Effect of Bypass-Flow on Leaching of Salts in a Cracking Soil in the Nile Delta

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Article Effect of Bypass-Flow on Leaching of Salts in a Cracking Soil in the Nile Delta

Haruyuki Fujimaki * and Hassan Mohamed Fahmy Abd El Baki

Arid Land Research Center, Tottori University, Tottori 680-0001, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-857-21-7040; Fax: +81-857-29-6199

Abstract: Salinity is a major threat to the sustainability of irrigated agriculture in arid and semi-arid regions. Leaching is the primary measure for removing excess salts from the root zone, but not all water applied to the soil surface contributes to the removal of salts. In clayey soils, bypass flow along cracks can occur without being mixed with saline pore water in the matrix. To present a field dataset to quantitatively evaluate the contribution of bypass flow to the leaching of salts, soil sampling and monitoring of groundwater and discharge from a tile drain were carried out in farmland having a cracking soil in the Nile Delta. The electrical conductivities of 1:2 extracts were measured to evaluate the salinity of the soil. The first evidence for the occurrence of significant bypass flow through cracks was the salinity of the pore water, which was nearly triple that of the shallow groundwater and outflow from drainage. Second, the difference in root zone salinity before and after paddy rice cultivation was not significant. Third, the gradient of the groundwater table was very small. in spite of the low saturated hydraulic conductivity. Fourth, the salinity of the outflow from the tile drain dropped just after irrigation or rain. These results indicated that bypass flow through cracks played a significant role in the drainage process in the soil, and that nearly half of the water bypasses through cracks in the field with a cracking soil. Keywords: salinity stress; solute transport; preferential flow; drainage Citation: Fujimaki, H.; Abd El Baki, H.M.F. Effect of Bypass-Flow on Leaching of Salts in a Cracking Soil in the Nile Delta. Water 2021, 13, 993. 1. Introduction https://doi.org/10.3390/w13070993 Since the dawn of civilization, salinity has been a major threat to the sustainability of irrigated agriculture in arid and semi-arid regions. For example, Alexakis et al. [1] assessed Academic Editor: Francesco Fiorillo the soil salinization in western Greece and found that the soil salinity is mainly controlled by seawater intrusion or other factors such as the application of salt-rich drainage water [2]. To Received: 5 March 2021 remove excess salts from the root zone to mitigate the salinity hazard, more water than that Accepted: 2 April 2021 Published: 4 April 2021 required to meet crop evapotranspiration is periodically applied [3]. Such an intentional “over-irrigation” is called leaching, which has been the primary measure and widely

Publisher’s Note: MDPI stays neutral practiced for salinity control. A guideline for calculating leaching requirements, how much with regard to jurisdictional claims in water should be applied for leaching, was presented by Food and Agriculture Organization published maps and institutional affil- (FAO) irrigation and drainage paper 29. However, not all water applied to the soil surface iations. contributes to removing salts. In clayey soils, bypass flow along cracks formed with drying and shrinking can occur without being mixed with saline pore water in the matrix. FAO paper 29 recommends breaking cracks by tillage and applying water intermittently to reduce bypass flow. However, no procedure to determine the additional water required to compensate the bypass flow has been presented. Recently, Minhass et al. [4] reviewed Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. recent developments in salinity management studies but did not refer to the matter of This article is an open access article bypass flow. The lack of field data and quantitative evaluation of the contribution of bypass distributed under the terms and flow may account for the inadequate guidelines and undervaluing of this problem. Surface conditions of the Creative Commons irrigation is still dominant in developing countries, and leaching is usually carried out Attribution (CC BY) license (https:// under continuous ponding [5]. creativecommons.org/licenses/by/ Oster et al. [6] compared three methods of leaching: continuous ponding, intermittent 4.0/). ponding, and sprinkler, and noted that the lower leaching efficiency of continuous ponding

