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Abstract

Crop yields may suffer from shallow water tables in the soil. The crop tolerance to shallow water tables can be found from a statistical analysis of field measurements. When shallow water tables affecting yield negatively prevails, one speaks of a water logging problem. The shallowest permissible depth at which no yield reduction occurs can be called critical water table depth and, it can serve as a drainage criterion The cases discussed here are a representation of what could be found in literature on the relation between crop yield and seasonal average depth of the water table (DWT) measured in farmers' fields. Such data are relatively scarce. Data collected in farmers' fields often show considerable scatter (random variation). One will need statistical methods to interpret the data relationships: Method 1. Visual estimates of envelope curves Method 2. Segmented regression Method 3. Partial regression Method 1. Visual estimates of envelope curves A first impression of the relation between depth of the water table and crop yield can be obtained using visually drawn envelope curves.
Crop yield and depth of water table, statistical analysis of data measured in
farm lands.
R.J. Oosterbaan, 18-08-2199
Abstract
Crop yields may suffer from shallow water tables in the soil. The crop tolerance to shallow
water tables can be found from a statistical analysis of field measurements. When shallow
water tables affecting yield negatively prevails, one speaks of a water logging problem.
The shallowest permissible depth at which no yield reduction occurs can be called critical
water table depth and, it can serve as a drainage criterion
The cases discussed here are a representation of what could be found in literature on the
relation between crop yield and seasonal average depth of the water table (DWT) measured in
farmers' fields. Such data are relatively scarce.
Data collected in farmers' fields often show considerable scatter (random variation). One will
need statistical methods to interpret the data relationships:
Method 1. Visual estimates of envelope curves
Method 2. Segmented regression
Method 3. Partial regression
Method 1. Visual estimates of envelope curves
A first impression of the relation between depth of the water table and crop yield can be
obtained using visually drawn envelope curves.
In the following examples the field data concerning the yield of crops versus the depth of the
water table were obtained as follows:
- Banana (data from Surinam), [Ref. 1]
- Cotton (data from Egypt), [Ref. 2]
- Sugarcane (data from Australia), [Ref.3]
- Winter wheat (data from England), [Ref. 4]
The envelopes are given in green color.
The banana plantations (banana is a perennial crop) investigated in Surinam show, in this envelope
analysis, a clear yield decline at an average depth of the water table (ADWT) < 0.75 m while at ADWT
values > 0.80 m there is no more yield reduction and the yield stays stable. This is the range of "no
effect". The critical value of ADWT may be estimated at 0.8 m.
The field measurements of cotton yield in the irrigated lands of the Nile Delta, Egypt, when analyzed
with envelope curves, show yield reductions at an average depth of the water table (ADWT) < 0.9 m
whereas above this level there is no more yield decline and the yield stays stable at its maximum. This
is the range of "no effect". The critical value of ADWT may be estimated in between 0.9 m for the
upper envelope and 1.2 m for the lower envelope, say 1.05 m.
Sugarcane is a crop that needs at least a 9-month growing season if not 1 year or more. The data,
interpreted with by envelopes, illustrate that an average depth of the water table (ADWT) < 0.60 m
causes yield reductions while there is no effect when ADWT > 0.80 m. The critical value of ADWT may
be estimated at 0.7 m.
In England, the winter wheat is sown before wintertime sets in. In winter it starts its vegetative
development, but maturation and harvest occur in summer. The water table depth (DWT) in summer is
usually deep enough not to pose a problem. However, in winter, shallow water tables and water
logging may occur, and the data, interpreted with envelopes illustrate that a DWT < 0.3 m during
winter causes yield reductions while there is no effect when DWT > 0.5 m. The critical value of DWT
may be estimated in between 0.3 m for the upper envelope and 0.5 m for the lower envelope, say 0.4
m
Method 2. Segmented regression
With segmented regression the breakpoint (BP) between the horizontal line and the downward
sloping line can be found by a numerical procedure, assuming a range of BP values doing a
linear regressions to the left and one to the right of the BP and taking care that the two lines
intersect each other in the BP, and finally selecting that BP value that produces the least sum
of squares of deviations of observed values from the regression lines (Least Squares or LS
method).
The software program SegRegA [Ref. 5] does such a kind of analysis and is used in the
following computations. The type of segmented analysis was taken as 4, as shown in the next
figure.
The results of SegRegA for the same crops as used in Method 1 are demonstrated below.
The breakpoint (BP) for banana is at ADWT= 0.85 m.
The breakpoint (BP) for cotton is at ADWT= 0.85 m. Owing to the large variation of the data
in vertical direction, the confidence interval of BP is quite wide.
