A and B, respectively. In both figures, the first point for each experiment represents the initial uniformity of soil water content. Water was much more uniformly distributed in the soil than that measured on the surface. The value of CU, still exceeded 90% even when the surface-measured water application uniformity (CU) was below 60%. Fig. 2a also indicates that CU, tends to decrease during the process of water application for Soil A. After water application ceased, CU, began to increase with time. The ultimate value of CU, appears to be around the initial uniformity of soil water content. 3.2. Effect of irrigation
variables
on water redistribution
3.2.1. EfSect of water application uniformity As can be seen in Fig. 2a and b, for different water application uniformities, CU, reached almost the same ultimate value after a reasonable time of redistribution. For Soil A, CU, approximated 97% after 24 h redistribution, the value of CU, approached 95% after a certain time of redistribution for Soil B. It is clear that the effect of water application uniformity is not as important as originally supposed. Even for a very low uniformity of CU of 53% (Fig. 2b, No. Bl), CU, had reached 95% after 4.5 h redistribution. This is a desirable value of uniformity being strived for in many commercial installations. When the uniformity of water application is higher, the maximum value of CU, might be reached sooner than the lower CU event, but this is not important. What is important, however, is that the maximum value of CU, might be equally high whether the value of CU is low or high. 3.2.2. Effect of initial soil moisture conditions and total water application We defined CU, max as the maximum value of CU, during the observed process of water redistribution. In order to analyze the effect of initial water content and its
Time after water Fig. 2. Uniformity
coefficient
applied
(min)
Time after water
of soil water content, CU,, as a function
applied
(min)
of time after water application
ceased.
J. Li, H. Kuwano / Agricultural
Water Management
32 (1996) 29-36
33
uniformity and total water application on CU, max, the relationship between CU, max and each of the factors was correlated, respectively. The regression equations with the coefficients of correlation (r2) for Soil B are as follows: CU, IIlax= 106.6wc0~”
( r2 = 0.743)
(3)
CU, max = 1 .6CUi,90 (r* = 0.513)
(4)
CU,nl,X = 86.5TW”.03
(5)
(r* = 0.757)
where WC is the initial soil water content (cm’ cmm3>, ranging from 0.25 to 0.35; CU,, is the initial uniformity of soil water content (%), ranging from 91 to 96%; and TW is total water application, ranging from 7 to 25 mm. Eqs. (3) to (5) indicate that CU, max increases with any of WC, CU,, and TW. The relationship between CU, max and initial soil water content and its uniformity and total water application was correlated to investigate the relative importance of the above mentioned factors to CU, max: CU, IIlax= 8.2WC”~01CU,q.52TWo.03 (I’ = 0.884)
(6)
Based on Eq. (6), sensitivity analysis was conducted showing that CU, max is more sensitive to initial uniformity of soil water content (CU,,) than to either initial water content (WC) or total water application (TW), but CU, max is more sensitive to TW than to WC. 3.3. Empirical function
to represent
the distribution
of water in the soil
Many researchers have studied the suitable function to represent the distribution of water application from stationary overlapped or center-pivot systems. Elliot et al. (1980) reported that a normal distribution was generally better than a uniform distribution for simulated solid sprinkler irrigation events. Heermamr et al. (1992) stated that the normal distribution was the best of the normal, log normal, uniform and specialized power for center pivot. However, the function to represent the distribution of water in the soil after infiltration under different uniformities of water application has not been reported. Therefore, we used the Kolmogorov-Smimov test to determine the adequacy of the fit of the soil water content data at the 10 cm depth after infiltration to the normal distribution. The non parametric test is expressed as: D+=maxlF,(x)
-F(x)
(7)
where D+ is the maximum deviation between the cumulative distribution and the empirical distribution; F, is cumulative distribution of normal distribution function, and F is empirical distribution of soil water content. Examples of the typical Kolmogorov-Smirnov test statistics for experiments conducted on Soil B are tabulated in Table 2. All of the tests can be described by the normal distribution at the 0.05 level. Thus, the normal distribution is a suitable function to represent the distribution of soil water content under a wide range of water application uniformities. The confidence limits of 95% of CU, were determined based on the fact
J. Li, H. Kuwurw/Agriculrurul
34
Wurer Management 32 (1996) 29-36
Table 2 The Kolmogorov-Smimov goodness of fit statistics for cumulative and the confidence limits of 95% for CU, No.