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Water 2021, 13, 993 Oster et al. [6] compared three methods of leaching: continuous ponding, intermit- 2 of 11 tent ponding, and sprinkler, and noted that the lower leaching efficiency of continuous ponding is attributable to bypass flow in cracks and macropores. Moreno et al. [7] reported a 10 times largeris attributable apparent to intake bypass rate flow for in ground cracks and with macropores. cracks than Moreno a matrix et al.in [Las7] reported a 10 times Marismas, Spain, largerand recommended apparent intake a shorter rate for irrigation ground with interval cracks and than lower a matrix input in each Las Marismas, Spain, time. Corwin et al.and [8] recommendedcarried out a lysimeter a shorter experiment irrigation interval and noted and lowerthat the input effect each of time.by- Corwin et al. [8] pass flow was smallcarried because out it aoccurs lysimeter only experimentin the top 30 and cm, notedalthough that most the effectwater ofis taken bypass flow was small up by the annual irrigatedbecause itcrop occurss from only the in top the 30 top cm. 30 Still, cm, althoughthere is a mostlack of water fieldis data taken to up by the annual quantitatively evaluateirrigated how crops much from additional the top water 30 cm. is needed Still, there to attain is a the lack target of field salinity data to quantitatively in the root zone. evaluate how much additional water is needed to attain the target salinity in the root zone. The objective of thisThe study objective was, therefore, of this study to present was, therefore, a field dataset to present from a cracking field dataset soil from cracking soil in the Nile Delta toin quantitatively the Nile Delta evaluate to quantitatively the contribution evaluate of the bypass contribution flow in the of bypassleaching flow in the leaching of salts. of salts.

2. Materials and Methods2. Materials and Methods ◦ The field observationThe field was observation carried out was in carried an experimental out in an experimental farmland in farmland Sakha in(31° Sakha (31 05’53.9” N, ◦ 05’53.9” N, 30°55’19.130 55’19.1”” E), Egypt, E), Egypt,which was which managed was managed by the Agricultural by the Agricultural Research Research Cen- Center of Egypt ter of Egypt (Figure(Figure 1). The1). field The fieldwas under was under a series a series of cropping of cropping experiment experimentss to evaluate to evaluate actual evap- actual evapotranspirationotranspiration rates from rates a fromsurface a surface irrigated irrigated field using field the using eddy the correlation eddy correlation method [9]. method [9]. CultivatedCultivated crops cropsand periods and periods are listed are listedin Table in Table 1. All1 .crops All crops were were irrigated irrigated with surface with surface irrigation.irrigation. The electrical The electrical conductivity conductivity of the of irrigation the irrigation water water fluctuated fluctuated be- between 0.4 and −1 tween 0.4 and 0.5 dS0.5 m dS−1.m .

Figure 1. LocationFigure 1. ofLocation the study of thesite. study Area site.painted Area green painted represents green represents farmland farmlandand cities. and cities.

Table 1. Cultivation recordThe of the farmland farmland. had tile drainage pipes, whose inner diameter, depth, and length were Period approximately 0.072, 1.5,Crop and 50 m, respectively.Irrigation No envelope Method material was used for the tile drainage pipes. Nine observation wells were installed to monitor the groundwater 2011/2012 winter Wheat Basin level and EC at an equal spacing of 6.25 m along a line perpendicular to the tile drains, 2012 summer Rice Basin as illustrated in Figure2. Groundwater level was measured using a water level meter 2012/2013 winter(Yamayo, WL10M, Tokyo,Wheat Japan). Basin

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2013 summer Maize Furrow Water 2021, 13, 993 3 of 11 2013/2014 winter Sugarbeet Furrow 2014 summer Rice Basin

The farmlandTable had 1. Cultivation tile drainage record pipes of the, whose farmland. inner diameter, depth, and length were approximately 0.072, 1.5, and 50 m, respectively. No envelope material was used for the Period Crop Irrigation Method tile drainage pipes. Nine observation wells were installed to monitor the groundwater level and EC at an equal2011/2012 spacing winter of 6.25 m along a line perpendicular Wheat to the tile drains Basin, as 2012 summer Rice Basin illustrated in Figure 2012/20132. Groundwater winter level was measured Wheat using a water level meter (Ya- Basin mayo, WL10M, Tokyo,2013 Japan summer). Maize Furrow On 18 April 2012,2013/2014 23 April winter 2014, and 20 October 2014 Sugarbeet soil samples were taken to Furrow obtain soil salinity profiles.2014 The summer first sampling was carried Rice out at two randomly selected Basin locations, while the others were taken at certain intervals from the lateral drains.

Figure 2. Structure of lateral and collector drains. Monitoring of discharge was carried out in man- Figure 2. Structure of lateral and collector drains. Monitoring of discharge was carried out in manhole 1. Orange lines hole 1. Orange lines represent roads. represent roads.

