ReseaRch PaPeR Journal of Agricultural and Marine Sciences Vol. 22 (1): 8-17 DOI: 10.24200/jams.vol22iss1pp8-17 Received 15 May 2016 Accepted 19 Feb 2017 Moisture and temperature in a proppant-enveloped silt block of a recharge dam reservoir: Laboratory experiment and 1-D mathematical modelling Anvar Kacimov1 , Ali Al-Maktoumi*, Said Al-Ismaily1, and Hamed Al-Busaidi1 * 1 Ali Al-Maktoumi ( ) , Sultan Qaboos University, College of Agri- cultural and Marine Sciences, Dpt. of Soils Water and Agricultural En- gineering. Box 34, Al-Khod 123. Sultanate of Oman. Email: ali4530@ squ.edu.om Introduction Layering, i.e. vertical alternation of textures with distinct interfaces between layers, is the backbone of soil sciences in applications to agronomy and ecohydrology (see e.g. Connolly, 1998, Noy-Meir, 1973). In soil physics, water upward-downward fluxes (evapo- ration-infiltration-redistribution) are usually considered as 1-D steady or transient phenomena, with effective wa- ter conductance-capillarity properties derived by con- jugation of individual layers of the soil profile (see e.g., Assouline et al., 2014, Fehmi and Kong, 2012, Gardner and Fireman 1958, Hillel and Talpaz, 1977, Khan, 1988, Ripple et al., 1970, Willis, 1960, Warrick and Yeh, 1990, Wuest and Schillinger, 2011, Zhu and Warrick, 2012). مستوى الرطوبة واحلرارة يف الكتل الطمية املغلفة ابلرمل يف حبرية سد التغذية: جتربة معملية ومنذجة حتليلية أحادية البعد أنفر كاسيموف1 وعلي املكتومي*وسعيد االمساعيلي1 ومحد البوسعيدي1 Abstract. Mosaic 3-D cascade of parallelepiped-shaped silt blocks, which sandwich sand-filled cracks, has been discovered in the field and tested in lab experiments. Controlled wetting-drying of these blocks, collected from a dam reservoir, mimics field ponding-desiccation conditions of the topsoil layer subject to caustic solar radiation, high tem- perature and wind, typical in the Batinah region of Oman. In 1-D analytical modelling of a transient Richards’ equation for vertical evaporation, the method of small perturbations is applied, assuming that the relative permeability is Avery- anov’s 3.5-power function of the moisture content and capillary pressure is a given (measured) function. A linearized advective dispersion equation is solved with respect to the second term in the series expansion of the moisture content as a function of spatial coordinates and time. For a single block of a finite thickness we solve a boundary value problem with a no-flow condition at the bottom and a constant moisture content at the surface. Preliminary comparisons with theta-, TDR- probes measuring the moisture content and temperature at several in-block points are made. Results corroborate that a 3-D heterogeneity of soil physical properties, in particular, horizontal and vertical capillary barriers emerging on the interfaces between silt and sand generate eco-niches with stored soil water compartments favourable for lush vegetation in desert conditions. Desiccation significantly increases the temperature in the blocks and re-wet- ting of the blocks reduces the daily average and peak temperatures, the latter by almost 15°C. This is important for planning irrigation in smartly designed soil substrates and sustainability of wild plants in the region where the top soil peak temperature in the study area exceeds 70°C in Summer but smartly structured soils maintain lash vegetation. The layer of dry top-blocks acts as a thermal insulator for the subjacent layers of wet blocks that may host the root zone of woody species. Keywords: Soil capillary barrier; soil heterogeneity; hydropedology; soil moisture content; linearized Richards’ equation. امللخــص: خــال دراســة التغيــرات يف تربــة ســد اخلــوض مت العثــور علــى تشــكيله فريــدة للرتبــة الطميــة ذات النمــط الكتلــي ذو األســطح املتعــددة واملغلفــة بالرمــل، والــي تشــكلت بفعــل عوامــل عديــدة منهــا طوبوغرافيــة الســطح وترســبات الطمــي والرمــل مليــاه الفيضانــات ذات الســلوك غــر املنتظــم. مت دراســة ســلوك املــاء واحلــرارة يف هــذه الكتــل خمربيــا وباســتخدام النمذجــة التحليليــة. صممــت التجربــة لكــي حتاكــي الوضــع يف ســد التغذيــة وذلــك بالتحكــم يف دورات الرطوبة واجلفاف للكتل الطمية وتعريضها لإلشــعاع الشمســي ودرجات احلرارة املرتفعة. كما مت اســتخدام معادلة ريتشــارد اخلطية حلســاب معدل البخــر العمــودي باعتبــار ثابــت أفرنيانــوف لرطوبــة الرتبــة هــو 3.5 وأمــا ثابــت الضغــط الشــعري فتــم قياســه أيضــا. مت مقارنــة نتائــج التجــارب املعمليــة مــع نتائــج النمذجــة التحليلــي وأثبتــت