Bl-01 * Bl-02 Bl-03 B2-01 B2-02 B2-03 B3-01 B3-02 B4-01 B4-02 B4-03 B.5-01 B5-02
95.5 94.5 94.2 93.8 91.5 94.2 94.2 95.9 92.4 90.9 91.3 95.3 94.2
* No. B l-01 represents
distribution
Mean 3 (cm’ cm- 3,
D+
0.28 0.35 0.33 0.31 0.35 0.35 0.35 0.35 0.24 0.29 0.28 0.34 0.38
0.13 0.10 0.13 0.17 0.18 0.23 0.23 0.17 0.14 0.14 0.13 0.2 1 0.15
the first time measurement
Confidence
data
limit
(%I 92.2-95.9 90.3-94.9 90.4-94.9 89.3-94.4 84.3-91.9 90.2-94.8 90.2-94.8 92.8-96.2 87.7-93.5 86.5-92.8 86.0-92.6 92.4-96.0 89.7-94.5
of soil water distribution
for experiment
that the distribution of soil water content can be represented function and are also presented in Table 2.
3.4. Influence
function vs. the empirical
of sample number on the observation
No. B 1.
by the normal distribution
accuracy
of soil water uniformity
The sample number of soil water content is of concern to researchers because a larger number of samples will be labor consuming but a smaller number of samples may lead to a low observation accuracy for soil moisture distribution. Fig. 3 presents several examples of the observed value of CU, as a function of the number of samples for the experiments conducted on Soil B. If one considers the 2 m by 2 m sampling grid to yield
92 9O-,,,,,,,fi,,,fi,” 4 6 8
10
12
14
16
18
20
‘22
Number of points Fig. 3. Observed
values of CLJ, as a function of sample number of soil water content.
J. Li. H. Kawano /Agricultural
Water Management
32 (1996) 29-36
35
the best estimation of the true distribution of water contents, it can be found that the increase of sampling interval (i.e. reduction in amount of data) results in an increased estimate for uniformity coefficient. As can also be seen in Fig. 3, the effect on the observed value of CU, of sample number becomes quite significant when the sample number is less than nine but this effect becomes insignificant as the number exceeds nine. Analyzing the influence of the number of samples on the observation accuracy of soil moisture distribution for the experiments conducted on Soil A, the same result was obtained. If the confidence limits of 95% of CU, (Table 2) are taken as a judgment criterion, the observed values of CU, are within their confidence limits as the sample number exceeds nine. It is therefore reasonable to conclude that the sample number of water content for evaluating soil water uniformity should not be less than nine for this study.