The electrical conductivityOn 18 April 2012, (EC) 23of April(soil-to 2014,-water and ratio 20 October) 1:2 suspension 2014 soil was samples measured, were taken to obtain and pore watersoil EC salinity was calculated profiles. Theusing first the sampling gravimetrically was carried measured out at twovolumetric randomly water selected locations, content [10]. Assumingwhile the othersno dissolution were taken of low at certain solubility intervals salts nor from desorption the lateral occurs drains. by dilution, and a linearThe relationship electrical between conductivity concentration (EC) of (soil-to-water and EC, pore ratio) water 1:2 conductivity, suspension was measured, sw (dS m−1), canand be pore calculated water ECas was calculated using the gravimetrically measured volumetric water content [10]. Assuming no dissolution of low solubility salts nor desorption occurs by Nρb dilution, and a linear relationshipsw = betweenS concentration and EC, pore water(1) conductivity, −1 θρw σsw (dS m ), can be calculated as where N is the dilution factor (in case of 1:2 method, N = 2), b is bulk density (Mg m−3),  Nρ w −3 b S is volumetric water content, is density of water (Mgσsw m=), andσ S is EC of the suspension (1) (dS m−1). θρw EC was measured with an EC meter (Horiba, B-173, Kyoto, Japan), and calibration where N is the dilution factor (in case of 1:2 method, N = 2), ρ is bulk density (Mg m−3), θ using 1 M KCl solution was carried out just before each measurement. b is volumetric water content, ρ is density of water (Mg m−3), and σ is EC of the suspension There were manholes for maintenancew work at every three lateral tile drainageS pipes (dS m−1). along the collector drainage pipe. To observe the discharge rate from the lateral pipes, we EC was measured with an EC meter (Horiba, B-173, Kyoto, Japan), and calibration installed a PVC pipe with 50 cm length and 2.5 cm diameter into a manhole, so that water using 1 M KCl solution was carried out just before each measurement. outflowed or inflowThereed through were manholes the pipe,for as maintenanceillustrated in workFigure at 3. every Pressure three in lateral the lateral tile drainage pipes pipe was measuredalong thewith collector a water drainage level sensor pipe. (Senses, To observe JW8000 the discharge-02M, Tokyo, rate fromJapan the), and lateral pipes, we water level in theinstalled manhole a PVC was pipe also with monitored. 50 cm length Assuming and 2.5that cm head diameter losses intoat the a manhole,inlet and so that water outlet were negligible,outflowed discharge or inflowed rate, through Q (m/s), the was pipe, calculated as illustrated using inthe Figure Hazen3.– PressureWilliam in the lateral Equation [11]:pipe was measured with a water level sensor (Senses, JW8000-02M, Tokyo, Japan), and water level in the manhole was also monitored. Assuming that head losses at the inlet and 10.67l 0.54 outlet were negligible,Q = dischargeC [ rate, Q (m/s),] was calculated using the(2) Hazen–William H 4.87( ) Equation [11]: D hi − ho " #0.54 10.67l = Q CH 4.87 (2) D (hi − ho)

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wwherehere CCHH isis the the Hazen Hazen–William–William coefﬁcient,coefficient,l isl is length length of theof the pipe pipe (m), (m),D is D diameter is diameter (m) of the pipe, h and h are the pressure head at the inlet and outlet of the pipe (m), respectively. (m) of the pipe,i hi oand ho are the pressure head at the inlet and outlet of the pipe (m), respectively.When water When level inwater the manholelevel in the was manhole lower than was thelower outlet than of the the outlet PVC pipe,of theh PVCo was pipe, set at 0. A value of 130 for C of the PVC pipe was used. EC of the discharged water was also ho was set at 0. A valueH of 130 for CH of the PVC pipe was used. EC of the discharged watermonitored was also using monit anored EC sensor using (ES-2,an EC METER,sensor (ES Pullman,-2, METER WA,, Pullman, USA) WA, USA)