النتائــج تأثــر احلواجــز الشــعرية للرتبــة خاصــة لألســطح البينيــة للطمــي والرمــل، والــي أدت إىل االحتفــاظ بـــماء الرتبــة كحويصــات توفــر امليــاه لألعشــاب والشــجرات يف البيئــة الصحراويــة، وأدى جفــاف الرتبــة إىل رفــع درجــة حــرارة الكتــل الطميــة كمــا أن إعــادة ترطيــب الرتبــة ســاعد علــى خفــض معــدالت درجــة احلــرارة اليوميــة وخفــض الدرجــة القصــوى مبعــدل 15 درجــة مئويــة. لقــد أوجــدت طبقــات الرمــل احمليطــة بالكتــل الطميــة حاجــزا حراريــا وهيدرولوجيــا يعيــق خــروج املــاء مــن الكتــل إىل طبقــات الرمــل وبالتــايل أعــاق عمليــة التبخــر، ممــا أدى إىل بقــاء املــاء يف الكتــل الطميــة والــذي يعــد مهمــا للــري ودميومــة الزراعــة يف بيئــة تصــل درجــة حــرارة تربتهــا إىل 70 درجــة مئويــة يف فــرتة الصيــف. الكلمات املفتاحية: معادلة ريتشارد اخلطية، حمتوى رطوبة الرتبة، هيدروبيدولوجي، الرتبة الغر متجانسة، احلواجز الشعرية للرتبة 9Research Article Kacimov, Al-Maktoumi, Al-Ismaily, Al-Busaidi Spatially patchy, i.e. 2-D and time-wise persistent distri- butions of the volumetric moisture content (VMC) in a seemingly homogeneous topsoil have been discovered and described on the scale of a mini-watershed/cultivat- ed field and attributed to soil aggregates (Guber et al., 2003, Pachepsky et al. 2005), i.e. a 3-D composite with a size of an elementary cell (aggregate) of several millime- ters, which is superior in terms of soil water dynamics as compared to unstructured soils (see e.g. Sawiñski et al., 2011). Lehman and Or (2009, 2013) studied a similar phenomenon of 2-D patchy textural pattern of the soil (macroscale) and pore bundles (microscale), which con- duct and evaporate moisture in a spatially mosaic way. Al-Ismaily et al., (2013), discovered an essentially 3-D and temporarily very stable patchiness of the soil-struc- ture, which is not detectable by standard on-surface measurements of the moisture content or evaporation rate i.e. by such common instruments as theta-probes, surface-mounted tensiometers or evaporimeters. Here- after this structure is called a “smart design”. This patchi- ness becomes evident either in pedons of 1.5-2.0 m deep or by observing distinct ecotones of emerging vegeta- tion. The vegetation, as a proxy-indicator of structural heterogeneity, serves as a footprint, with high transpi- ration detectable by sapflow meters. The cascades of silty blocks of sizes of 30-40 cm and cracks of apertures of up to several cm (Fig. 1A) were found in pedons dug inside the reservoir of the Al-Khod recharge dam in Oman. The cracks were filled with a medium-size sand, which, by analogy with fracking in reservoir engineer- ing, is called a “proppant”. Consequently, the whole cas- cade of the soil structure is a triple-periodic composite, with sharp contrasts of hydraulic and thermal properties between texturally contrasting components (blocks and filled fractures). Al-Ismaily et al., (2015), Al-Maktoumi et al. ( 2014), Al-Saqri et al. (2016) studied further hydro- logical and geotechnical applications of natural “smart design” patterns. In arid regions such as Oman, both the natural and cultivated vegetation relies on the soil substrate as an eco-refuge, in the hostile ambient atmospheric condi- tions (Brown, 1974, Lambers et al., 2008) of annual pre- cipitation of about 100 mm and air average temperature of about 30°C. The water deficit conjugated with heat stress and, in case of poor irrigation practices, ensued secondary soil salinization (see e.g Geng and Boufadel, Figure 1. Smart block-fracture structure in the field and experimental replicate: (A) Silt blocks in a pedon dug in the reservoir area of the Al-Khod dam (left panel); (B) surface view of the site (right panel), (C) Silt block (light colour) collected from the reservoir and trimmed to fit the blue plastic box. Sheaths of loose sand (proppant) have darker colour, and D) Measurements of VMC-temperature after the first ponding. A C B D 10 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22 Issue 1 Moisture and temperature in a proppant-envelopped silk block 2015), are eco-constraints in hot deserts, which were prognosticated to amplify in the so-called global warm- ing scenarios (see e.g., Clair and Lynch, 2010). These constraints are mitigated by plants’ adaptation in textur- ally heterogeneous soils, as Noy-Meir (1973) elucidated. Since his seminal paper, the temporal and spatial soil water dynamics (SWD) in hydraulically-thermally com- mingled soil compartments (aggregates and layers) be- came