4. Conclusions The redistribution of water in the soil under varying uniformities of sprinkler irrigation was observed on two different soil types to investigate the effects of the irrigation variables on the area1 distribution of water content. The distribution of water in the soil after application can also be calculated by a two-dimensional model as used by Hart (1972). Model simulation has an advantage of investigating distribution of water under more initial and boundary conditions than field experiments but the validity of the model must be verified by field experiments. The following conclusions were supported by this study: (1) The water within the soil was more uniformly distributed than the surface-measured distribution of water. This conclusion is similar to Hart’s simulation result (1972), and our results from the field experiments confirmed and strengthened his data. (2) Improving extent of water redistribution in the soil is a function of many irrigation variables. All of those investigated in this study - initial soil water content and its uniformity, uniformity of sprinkler irrigation, total water applied and soil type were important. The uniformity of initial soil water content and the total water applied appear to be more important than the others. (3) A system designed using the current design criteria for sprinkler uniformity, such as, CU 2 75%, or CU 2 80%, may not be the most economical if the system is mainly aimed at producing desirable uniform soil moisture distribution. This conclusion may not necessarily apply to arid regions where the irrigation amount for an irrigation event is larger than in humid regions, thus a low uniformity may lead to an excessive deep percolation and ground water pollution. (4) The distribution of water in the soil under a wide range of sprinkler irrigation uniformities can be represented by a normal distribution function. (5) The influence of the number of samples of soil water content on the observation accuracy of soil moisture distribution is significant, especially when the number is less than nine. In order to guarantee the observation accuracy, the sample number should not be less than nine for this study. The heterogeneity of soil may affect the required sample number.
36
J. Li, H. Kawano/Agricultural
Wuter Management 32 (1996) 29-36
References Christiansen, J.E., 1941. The uniformity of application of water by sprinkler systems. Agric. Eng., 22: 89-92. Davis, J.R., 1963. Efficiency factors in sprinkler system design. Sprinkler Inig. Assn. Open Tech. Conf. Proc., pp. 13-50. Elliot, R.L., Nelson, J.D., Lofits, J.C. and Hart, W.E., 1980. Comparison of sprinkler uniformity models. J. Irrig. Dram. Eng., AXE, 106 (IR4): 321-330. Hart, W.E., 1961. Overhead irrigation pattern parameters. Agric. Eng., 42 (7): 354-355. Hart, W.E., 1972. Surface distribution of nonuniformly applied surface waters. Trans. ASAE, 5 (4): 656-661, 666. Heermamr, D.F., Duck, H.R., Serafim, A.M. and Dawson, L.J.. 1992. Distribution functions to represent center-pivot water distributions. Trans. ASAE, 35 (5): l&5- 1472. Hillel, D., 1971. Soil and Water - Physical Principles and Processes, Academic Press, NY. Kutilek, M. and Nielsen, D.R., 1994. Soil Hydrology. Cremlingen-Destedt, Calena-Verl. Marek, T.H., Undersander, D.J. and Ebeling, L.L., 1986. An areal-weighted uniformity coefficient for center-pivot irrigation systems. Trans. ASAE, 29 (61: 1665-1667. Shoji, S., Naniyo, M. and Dahlgren, R.A., 1993. Volcanic Ash Soil, Genesis, Properties and Utilization. Elsevier, Amsterdam. Wanick, A.W., 1983. Interrelationship of irrigation uniformity parameters. J. Irrig. Drain. Eng., ASCE, 109: 317-332.
Agricultural Water Management 32 (1996) 29-36
The area1 distribution of soil moisture under sprinkler irrigation Jiusheng Li aT*, Hiroshi Kawano b aDepartment of Hydraulic Engineering, Tsinghua University, Beijing 100084, Chinu b Faculty of Agriculture, Kagawa University, Kagawa 761-07, Japan
Accepted 29 April 1996
Abstract The area1 distributions of soil water content under varying uniformities of sprinkler water application were observed on two different soil types, to quantify the relationship between the subsurface distribution of soil moisture and water application on the ground surface. Field experimental results showed evidence of the importance of redistribution of the unevenly applied surface water. The water within the soil is more uniformly distributed than that applied through a sprinkler irrigation system. The extent of water redistribution within the soil profile depends mainly on the uniformity of initial soil water content and the total applied water. The distribution of water in the soil under a wide range of water application uniformities can be represented by a
normal distribution function. The analyses for the influence of the number of samples on observation accuracy of soil moisture uniformity indicated that the number should not be less than nine. Keywords: Sprinkler irrigation; Uniformity; Soil water content
1. Introduction Sprinkler irrigation tests commonly intercept the falling water with catch-cans on a horizontal surface, such as the ground. The mean application and the uniformity coefficient are computed for the area1 distribution of water. Extensive research has been made on the surface distribution of water from sprinklers (Christiansen, 1941; Hart, 1961; Elliot et al., 1980; Warrick, 1983; Marek et al., 1986; Heermann et al., 1992). However, the yield response of the crop is affected by the water within its root zone.