FigureFigure 3. 3.SetupSetup for for monitoring monitoring discharge discharge rate rate from from the the lateral lateral tile tile drainage drainage pipe. pipe. 3. Results and Discussion 3. Results and Discussion 3.1. Salinity of Soil Solution 3.1. Salinity of Soil Solution Profiles of soil moisture and salinity under wheat cultivation are shown in Figure4. BothProfiles profiles of showedsoil moisture a slightly and decreasingsalinity under EC wheat of the soilcultivation solution are with shown depth. in Figure The EC 4. of Bothsoil profiles solution showed (pore water a slightly EC) was decreasing nearly 10 EC times of thatthe soil of the solution irrigation with water, depth. which The impliedEC of soila low solution effective (pore leaching water fraction,EC) was butnearly still 10 lower times than that the of threshold the irrigation value water, of yield which reduction im- plieford wheata low [3effective]. According leaching to FAO fractio 29 [n,3], but the still yield lower of wheat than reduces the threshold from its value potential of yield value reductionif average for pore wheat water [3]. conductivity According to is FAO higher 29 than[3], the 12 dSyield m− of1, wheat owing reduces to salinity from stress. its potential Ricevalue is if widelyaverage cultivated pore water in conductivity nearly half is of higher farmlands than 12 in dS the m summer−1, owing into salinity the Nile stress.Delta [12,13]. Owing to its large water requirement, the Egyptian government has tried to restrict rice cultivation. However, continuous ponding may have a side effect of the enhancement of leaching salts [13]. Therefore, soil samples before and after rice cultivation were taken in 2014. Figure5 shows the profiles of pore water EC before transplanting of rice (at the end of sugarbeet cropping).

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Figure 4. 4. PoresPores of ofwater water content content and andsalinity salinity on 18 on April 18 April2012. 2012.

Rice is widely cultivated in nearly half of farmlands in the summer in the Nile Delta [12,13]. Owing to its large water requirement, the Egyptian government has tried to restrict rice cultivation. However, continuous ponding may have a side effect of the enhancement of leaching salts [13]. Therefore, soil samples before and after rice cultivation were taken in 2014. Figure 5 shows the profiles of pore water EC before transplanting of rice (at the end of sugarbeet cropping).

Figure 5. Profiles of pore water salinity at different distances from the lateral under sugar beet Figure 5. Profiles of pore water salinity at different distances from the lateral under sugar beet cropping (23 April 2014). cropping (23 April 2014). To investigate whether there was significant difference in salinity at different distances To investigate whether there was significant difference in salinity at different dis- tanceto thes to lateral, the lateral, soil soil sampling sampling was was carried carried outout at at five five locations locations,, with with equal equal spacing spacing (10 (10 m) m)between between the the lateral. lateral. The profiles profiles labeled labeled 1 and 1 and 5 were 5 were taken taken above abovethe laterals. the laterals. Except Except for the the soil soil surface surface,, where where salt accumulation salt accumulation driven drivenby evaporation by evaporation occurred betwee occurredn ir- between rigation,irrigation, the thepore pore water water EC was EC fairly was uniform fairly uniform and close and to that close of Figure to that 4. of Profiles Figure of4 .the Profiles of

salinitythe salinity of soil of solution soil solution after rice after cultivation rice cultivation are shown are shownin Figure in 6. Figure Since6 no. Since significant no signiﬁcant effect of of the the distance distance to tolaterals laterals was was found found in Figure in Figure 5, samplin5, samplingsgs were carried were carriedout at just out at just two location locations:s: above above the the lateral lateral andand intermediate intermediate between between two. two.

