Dimitrios Papadopoulos

Statistical Substantiation of the Leaching Rates

In this book:

An attempt is made to substantiate the calculation of the leaching rates using methods of Mathematical Statistics and Mathematical Physics (the parabolic equation of movement of salt and water) taking into account the random nature of the distribution of salts in the under consideration area.

A short review of the existing methods and formulae for the calculation of the leaching rates as well as a solution of the equation of movement of salt and water in a limited layer are provided.

The effect of non-homogeneity of the distribution of salts by depth on the quantity of water needed is also shown.

The use of Mathematical Statistics is shown using data on salinity of a range of lands in Central Asia (Kzyl Orda, Bolshoi Asht, some sovkhozes in Golodnaya Steppe, Dzhizak). The data were provided by Research and Developments Institutes Rosgyprovodkhoz (Moscow) and Sredazgyprovodkhoz (Tashkent).

The question of the sample size during the subdivision of lands into homegeneous areas by soil properties is also discussed.

Technico-economical substantiation of the value of salt to be used for the calculation of the leaching rates is provided. For this purpose the economical loss due to under-leaching was compared with the increase of water expenses when a higher value of the salt content is used for the calculations.


The problem of salinity control in irrigated lands is a fairly old one. Academician A. F. Middendorf said in 1882: "Not weakly should the man retreat in front of abundance of salt in soil: salt easily leaves it by itself; too easily. With the help of water the man should utilise the beneficial salt for his purposes". V. V. Dokuchaev – one of the founders of the Soil Science in Russia – said in 1891: "Solonchaks are fearful to us only because we do not know how to handle them". The words of Professor N. A. Dimo (1913) sound very contemporary: "For a planned control of salinity it is necessary to control the water in the whole region, take into account the character of soil and the degree of the natural salinization, be able to remove the excess from the surface and from the deeper layers of soil; at every moment determine the level of salt content reached and project this onto the conditions and cultures for which measures of melioration of solonchaks and other saline soils are taken". As far back as 1882 the Zhilinsky expedition conducted leaching experiments in a solonchak field – the so-called Acheretinsk Yerik, and in 1915-1916 in Golodnaya Steppe. Starting approximately in 1928 in Uzbekistan and Azerbaijan where the salinity problem was especially acute, experimental stations (still functioning) were built

Currently because of the expansion into new regions on the primary saline lands and the existence of large areas with secondary salinity in irrigated lands, the problem of salinity control is even more urgent.

“According to the latest data saline soils occupy about 954 mln ha or more than 7% of dry land on earth. In Europe saline soils and soils potentially exposed to salinity occupy 51 million hectares, in Asia – 318 million hectares, in America – 147 million hectares, in Africa – 80 million hectares, in Australia and Oceania – 358 million hectares. In the [former] Soviet Union all kinds of saline soils and soils potentially exposed to salinity occupy 218 mln ha (V. V. Egorov), or about 10% of the territory. Solonchaks and solonchak-like soils occupy about 60 million hectares… Currently about half of the irrigated lands of the country is to some degree saline” (Plusnin, Golovanov 1983).

Content of salt in the soil above certain level has as a consequence the increase of osmotic potential of the soil solution which in its turn reduces the water supply to the plants and results in sickness or death of plants (Plusnin, Golovanov 1983). For example, the critical value of chlorine content in the top one meter of soil during the growth period for cotton is 0.04-0.05% (data SOYUZNIHI). In soils with even low salinity the vegetation period is delayed for 30-40 or more days; flowering and opening of cotton bolls are also significantly delayed. The productivity of cotton in the field Fedchenskoe is shown in the table below.

Table 1. Productivity of cotton by harvest
No 1 2 3 Total
Date 23/98/1029/10ц/га %
No salinity 7.459.6114.3031.40 100
Low salinity 3.683.44 7,8014.90 47.50
Medum salinity0 0 5.455.45 17.40

After leaching productivity increased from 1.7 t/ha (chlorine content in the 1 m layer –0.028%) to 3.81 t/ha (chlorine content 0.012%). Using Table 1 above we can build the table of productivity loss depending on the salt content:

Table 2. Productivity loss of cotton depending on the salt content
SalinityNo SalinityLow SalinityMedium Salinity
Loss of yield %05080

I. A. Gerardi proposes the following table of loss of yield for cotton:

Table 3. Productivity loss of cotton depending on the salt content by Gerardi
Very strong
Loss of yield %020-3040-6080100