* Corresponding author. Fax: (10)259-5699. 0378-3774/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO378-3774(96)01261-9
30
J. Li, H. Kawano/Agriculturul
Water Management 32 (1996) 29-36
Therefore, the distribution of water within the soil is more important than its distribution on the soil surface. As early as 1963, Davis had indicated that the measured surface distribution is not a good indicator of yield (Davis, 1963). Hart (1972) studied the subsurface distribution of nonuniformly applied surface waters using a transient model and found that the water within the soil is more uniformly distributed than indicated by the initial surface-measured distribution. However, no field experiments were accompanied with his simulation. The objectives of this study were to quantify the relationship between the area1 distribution of soil moisture and the uniformity of water application, and to investigate the relative importance on the redistribution of water within the soil of the irrigation variables including initial water content and its uniformity, uniformity of water application, total applied water and soil type, by field experiments.
2. Field experiments The experiments were conducted on a volcanic ash soil (referred to as Soil A) with a bulk density of 0.74 g cmw3 and a saturated water content of 0.64 + 0.02 cm3 cmm3 (mean f standard deviation). The soil has a considerably high water holding capacity (Fig. 1). Shoji et al. (1993) fully described the properties of this soil type. For Soil A, four medium sprinklers were arranged in a 12 m by 12 m square spacings. The area enclosed by the four sprinklers was divided into 2 m square grids. A catch-can with 20 cm inside diameter was placed at the center of each grid to measure water application depth and uniformity. Soil water content for each grid was measured at a 10 cm depth and 20 cm apart from the can by an electrical resistance (gypsum block) method (Kutilek and Nielsen, 1994). Three replications were used for each measurement. The depth of 10 cm from the surface may represent the middle position of wetted depth for a normal irrigation amount in humid regions, such as Japan. The humid conditions would avoid salt accumulation by the substantial drainage at various times of the year because a rainfall event could usually be expected. In order to determine the initial soil water content and its distribution, water content for each grid was measured by the gypsum block method before the beginning of water application. Water content for each grid was
_. 0.0
0.2
0.4
0.6
Water content (cm3 / cm3) Fig.
I. Soil moisture characteristic
curves for Soils A and B.
J. Li, H. Kawano/Agricultural Table 1 A summary
of the experimental
conditions
Wuter Management 32 (1996) 29-36
and uniformity
coefficients
of water applications
AR (mm hh’)
No.
Soil A Al A2 A3 A4 A5 * A6 * A7 Soil B Bl B2 B3 B4 * B5
31
WC km3 cm- 3>
5.4 5.8 8.2 8.0 8.0
5.4 5.0 24.6 8.0 8.0 13.9 51.6
61 72 85 90 91 98 98
96 96 97 91 96 91 96
0.45 0.45 0.45 0.46 0.46 0.48 0.45
15.0 11.3 12.2 11.5
10.0 13.2 7.0 17.0 21.0
53 60 61 69 98
96 94 92 95 94
0.29 0.32 0.25 0.34 0.35
* Water was applied by rainfall events, others by sprinkler irrigation. AR: average application rate; TW: total water application; CU,,: initial uniformity of soil water content; and WC: initial soil water content.