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Figure 6. Profiles of pore water salinity at different distances from the lateral after rice cultivation Figure 6. Profiles of pore water salinity at different distances from the lateral after rice cultivation (20(20 October October 2014). 2014). σ ByBy using using the the relationship relationship between between EC a ECnd total and dissolved total dissolved solids, solids,sw can besw convertedcan be converted toto concentration. concentration. By By integrating integrating the the product product of volumetric of volumetric water water content content and concentra- and concentration − tionacross across soil soil profile, profile, stored stored salts salts aboveabove a certain certain depth depth can can be beobtained. obtained. EC (dS EC m (dS−1) can m 1) can be beconverted converted to to concentration concentration of of salts salts (or (or “total “total dissolved dissolved solids”) solids”) (g L (g−1) Lby− 1multiplying) by multiplying by bya factora factor of of 0.64 0.64 [[3].3]. Stored Stored salts salts above above the thedepth depth of 80 ofcm 80 before cm before and after and rice after cultivation rice cultivation werewere 64 64 and and 63 63 mg mg cm cm−2, −respectively.2, respectively. Even Evenafter nearly after nearly continuous continuous ponding ponding during rice during rice cultivation,cultivation, salinity salinity did did not notsignificantly significantly decrease. decrease. These Theseresults resultsindicate indicate that a significant that a significant partpart of of the the infiltrated infiltrated water water may have may bypassed have bypassed through throughcracks without cracks flowing without into flowingthe into soil matrix. The soil was characterized by a low saturated hydraulic conductivity (1.4 cm the soil matrix. The soil was characterized by a low saturated hydraulic conductivity d−1 [13]) for disturbed, repacked soil samples, and by swelling-and-shrinking, responding (1.4 cm d−1 [13]) for disturbed, repacked soil samples, and by swelling-and-shrinking, to changes in water content. Kubota et al. (2017) observed a 12% soil depression (i.e., 36% decreaseresponding in volume) to changes using in a water depression content. gauge, Kubota which et occurred al. (2017) in observed the top 20 a 12%cm in soil May depression 2014(i.e., for 36% the decrease soil [13]. Okuda in volume) et al. [14] using investigated a depression the effect gauge, of leaching which occurred carried out in twice the top 20 cm duringin May the 2014 winter for in the Uzbekistan soil [13]. and Okuda reported et al. that [14 even] investigated after 310 mm the of effectleaching of leachingand 127 carried mmout of twice rain, during which may the winterbe nearly in one Uzbekistan pore volume and down reported to 80 that cm, even75% of after salts 310 remained mm of leaching inand top127 100 mmcm. Thisof rain, may also which indicate may the be difficulty nearly one of leaching pore volume by ponding down for to fine 80 textured cm, 75% of salts soilremaineds. in top 100 cm. This may also indicate the difficulty of leaching by ponding for fine textured soils.

3.2. Change in Depth and EC of Groundwater The temporal change in ground water depth is shown in Figure7. Regardless of distance from the laterals, the ground water level was nearly synchronized and quite uniform. This clearly violates the assumption of homogeneity often used in numerical simulations of water ﬂow and solute transport in soils. The most simpliﬁed prediction of the depth of a groundwater table would be Hooghout’s steady-state solution [14]: r q 2 h = h0 + (Sx − x ) (3) Ks

−1 where h is ground water level (m), q is groundwater recharge rate (m d ), Ks is saturated − hydraulic conductivity (m d 1), S is spacing of the lateral drain (m), x is distance from lateral drain (m), and h0 is h at x = 0. Water 2021, 13, x FOR PEER REVIEW 8 of 12

3.2. Change in Depth and EC of Groundwater The temporal change in ground water depth is shown in Figure 7. Regardless of distance from the laterals, the ground water level was nearly synchronized and quite uniform. This clearly violates the assumption of homogeneity often used in numerical simulations of water flow and solute transport in soils. The most simplified prediction of the depth of a groundwater table would be Hooghout’s steady-state solution [14]:

q 2 h = h0 + √ (Sx − x ) (3) Ks

−1 where h is ground water level (m), q is groundwater recharge rate (m d ), Ks is satu- Water 2021, 13, 993 7 of 11 rated hydraulic conductivity (m d−1), S is spacing of the lateral drain (m), x is distance from lateral drain (m), and h0 is h at x = 0.

Figure 7. Changes in the groundwater depth. Figure 7. Changes in the groundwater depth. Figure8 shows the distribution of groundwater depth calculated using Equation (3) at q Figure= 0.0005 8 shows m/d, the which distribution is a typical of groundwater drainage rate depth under calculated the recommended using Equation leaching (3) at q = 0.0005 m/d, which is a typical drainage rate under the recommended leaching frac- fraction of 0.15–0.2 [3] and measured Ks. As much as 1 m of difference in ground water tion of 0.15–0.2 [3] and measured K . As much as 1 m of difference in ground water depth depth should occur if the soil weres homogeneous, but in reality only a one-tenth difference should occur if the soil were homogeneous, but in reality only a one-tenth difference be- between the highest and the lowest levels occurred in the field. This large discrepancy Water 2021, 13, x FOR PEER REVIEWtween the highest and the lowest levels occurred in the field. This large discrepancy9 of is 12 is another piece of evidence that bypass flow caused by cracks plays a dominant role in another piece of evidence that bypass flow caused by cracks plays a dominant role in groundwater flow in cracking soils. groundwater flow in cracking soils.