a topic of intensive studies in hydropedology and hydroecology (see e.g. Lin et al., 2006, Porporato and Ro- driguez-Iturbe, 2002). As is evident from (Fig. 1A), right photo, woody species (e.g. castor oil plants) thrive on the “smartly designed” substrate. The top-most blocks are deadly dry and hot but starting from the second layer of blocks (see the pedon in Fig. 1A) the moisture content is amazingly high, despite a continuous transpiration by the plant roots. Temperature distributions and heat fluxes in hetero- geneous soils in temperate and relatively humid climates (Arkhangelskaya, 2012, Goncharov and Shein, 2006, Physics, 1963), where plants’ cultivation is impeded by the deficit of solar radiation, are controlled by agroengi- neering techniques (e.g. reducing the albedo of the soil surface, its mechanical undulations, mulching, etc.) such that the topsoil serves as a heat condenser. In Oman and other arid tropics the situation is opposite: plants’ roots suffer from excessive heating and, consequently, tillage, mulching, increasing albedo, subsurface irrigation and other soil-water management techniques (see e.g. Lip- iec et al., 2013) serve for thermal insulation against con- ductive heat transfer from an extremely hot soil surface (peak temperature of which in June reaches 72-73°C in the study area) to the root zone. The discovered “smart design” of the soil structure was replicated in an on-farm experiment and showed an excellent water saving efficiency for crop cultivation in Oman (Al-Maktoumi et al., 2014) and in growing orna- mental plants as passive thermal coolers of building en- velopes (Kacimov et al., 2010). The objective functions in the agroengineering design and optimization included biomass, yield and leaf-area index. Structural patchiness of the edaphic factor, band-type distribution of the plant roots and ensued transpiration and SWD was discov- ered and discussed in geotechnical applications by Kaci- mov and Brown (2015). In this paper, we elaborate on the effect of the soil texture and structure on SWD and soil temperature. We report the results of natural evaporation and heating of one isolated silt block, collected from a reservoir site, shown in figure 1A, and sheathed by texturally the same “proppant” (wadi sand) as in Al-Ismaily et al., (2013). The main purpose was to understand how the top-most blocks of silt in (Fig. 1A) dries out and how tempera- ture varies inside the block during this post-ponded desiccation. For this purpose, we had to quantify the capillary properties of the blocks in controlled wetting and drainage conditions. The average saturated hydrau- lic conductivity, ks=0.023 m/day, of the blocks was well known from the previous experiments conducted by double-ring and tension infiltrometers and laboratory permeameter tests. In the field ks variations within the Al-Khod dam area were reported for silt blocks in com- parisons with regular soils in the off-reservoir area (Al- Saqri et al., 2016). Moreover, ks is, generally speaking, varies vertically within any silt block because of textural variation during Stokes’ sedimentation (Al-Ismaily et al., 2013). In this paper, ks is a constant (apparent or effec- tive) quantity and its variability is not considered in the physical and mathematical models. The parameters of the unsaturated conductivity and water-holding capacity of silt were parametrically in- volved in mathematical modelling, in which we used linearization of Richards’ equation (Kulabukhova and Polubarinova-Kochina, 1959, abbreviated hereby as KPK-59). 3-D distributions of a transient moisture con- tent within the block and “proppant”, obtained from probes and modelling of 1-D flow, are important for as- sessing the capillary barrier phenomenon (impedance of water drainage from a wet silt to dry sand) and enhanced counter-evaporation properties of the “smart design” in (Fig. 1). Both in the field of “smartly designed” soil sub- strate and in our lab replication, a detailed 3-D moisture content and temperature distributions require a net- work of monitoring probes. In our experiment, there were only 3 functioning probes that is, of course, a seri- ous hindrance in validation of the mathematical model. Imbibition-desiccation experiment A silt block was collected from the first layer of a 4-lay- ered cascade of similar blocks (two layers separated by a thin layer of wadi sand are shown in figure 1A) from a site of the dam reservoir, which is unique from pedo- logical, hydroecological, sedimentological and hydro- logical viewpoints (Al-Ismaily et al., 2013, 2015). The block was tooled into a rectangular parallelepiped to fit a plastic box. Between the box walls-bottom and the five sheathed faces of the block we put a coarse sand (see figure 1B), also collected from a wadi which crosses the Figure 2. Sketch of the experiment in Figure 1C . 