also measured at different times after water application ceased, to investigate the redistribution of water within the soil. Seven experiments with the Christiansen uniformity coefficient (CU) from 61 to 98% (including two rainfall events) were conducted on Soil A. Field experiments were also conducted on a different texture of soil from Soil A. The soil was classified as a sandy loam (referred to as Soil B) according to the international classification standard (Hillel, 1971). The bulk density was 1.20 g cmm3 and the saturated water content was 0.40 + 0.03 cm3 cm-3 (mean f standard deviation). Fig. 1 also shows the soil moisture characteristic curve for Soil B. The arrangement and procedures for experiments conducted on Soil B were the same as those for Soil A except for sprinkler spacing and measuring method of soil water content. The sprinkler spacings were 6 m by 14 m and water content for each grid was sampled around the center of the grid by a 100 cm3 ring (a gravimetric method) at the depth of 7.5 to 12.5 cm (average 10 cm). Five experiments with CU ranging from 53 to 98% (including one rainfall event) were conducted (Table 1). All of the experiments were conducted on bare fields. The experimental conditions and the corresponding uniformities of water application are summarized in Table 1.
3. Results
and discussion
3.1. Uniformity
of soil water redistribution
The Christiansen
uniformity
coefficient
of soil water content (CU,)
is defined as:
(1)
J. Li, H. Kuwano/Agricultural
32
cu,=
[I- (;)t+,Nij]x
Water Management 32 (1996) 29-36
(2)
loo
where ei is the observed soil water content for the ith point, 8 is the mean of Bi, and N is the number of points. Fig. 2a and b present the uniformity of soil water content (CU,) as a function of time after water application ceased, for varying water application uniformities on Soils A and B, respectively. In both figures, the first point for each experiment represents the initial uniformity of soil water content. Water was much more uniformly distributed in the soil than that measured on the surface. The value of CU, still exceeded 90% even when the surface-measured water application uniformity (CU) was below 60%. Fig. 2a also indicates that CU, tends to decrease during the process of water application for Soil A. After water application ceased, CU, began to increase with time. The ultimate value of CU, appears to be around the initial uniformity of soil water content. 3.2. Effect of irrigation
variables
on water redistribution
3.2.1. EfSect of water application uniformity As can be seen in Fig. 2a and b, for different water application uniformities, CU, reached almost the same ultimate value after a reasonable time of redistribution. For Soil A, CU, approximated 97% after 24 h redistribution, the value of CU, approached 95% after a certain time of redistribution for Soil B. It is clear that the effect of water application uniformity is not as important as originally supposed. Even for a very low uniformity of CU of 53% (Fig. 2b, No. Bl), CU, had reached 95% after 4.5 h redistribution. This is a desirable value of uniformity being strived for in many commercial installations. When the uniformity of water application is higher, the maximum value of CU, might be reached sooner than the lower CU event, but this is not important. What is important, however, is that the maximum value of CU, might be equally high whether the value of CU is low or high. 3.2.2. Effect of initial soil moisture conditions and total water application We defined CU, max as the maximum value of CU, during the observed process of water redistribution. In order to analyze the effect of initial water content and its
Time after water Fig. 2. Uniformity
coefficient
applied
(min)
Time after water
of soil water content, CU,, as a function
applied
(min)
of time after water application
ceased.