−1 −1 Figure 8. Ground water level calculated by Hooghoudt Equation (q = 0.05 mm d−1 , K = 1.4 cm d ). Figure 8. Ground water level calculated by Hooghoudt Equation (q = 0.05 mm d , Ks =s 1.4 cm d−1) Changes in the EC of groundwater at each observation well is shown in Figure9. ExceptChanges for the in EC the at EC No.6 of groundwater on 12 April, at EC each values observation were fairly well uniform is shown and in Figure stable. 9. The averageExcept for value the EC on 18at No.6 April, on when 12 April, soil samplingEC values waswere also fairly carried uniform out and asshown stable. inThe Figure av- 4, waserage 1.6, value which on 18 was April nearly, when one-third soil sampling of that was of the also pore carried water. out This as shown large differencein Figure 4, was alsowas attributable1.6, which was to thenearly dominance one-third of of bypass that of ﬂow. the pore water. This large difference was also attributable to the dominance of bypass flow.

Figure 9. Changes in the EC of groundwater in each observation well.

3.3. Discharge Rate and EC of Outflow from the Lateral Drain The discharge rate calculated with Equation (2) and divided by the collecting area is shown in Figure 10. Discharge started quickly, just after irrigation. Sometimes inverse flow into the lateral drain occurred because the water level in the manholes often sharply rose, owing to inflow through the collector pipe into the manhole. This complicated motion may have been caused by larger-scale bypass flow and/or non-uniform application of water. Figure 10 also shows the EC of outflow from the lateral drain, which tended to drop immediately after irrigation or rain events and recovered to a steady value of around

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−1 Figure 8. Ground water level calculated by Hooghoudt Equation (q = 0.05 mm d , Ks = 1.4 cm d−1)

Changes in the EC of groundwater at each observation well is shown in Figure 9. Except for the EC at No.6 on 12 April, EC values were fairly uniform and stable. The average value on 18 April, when soil sampling was also carried out as shown in Figure 4, Water 2021, 13, 993 8 of 11 was 1.6, which was nearly one-third of that of the pore water. This large difference was also attributable to the dominance of bypass flow.

FigureFigure 9. ChangesChanges in in the the EC EC of groundwater of groundwater in each in eachobservation observation well. well.

3.3.3.3. Discharge Rate Rate and and EC EC of Outflow of Outflow from from the Lateral the Lateral Drain Drain The d dischargeischarge rate rate calculated calculated with with Equation Equation (2) and (2) divided and divided by the bycollecting the collecting area is area is shownshown in Figure 10.10. Discharge Discharge started started quickly quickly,, just just after after irrigation. irrigation. Sometimes Sometimes inverse inverse flow intoflow theinto lateral the lateral drain drain occurred occurred because because the the water water level in in the the manholes manholes often often sharply sharply rose, owingrose, owing to inflow to inflow through through the the collector collector pipepipe into the the manhole manhole.. This This complicated complicated mo- motion maytion may have have been be causeden caused by by larger-scale larger-scale bypassbypass flow flow and/or and/or non non-uniform-uniform application application of Water 2021, 13, x FOR PEER REVIEW 10 of 12 water.of water. Figure Figure 10 10 also also shows shows the the ECEC ofof outflowoutflow from from the the lateral lateral drain, drain, which which tended tended to to drop immediatelydrop immediately after after irrigation irrigation or or rain rain events events andand recovered recovered to to a steady a steady value value of around of around 1.8. This implies that the bypass flow having low EC came first, followed by flow through the 1.8. This implies that the bypass flow having low EC came first, followed by flow through matrix.the matrix. Zero Zero EC EC values values occurred occurred whenwhen waterwater level level inside inside the the lateral lateral pipe pipe was was lower lower than

thethan electrode the electrode of the of the sensor. sensor.

Figure 10. 10. TimeTime variation variation of discharge of discharge rate from rate fromthe tile the drain, tile EC drain, of discharge EC of discharge,, and water and level water in level in thethe manhole. manhole. 3.4. Estimation of the Contribution of Bypass Flow All the results presented above\ clearly indicate that bypass flow played a significant role. Although it is difficult to parameterize the contribution of bypass flow in each field, we present a simple way for evaluating the magnitude of the contribution of bypass flow over entire water flow. As depicted in Figure 11, the drainage water or near-surface ground water is a mixture of matrix and bypass flow.

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1.8. This implies that the bypass flow having low EC came first, followed by flow through the matrix. Zero EC values occurred when water level inside the lateral pipe was lower than the electrode of the sensor.

Water 2021, 13, 993 9 of 11 Figure 10. Time variation of discharge rate from the tile drain, EC of discharge, and water level in the manhole.