11Research Article Kacimov, Al-Maktoumi, Al-Ismaily, Al-Busaidi dam reservoir. The upper face of the block was open to the atmosphere. Consequently, the experiment in (Fig. 1B)models the topmost blocks of (Fig. 1A) Experimental design A system of Cartesian coordinates Oxyz is selected as de- picted in (Fig. 2). The sizes of the block and sand sheath in (Fig. 1B) as well as the loci of the probes, placed in the xOz plane of the block, are shown in (Fig. 2) Wired sensors, connected to a data logger (5TM Sen- sor – Decagon Em50), were inserted into the silt and sand. A data logger, port 4 recorded information (VMC and temperature) from the sheath, port 2 – from the block centre and port 1 – from the sensor close to the silt-sand interface (Fig. 2). Probe 2 defaulted for a short time as indicated in (Fig. 3a). The experiment started with an instantaneous ponding i.e. full saturation of the dry block and the sheath. During this imbibition phase water was added and its temperature eventually equil- ibrated with that of the soil. After that, measurements started on March 20, 2014 at 3:40 pm. The probes re- corded VMC and temperature in °C every 20 min. The first desiccation cycle lasted till April 12, 2014. On that day the system was ponded again, the block and sheath “proppant” re-saturated for two days. The second des- iccation cycle started on April 16, 2014 and continued until the three VMC-curves (sand, block centre and periphery close to the silt-sand interface, see Fig. 2) Figure 3. VMC (a) and temperature (b) as a function of time during the imbibition-dessication experiment. 12 SQU Journal of Agricultural and Marine Sciences, 2017, Volume 22 Issue 1 Moisture and temperature in a proppant-envelopped silk block reached almost horizontal asymptotes on May 10, 2014. Figure 3a and 3b illustrates VMC and temperature curves during the two cycles of the experiment. VMC curves (Fig. 3a) have periodic blips, which reflect diurnal variations of the moisture content due to sorption-de- sorption of air humidity, as we witnessed in the farm ex- periments (Al-Maktoumi et al., 2014). As is evident from the temperature curves in (FIg. 3b), the temperature diurnally fluctuates with a general trend of an increas- ing daily average temperature during one post-wetting desiccation cycle. This trend is obviously caused by pro- gressively decreasing latent heat losses due to gradually decreasing evaporation from the block surface. The thermal gradient between the block and “prop- pant” becomes more pronounced as the VMC becomes low. For example, considering the period at the end of the first desiccation cycle (7th April 2014 -13th April 2014), when the VMC of 0.2 for the block and of 0.05 for the sand were recorded, the temperature difference between two points is 3-5°C while when the VMC is at saturation for both the silt and “proppant” (after rewetting on 15th April 2014), the difference in temperature is about 1°C only and less as the soil temperature equilibrates with that of the added water. The difference in VMC becomes high because the sand loses moisture faster compared to the fine textured soil of the block. Correspondingly, the difference in temperature reaches about 6°C when the difference in VMC is 0.224, considering the data of mid-day of 23rd April 2014. As the soil desiccates the temperature difference between sand and silt becomes small (around 2°C). The thermal gradient between the block and the sand sheath reverses at night time (Fig. 4). Figure 4 plots the difference in temperature readings by the two sensors for the period from 15/4/2014 at 10:45 am to 24/4/2014 at 4:00 am. The sand is observed to cool faster during the night than the block and heated-up faster during the day. This could be attributed to variation in heat con- ductance as to the soil texture or to the effect of the walls through which the whole box in (Fig. 1a) loses or gains heat. KPK-59 mathematical model of SWD Evaporation from initially saturated soil massifs is a 3-stage, two phase (moisture and vapour), non-isother- mal and transient transport of mass and energy, with