J. Li, H. Kuwano / Agricultural
Water Management
32 (1996) 29-36
33
uniformity and total water application on CU, max, the relationship between CU, max and each of the factors was correlated, respectively. The regression equations with the coefficients of correlation (r2) for Soil B are as follows: CU, IIlax= 106.6wc0~”
( r2 = 0.743)
(3)
CU, max = 1 .6CUi,90 (r* = 0.513)
(4)
CU,nl,X = 86.5TW”.03
(5)
(r* = 0.757)
where WC is the initial soil water content (cm’ cmm3>, ranging from 0.25 to 0.35; CU,, is the initial uniformity of soil water content (%), ranging from 91 to 96%; and TW is total water application, ranging from 7 to 25 mm. Eqs. (3) to (5) indicate that CU, max increases with any of WC, CU,, and TW. The relationship between CU, max and initial soil water content and its uniformity and total water application was correlated to investigate the relative importance of the above mentioned factors to CU, max: CU, IIlax= 8.2WC”~01CU,q.52TWo.03 (I’ = 0.884)
(6)
Based on Eq. (6), sensitivity analysis was conducted showing that CU, max is more sensitive to initial uniformity of soil water content (CU,,) than to either initial water content (WC) or total water application (TW), but CU, max is more sensitive to TW than to WC. 3.3. Empirical function
to represent
the distribution
of water in the soil
Many researchers have studied the suitable function to represent the distribution of water application from stationary overlapped or center-pivot systems. Elliot et al. (1980) reported that a normal distribution was generally better than a uniform distribution for simulated solid sprinkler irrigation events. Heermamr et al. (1992) stated that the normal distribution was the best of the normal, log normal, uniform and specialized power for center pivot. However, the function to represent the distribution of water in the soil after infiltration under different uniformities of water application has not been reported. Therefore, we used the Kolmogorov-Smimov test to determine the adequacy of the fit of the soil water content data at the 10 cm depth after infiltration to the normal distribution. The non parametric test is expressed as: D+=maxlF,(x)
-F(x)
(7)
where D+ is the maximum deviation between the cumulative distribution and the empirical distribution; F, is cumulative distribution of normal distribution function, and F is empirical distribution of soil water content. Examples of the typical Kolmogorov-Smirnov test statistics for experiments conducted on Soil B are tabulated in Table 2. All of the tests can be described by the normal distribution at the 0.05 level. Thus, the normal distribution is a suitable function to represent the distribution of soil water content under a wide range of water application uniformities. The confidence limits of 95% of CU, were determined based on the fact
J. Li, H. Kuwurw/Agriculrurul
34
Wurer Management 32 (1996) 29-36
Table 2 The Kolmogorov-Smimov goodness of fit statistics for cumulative and the confidence limits of 95% for CU, No.
Bl-01 * Bl-02 Bl-03 B2-01 B2-02 B2-03 B3-01 B3-02 B4-01 B4-02 B4-03 B.5-01 B5-02
95.5 94.5 94.2 93.8 91.5 94.2 94.2 95.9 92.4 90.9 91.3 95.3 94.2
* No. B l-01 represents
distribution
Mean 3 (cm’ cm- 3,
D+
0.28 0.35 0.33 0.31 0.35 0.35 0.35 0.35 0.24 0.29 0.28 0.34 0.38
0.13 0.10 0.13 0.17 0.18 0.23 0.23 0.17 0.14 0.14 0.13 0.2 1 0.15
the first time measurement
Confidence
data
limit
(%I 92.2-95.9 90.3-94.9 90.4-94.9 89.3-94.4 84.3-91.9 90.2-94.8 90.2-94.8 92.8-96.2 87.7-93.5 86.5-92.8 86.0-92.6 92.4-96.0 89.7-94.5
of soil water distribution
for experiment
that the distribution of soil water content can be represented function and are also presented in Table 2.
3.4. Influence
function vs. the empirical
of sample number on the observation
No. B 1.
by the normal distribution
accuracy
of soil water uniformity
The sample number of soil water content is of concern to researchers because a larger number of samples will be labor consuming but a smaller number of samples may lead to a low observation accuracy for soil moisture distribution. Fig. 3 presents several examples of the observed value of CU, as a function of the number of samples for the experiments conducted on Soil B. If one considers the 2 m by 2 m sampling grid to yield
92 9O-,,,,,,,fi,,,fi,” 4 6 8
10
12
14
16
18
20
‘22
Number of points Fig. 3. Observed
values of CLJ, as a function of sample number of soil water content.