3.4. Estimation Estimation of the Contribution of Bypass Flow All the results results presented presented above above\\ clearlyclearly indicateindicate thatthat bypass flowflow playedplayed a significant significant role. Although Although it it is is difficult difficult to parameterize the the contribution contribution of of bypass bypass flow flow in in each each field, field, we present a simple way for evaluating the magnitude of the contribution of bypass flow flow over entire entire water water flow. flow. As As depicted depicted in Figure in Figure 11, the 11, drainage the drain waterage or water near-surface or near- groundsurface groundwater is water a mixture is a mixture of matrix of and matrix bypass and flow.bypass flow.

Figure 11. Schematic of the concept of idealized bypass ﬂow which does not receive salts from the matrix.

Thus, assuming that water ﬂowing through cracks does not receive salts in micropores,

the total salt load to drainage, qdcd, would be given as a sum of that through the matrix, qscs, and that through bypass ﬂow, (qd − qs)ci:

qdcd = qscs + (qd − qs)ci (4)

where qd is groundwater recharge rate, cd is the concentration of drainage water, qs is groundwater recharge rate through matrix, cs is the concentration of soil water at the bottom of the root zone, and ci is the concentration of irrigation water. Rearranging Equation (4) gives q − q c − c σ − σ d s = d s ≈ d s (5) qd ci − cs σi − σs where σ is electrical conductivity, and subscripts are the same as c. Substituting the values of σd = 1.8, σi = 0.45, and σs = 3.5 into Equation (5) gives a value of 0.55 as the contribution factor of bypass ﬂow. We may state that nearly half of water bypasses through cracks in the ﬁeld with a cracking soil. In other words, nearly double the water is required to meet leaching requirements.

3.5. Reducing Bypass Flow As instructed in FAO 29, breaking cracks by tillage and applying water intermittently may reduce bypass flow. Surge flow irrigation may be regarded as a technique for intermittent ponding [15]. Sprinkler and drip irrigation methods may completely prevent bypass flow if irrigation intensity is restricted below the intake rate of the soil. To evaluate the effectiveness of these measures, leaching efficiency should be defined. As leaching is not necessarily carried out as a single event, and rather, frequently carried out under modern Water 2021, 13, 993 10 of 11

and precise management schemes, it is not easy to define leaching efficiency. Still, we would suggest the following equation for leaching efficiency, eL: Z 1 Eci eL = dt (6) t qicc

−1 where E is evapotranspiration rate (m d ), cc is the concentration of the most critical −1 location in the root zone, and qi is irrigation intensity (m d ). If qi and cc were the same as ci and E, respectively, eL would be unity (100%), which is theoretically impossible in reality. Still, by minimizing bypass ﬂow, we may enhance eL, just as we should do our best to maximize application efﬁciency and irrigation uniformity, although attaining 100% is physically impossible. Recent advances in soil moisture and salinity probes have enabled such evaluations.

4. Conclusions The nearly triple EC of pore water compared to shallow groundwater and outflow from drainage, the non-significant difference in root zone salinity before and after paddy rice cultivation, the too-small gradient of the groundwater table for its saturated hydraulic conductivity, and the drop in the EC of outflow from the tile drain just after irrigation or rain indicate that bypass flow through cracks played a significant role in the drainage process in a cracking soil in the Nile Delta. A simple analysis indicated that nearly half of the water bypasses through cracks in a field with cracking soil. Further studies to evaluate the leaching efficiency of various methods under cracking soil are required.

Author Contributions: Conceptualization, H.F.; methodology, H.F. and H.M.F.A.E.B.; validation, H.F. writing—original draft preparation, H.F.; writing—review and editing, H.M.F.A.E.B.; All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by Japan International Cooperation Agency and Japan Society for the Promotion of Science [grant name SATREPS “Sustainable Systems for Food and Bio-energy Production with Water saving Irrigation in the Egyptian Nile Basin”]. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are openly available in [http://www. alrc.tottori-u.ac.jp/fujimaki/data/egypt/drainage]. Acknowledgments: The authors are grateful to S. Yoshida (University of Tokyo) for providing us the shrinkage characteristic of the soil; Y. Kitamura for his advices for methodology of monitoring; Waleed Abou El Hassan (FAO) for his support in the field monitoring. Finally, the authors also express their deep appreciation to M. Satoh (University of Tsukuba) for his leadership in the project. Conflicts of Interest: The authors declare no conflict of interest.

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