Ryzhov has build the following graph for the conditions of Khorezm (Figure 1). The productivity falls from 3.1 t/ha to 1.7 t/ha when the concentration of the hard residue changes from 0.1% to 0.3% and from 1.7 t/ha to 1.1 t/ha when the concentration changes from 0.3% to 1.7%

Intro Graph 1
Figure 1 Productivity of cotton according to Ryzhov

We can see therefore that the productivity of cotton very strongly depends on the salt content and that even a small amount of salt noticeably reduces the yield. There are many different ways of melioration of lands (Kostyakov 1960, Plusnin, Golovanov 1983, Rozov and others), depending on the type of soil, character and kind of salinity etc. These include physical melioration (deep ploughing, deep subsoil knifing, sanding, etc), biological (use of farmyard manure, alfalfa), chemical (use of chemical substances to neutralize the free soda and replacement of absorbed Na with ions of Ca), electrical (processing of soil with direct current), and hydro-technical (leaching and drainage). Leaching and drainage, combined with other agro-technical, hydro-technical and organisational measures, are still the most successful methods of removal of salts for solonchaks (Plusnin, Golovanov 1983). Deep horizontal drainage allows demineralisation not only of the top layer of soil but also of the ground waters. Drainage most effectively solves the problem of managing and controlling water and salt regime of soil.

The importance of the ability to calculate the leaching rates is quite obvious. The first formula (in the USSR) was suggested in 1921 by N. Kostyakov. Later L. P. Rozov (1936), V. R. Volobuev (1948), V. M. Legostaev (1953) and other authors suggested their versions of the formula. In 1960 V. R. Volobuev introduced a new formula principally different from others in that it was based on the fact that the leaching rate consists of an amount of water saturating the soil and an additional amount displacing the water with dissolved salts. The formula was derived on the basis of generalization of the experimental data of many researchers and was a step forward compared with the other formulae because it excluded certain difficulties related to the determination of some of the participating parameters.

A new phase in the development of the theory of leaching started with the use of the apparatus of Mathematical Physics (Averyanov 1965, Averyanov 1960, Patrashev 1941, Reks 1969 etc]. The mathematical approach to the description of the processes of dissolution and transfer of salts allows the derivation of a differential equation whose solutions provide the ability to forecast the salt regime, calculate the leaching rates and some other parameters (Averyanov 1960, Golovanov 1971-1974 etc). Verification of the modelling of the movement of salts showed its validity for all practical purposes.

Quantitative analysis of the salinization is conducted on the basis of the salt sampling. Multiple determination of the salt content horizontally and vertically allows the use of the apparatus of Mathematical Statistics. The sampling should correctly reflect the properties of the area or, to use the statistical term, – correctly represent the properties of the general population. There are methods in Statistics that guarantee the representativeness of the sample. As is shown in a series of theorems such a method in a large enough sample is the randomness of selection when every element of the population has an equal to the others chance to be included in the sample.

Apparatus of Mathematical Statistics helps to resolve such important problems as

In 1969, the report of Research and Development of MHMI and in (Lab. Practicum 1970) the building of the curve of the initial salinization and calculation of the leaching rates on the example of the saline soils of Sovkhoz № 5 in Golodnaya Steppe is shown. In the report statistical properties and the distribution law was taken into account.

Research of V. Yu. Margulis (1969, 1971) also contributed to the infiltration of the ideas of Mathematical Statistics into the field of Reclamation of Lands.

In this thesis an attempt is made to substantiate the calculation of the leaching rates and prognosis of the water-salt regime in solonchaks using the methods of Mathematical Statistics and the equation of water and salt transfer taking into account the randomness of the distribution of salt in the under consideration region.

In Chapter 1:

In Chapter 2:

In Chapter 3:

Appendices 1-6 contain additional information on the source data, formulae for the determination of the leaching rates, the equation of movement of salt and water, some statistical tables

The main part of the work was completed in 1969-1972 during the PhD studies in the Department of Reclamation of Lands of the Moscow Hydro-Melioration Institute (currently Moscow State University of Environmental Engineering). Some of the results were used in contract work for various institutions.

The work was completed in 2002-2006 in Sydney Australia.

Source materials of the Research Institutes Sredazgyprovodkhlopok and Rosgyprovodhoz were used.

We express our deepest gratitude to:
Scientific supervisors – Doctor of Sciences, Academician S. F. Averyanov
and Doctor of Sciences, Academician A. I. Golovanov
as well as to Doctor of Sciences, Academician I. P. Aidarov
and Doctor of Sciences, Academician V. V. Shabanov for their support and advice on a number of issues