J. Li. H. Kawano /Agricultural
Water Management
32 (1996) 29-36
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the best estimation of the true distribution of water contents, it can be found that the increase of sampling interval (i.e. reduction in amount of data) results in an increased estimate for uniformity coefficient. As can also be seen in Fig. 3, the effect on the observed value of CU, of sample number becomes quite significant when the sample number is less than nine but this effect becomes insignificant as the number exceeds nine. Analyzing the influence of the number of samples on the observation accuracy of soil moisture distribution for the experiments conducted on Soil A, the same result was obtained. If the confidence limits of 95% of CU, (Table 2) are taken as a judgment criterion, the observed values of CU, are within their confidence limits as the sample number exceeds nine. It is therefore reasonable to conclude that the sample number of water content for evaluating soil water uniformity should not be less than nine for this study.
4. Conclusions The redistribution of water in the soil under varying uniformities of sprinkler irrigation was observed on two different soil types to investigate the effects of the irrigation variables on the area1 distribution of water content. The distribution of water in the soil after application can also be calculated by a two-dimensional model as used by Hart (1972). Model simulation has an advantage of investigating distribution of water under more initial and boundary conditions than field experiments but the validity of the model must be verified by field experiments. The following conclusions were supported by this study: (1) The water within the soil was more uniformly distributed than the surface-measured distribution of water. This conclusion is similar to Hart’s simulation result (1972), and our results from the field experiments confirmed and strengthened his data. (2) Improving extent of water redistribution in the soil is a function of many irrigation variables. All of those investigated in this study - initial soil water content and its uniformity, uniformity of sprinkler irrigation, total water applied and soil type were important. The uniformity of initial soil water content and the total water applied appear to be more important than the others. (3) A system designed using the current design criteria for sprinkler uniformity, such as, CU 2 75%, or CU 2 80%, may not be the most economical if the system is mainly aimed at producing desirable uniform soil moisture distribution. This conclusion may not necessarily apply to arid regions where the irrigation amount for an irrigation event is larger than in humid regions, thus a low uniformity may lead to an excessive deep percolation and ground water pollution. (4) The distribution of water in the soil under a wide range of sprinkler irrigation uniformities can be represented by a normal distribution function. (5) The influence of the number of samples of soil water content on the observation accuracy of soil moisture distribution is significant, especially when the number is less than nine. In order to guarantee the observation accuracy, the sample number should not be less than nine for this study. The heterogeneity of soil may affect the required sample number.
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References Christiansen, J.E., 1941. The uniformity of application of water by sprinkler systems. Agric. Eng., 22: 89-92. Davis, J.R., 1963. Efficiency factors in sprinkler system design. Sprinkler Inig. Assn. Open Tech. Conf. Proc., pp. 13-50. Elliot, R.L., Nelson, J.D., Lofits, J.C. and Hart, W.E., 1980. Comparison of sprinkler uniformity models. J. Irrig. Dram. Eng., AXE, 106 (IR4): 321-330. Hart, W.E., 1961. Overhead irrigation pattern parameters. Agric. Eng., 42 (7): 354-355. Hart, W.E., 1972. Surface distribution of nonuniformly applied surface waters. Trans. ASAE, 5 (4): 656-661, 666. Heermamr, D.F., Duck, H.R., Serafim, A.M. and Dawson, L.J.. 1992. Distribution functions to represent center-pivot water distributions. Trans. ASAE, 35 (5): l&5- 1472. Hillel, D., 1971. Soil and Water - Physical Principles and Processes, Academic Press, NY. Kutilek, M. and Nielsen, D.R., 1994. Soil Hydrology. Cremlingen-Destedt, Calena-Verl. Marek, T.H., Undersander, D.J. and Ebeling, L.L., 1986. An areal-weighted uniformity coefficient for center-pivot irrigation systems. Trans. ASAE, 29 (61: 1665-1667. Shoji, S., Naniyo, M. and Dahlgren, R.A., 1993. Volcanic Ash Soil, Genesis, Properties and Utilization. Elsevier, Amsterdam. Wanick, A.W., 1983. Interrelationship of irrigation uniformity parameters. J. Irrig. Drain. Eng., ASCE, 109: 317-332.