complex exchanges between the top soil, atmospheric boundary layer and plant roots and periodic interven- tion of irrigators who induce periodic imbibition-drain- age-redistribution cycles (Deol et al., 2014, Philip, 1991, Van Wijk, 1963, Shein and Goncharov, 2006). Taking into account complexity of evaporation, in this section we model isothermal SWD inside the blocks. Hysteresis of soil hydraulic properties, although evident from the two imbibition-drainage cycles in (Fig. 3a), is ignored in the KPK-59 model. As our focus is on the desiccation phase indicated in (Fig. 3), we disregard drainage of the sand and, consequently, do not conjugate flow in silt and sand. In other words we study SWD within the block only. Figure 4. Difference in temperature (°C) between the sheath and the centre of the block for selected period between 1/5/2014 12:00 pm and 11/5/2014 12:00 am (after re-wetting). 13Research Article Kacimov, Al-Maktoumi, Al-Ismaily, Al-Busaidi Geometrically, the experimental block in (Fig. 1B) mimics an elementary cell of the triple-periodic (in the domain -∞ < x < ∞ , -∞ < y < ∞ and 0 < z < ∞ , see Fig. 2) cascade of blocks and “proppant”-filled cracks (Fig.1A). Physically, the natural blocks in the reservoir bed, as compared with one in (Fig. 1B), have slightly different conditions at all faces but the upper one. Namely, the side and bottom faces of the natural block are less heated than that in (Fig. 1B), which is exposed to extra heat- ing from the four faces of the plastic box and from a hot ground surface. Another peculiarity of our experiment was in relating it to the so-called “coupled” flow of Leh- man and Or (2009). The Richards’ equation for a 3-D distribution of VMC, w(x,y,z,t) [unitless], and pressure head, p(x,y,z,t) [m], inside the silt block reads: ∂w ∂t = ∂ ∂x k(w) ∂p ∂x ⎛ ⎝⎜ ⎞ ⎠⎟ + ∂ ∂y k(w) ∂p ∂y ⎛ ⎝⎜ ⎞ ⎠⎟ + ∂ ∂z k(w) ∂p ∂z ⎛ ⎝⎜ ⎞ ⎠⎟ − ∂k(w) ∂z , (1) where t is time, k(w) is the unsaturated hydraulic con- ductivity and p(w) is the capillary pressure function (see e.g. Warrick, 2003). SWD described by eqn.(1) is iso- thermal. Both constituting relations, k(w) and p(w), are basic hydrophysical properties of the silt. We assumed k(w) to obey the following empiric Averyanov’s relation (see KPK-59) k(W)= k s w−w 0 m−w 0 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ n = k s Wn (2) where W is a normalized phase saturation, w0 is irreduc- ible moisture content of silt, m is porosity and n is an ex- ponent (usually assumed to be equal 3.5, see e.g. KPK-59, or pore-scale models in Al-Maktoumi et al., 2015, Kaci- mov and Kayumov, 2002). For p(w) the Van-Genuchten, Averyanov, Brooks-Corey or other empiric functions can be used. Pore-scale models can be also involved in derivations of both the capillary pressure function (Yang and Lu, 2012) and thermal conductivity of unsaturated soils (Youngs and Kacimov, 2007) . KPK-59 linearized the nonlinear parabolic PDE (1) in the following manner. The phase saturation in eqn.(2) was expanded as a series: W =W 0 (x , y,z,t)+ λW 1 (x , y,z,t)+ λ2W 2 (x , y,z,t)+…, (3) where λ is a parameter and W0, W1, W2, are functions to be found. We assume that W0=const, which is the ini- tial normalized full saturation of the block in the second desiccation cycle of (Fig. 3a). The series in (3) is truncat- ed and only the first two terms are retained. The corre- sponding truncations of (2) and capillary pressure curve give: k(W)= k s W 0 n + λnk s W 0 n−1W 1 (x , y,z,t), p(W)= p W 0( )+ λ ′p W0( )W1(x , y,z,t), (4) In the first line of eqn.(4) only the first term is retained, i.e. the unsaturated conductivity expansion is truncated as k(W)≈ksW0 n . This is actually the Averyanov unsatu- rated conductivity function at n=3.5 (although mathe- matically n can be an arbitrary positive number), which is plotted elsewhere (see e.g. Polubarinova-Kochina, 1977). The first derivative p’(W0) is a constant which, as we shall show below, is readily calculated from the selected capillary pressure function. Taking into account eqns. (3) and (4), eqn.(1) for the first-order term in the expansion is reduced to: ∂W 1 ∂t = D ∂2W 1 ∂x2 + ∂2W 1 ∂y2 + ∂2W 1 ∂z2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −u ∂W 1 ∂z , (5) where D= k s W 0 n ′p W 0( ), u= nksW0n−1 (6) are two constants. Obviously, eqn. (5) is a linear advec- tive dispersion equation (ADE), in which the parameter D is “diffusivity” and u is the “convective” (“velocity”) term. Eqn.(5) should be solved in the domain −a/2< x