The breakpoint (BP) for sugarcane is at ADWT= 0.65 m.
The breakpoint (BP) for winter wheat is at ADWT= 0.54 m. Owing to the large variation of
the data in vertical sense and the limited number of data to the right of BP, the confidence
interval of BP is quite wide. The winter wheat is grown in an area with water logging
problems as the majority of the data are to the left of BP. This is also the reason why the
variance analysis (ANOVA table) concludes that the Type 4 is statistically not significantly
different from a straightforward simple regression line and therefore not valid actually.
The use of SegReg entails the benefit of the confidence interval of BP, which, when wide,
gives a warning that its statistical significance is limited. Also the ANOVA table helps to
interpret the statistical significance of the results.
Method 3. Partial regression
Instead of using a regression model (in this case Type 4), that has a preconceived structure
with parameters that need to be optimized using the Least Squares (LS) principle, one can
also try to detect the longest range of X data over which there is no effect on the Y value. This
is call Partial Regression and can be performed using the PartReg program [Ref. 6]. PartReg
is not based on a model, and it has no parameters so that the LS method is not used. It simply
tries to detect a stretch of X data over which the best fitting line with the observed Y values
can be taken horizontal.
The results for the same crops as used in Method 1 and 2 are demonstrated below.
The breakpoint (BP) for banana is at ADWT= 0.65 m.
The breakpoint (BP) for cotton is at ADWT= 0.79 m.
The breakpoint (BP) for sugarcane is at ADWT= 0.58 m.
The breakpoint (BP) for winter wheat is at ADWT= 0.38 m.
Conclusions
The following table shows the critical depth of the water table (in m.) for the crops studied
and the methods used
Crop Method 1
(visual)
Method 2
(SegReg)
Method 3
(PartReg)
Banana 0.80 0.85 0.65
Cotton 1.05 0.85 0.79
Sugar cane 0.70 0.65 0.58
Winter wheat 0.40 0.54 0.38
The winter wheat is the most tolerant crop to shallow water tables and cotton the most
sensitive. Method 3 gives the shallowest water tables below which the crop yield declines. It
suggests the highest crop tolerance to shallow water tables. Also it demonstrates that the
regression line below the breakpoint (BP) not necessarily intersects the horizontal line
precisely at BP itself.
References
1. Lenselink, K.J. 1972. Drainage requirements for banana in the coastal plain (in Dutch, title
translated by author). In journal: De Surinaamse Landbouw, Vol. 20, pp. 22-36.
2. Nijland, H.J. and S. El Guindy 1984. Crop yields, soil salinity and water table depth
in the Nile Delta. In: ILRI Annual Report 1983, Wageningen, pp. 19-29. On line:
https://www.waterlog.info/pdf/egypt.pdf
3. Rudd, A.V. and C.W Chardon 1977. The effects of drainage on cane yields as measured by
water table height in the Machnade Mill area. In: Proceedings of the 44th Conference of the
Queensland Society of Sugar Cane Technology, Australia.
4. FDEU 1972. Annual Report. Field Drainage Experimental Unit, Ministry of Agriculture,
Cambridge, UK.
5. SegRegA, free software for segmented and other types of regression analyses. Download
from: https://www.waterlog.info/segreg.htm
6. PartReg2, free software for partial regression analysis to detect a horizontal segment in the
Y-X relation. Download from: https://www.waterlog.info/partreg.htm
List of publications in which SegReg is used:
https://www.waterlog.info/pdf/segreglist.pdf
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Book
The Drainage Research Institute in Cairo, Egypt, began in 1979 the Crash Program to acquire a rough quantitative insight into the effect of subsurface drainage on agricultural production in the Nile Delta. Since high watertables and soil salinities are the two main factors affected by drainage, they formed the basis of the study. Another important component was the assessment of agricultural production. The program was conducted on three sets of twin villages, one 'with' drainage, and the other 'without'. Attention was emphasized on five main crops: wheat, berseem, cotton, maize, and rice. This article discusses the relationship between crop yields, watertable depth, and soil salinity.
Drainage requirements for banana in the coastal plain (in Dutch, title translated by author)
  • K J Lenselink
Lenselink, K.J. 1972. Drainage requirements for banana in the coastal plain (in Dutch, title translated by author). In journal: De Surinaamse Landbouw, Vol. 20, pp. 22-36.
The effects of drainage on cane yields as measured by water table height in the Machnade Mill area
  • A V Rudd
  • C Chardon
Rudd, A.V. and C.W Chardon 1977. The effects of drainage on cane yields as measured by water table height in the Machnade Mill area. In: Proceedings of the 44th Conference of the Queensland Society of Sugar Cane Technology, Australia.