AN APPROACH TO MODELING AIR AND WATER STATUS OF HORTICULTURAL SUBSTRATES

AN APPROACH TO MODELING AIR AND WATER STATUS OF HORTICULTURAL SUBSTRATES W. C. Fonteno Department of Horticultural Science North Carolina State University, Raleigh, NC 27695-7609, USA Abstract There have been numerous investigations into the hydraulic properties of porous substrates used as root media for plant production in containers. Much of the discussion has focused on defining the parameters necessary to effectively describe this air and water status. The quantity of air and water is the result of physical influences of the medium, container geometry and extent of root development. Five container state parameters have been developed to describe the air and water status of the particular medium/container/plant combination at drainage equilibrium: total porosity, container capacity, air space, available water, and unavailable water. Empirical methods and mathematical procedures were combined to determine these parameters. Container geometry had a pronounced effect on the air and water status of substrates tested. An overall conceptual model is presented to help describe the overriding effects of cultural practices on air and water content of container media. 1. Introduction The physical environment surrounding roots in containers consisting of relative volumes of air, water and solid is largely determined by the relationship between water energy status and water content of the medium. This relationship is a reflection of the pore size distribution of the medium. A plot of this relationship, that is a plot of volumetric wetness (Θ) vs soil moisture tension (MT) is the soil moisture characteristic or moisture retention curve. Ever since Bunt (1961) reported moisture retention curves for pot-plant media, there has been considerable effort to determine the utility of these curves in explaining plant growth, and the best way to quantify these data for both descriptive and predictive purposes. DeBoodt and Verdonck (1972) used this procedure to characterize several substrates. They described certain ranges of the moisture characteristic curve as Air Space (0 to 1 kpa), Easily Available Water (1 to 5 kpa), and Water Buffering Capacity (5 to 10 kpa). White and Mastalerz (37) introduced the concept of container capacity (CC), that amount of water retained in a containerized substrate system after drainage from saturation, but before evaporation. White and Mastalerz noted difficulty in relating measured CC to a moisture characteristic curve. This was later determined to be because CC is a function of both medium and container (Klute, 1986). 67

Over the last five years, a set of five container state parameters have been developed to describe the air and water status of any medium/container combination at drainage equilibrium. Total porosity (TP), the volume of the medium not occupied by the solid fraction, can be quantified by measuring the amount of water held at saturation. Bilderback and Fonteno (1987) have shown that a combination of mathematical functions for both the moisture characteristic curve and container geometry provide a more consistent description of Container Capacity. Air space (AS) is defined as the difference between TP and CC. The question of whether water is available or unavailable to the plant involves both the distance the water is located from the root and the matric forces which bind the water to the substrate particles. From the work of Karlovich and Fonteno (1986), they concluded that 1) plants in containers 15 cm and smaller are normally exposed to matric tensions of0 to 50 kpa before rewatering and 2) within this range it is the volume of water held, not the matric tension which influences plant growth. We have also observed (unpublished data) that the unsaturated hydraulic conductivity is extremely low in horticultural substrates. Therefore, water is only available when roots are in very close or intimate contact. However, even with intimate root contact water held at MT greater than 1500 kpa is most often unavailable (UW) (Hillel, 1980). The difference between CC and UW is the amount of water available for plant growth (AW). The purposes of this paper are: 1) to demonstrate a mathematical approach to describing the air and water status of horticultural substrates in containers and 2) to examine the model s predictions of total porosity, container capacity, air space, unavailable water, available water and solid fraction for several container/medium combinations. 2. Materials and methods Eight replications of three media were packed (2) in aluminum cylinders (7.6 cm x 7.6 cm). Data were collected for moisture retained at 10 moisture tensions from 0 to 30 kpa, according to Karlovich and Fonteno (1986). All cylinders were seated onto the porous plate of a Kimax 600 ml 90 F Buchner filter funnel and saturated with water by slowly adding water over a period of 24 to 48 hr between the funnel wall and the outside of the aluminum ring. An airtight lid was placed on top of the funnel and positive air pressures were applied in increments which resulted in pressures at the medium center of 3.8, 10, 20, 40, 50, 75, 100, 200, 300 cm (H 2 O). Volume outflow was recorded for each increment. Normally, a period of 48 hr was required to establish equilibrium at pressures less than 50 cm and 24 hours for higher pressures. After measurement at 300 cm, each sample was removed and bulk density determined by calculating the volume of each sample and weighing each sample after drying 24 hr at 105 C (King, 1965). Moisture tension values were converted to kpa, then the integer 1 was added to each value. This allowed a log transformation at a MT value of zero. A nonlinear, 68

five-parameter function developed by Van Genuchten and Nielsen (1985) was used to describe the moisture retention data. Van Genuchten s function stems from an analysis by Brooks and Corey (1964), given by Θ = ( Θ s - Θ r )(αh) L + Θ r [1] where Θ s is the saturated water content, Θ r is the residual water content, α is the inverse of the air entry value, h is the log of the moisture tension and L is the pore size distribution index. In order to provide a better fit, Van Genuchten (1980) proposed: Θ = Θ r + (Θ s -Θ r )/[1+(αh) n ] m [2] where he assumed unique relations between n and m, i.e. m=1-(1/n). To improve flexibility, the new model has removed this restriction on n and m, so all 5 parameters are independent. Θ s and Θ r are known empirical parameters, while α, n and m are unknown and are determined using standard nonlinear least squares parameter estimation methods. Total porosity (TP) and unavailable water (UW) were equal to the volume wetness (Θ) at saturation and 1500 kpa, respectively. Container capacity (CC) was predicted by combining equation [2] with a mathematical function used to describe container geometry using procedures similar to those used by Karlovich and Fonteno (1986). The Percent Moisture Volume Moisture (ml) Height (cm) 16.9 15.0 13.0 11.0 9.0 7.0 5.0 3.0 1.0 100 50 0 % Moisture Retained by Volume Total Moisture 1657 ml Total Volume 3863 ml x 100 = modeled containers Container Capacity = 43% were mathematically sectioned into 0.1 cm tall increments. The Figure 1 - Determination of container capacity using moisture characteristic curve and container geometry. nonlinear equation was used to predict the percentage of water values at the midpoint of each 0.1 cm section. Multiplying the percentage of water value bythe volume of each pot section gave the water volume held in that section at container capacity. The water 32 33 34 36 39 43 49 59 69 151 153 156 160 168 180 199 229 261 69

volumes of all zones were summed to give the total water volume in the pot at container capacity. Figure 1 is a graphical representation of this concept (container sections were increased to 2.0 cm for clarity). Air space (AS) was calculated as the difference between TP and CC. Available water (AW) was calculated as the difference between CC and UW. These procedures were termed, Equilibrium Capacity Variables Model (ECV) by Milks (1986). The three media used were: 1) a 1 Canadian sphagnum peat : 1 vermiculite (grade #2) (v/v) medium similar to many of the so-called peat-lite mixes; 2) a 3 pinebark (aged) : 1 peat : 1 sand (concrete grade) (v/v/v) mixture and 3) a 1 Wagram sandy loam soil : 1 peat : 1 sand (v/v/v). Data for unavailable water (UW) were collected on a measured volume basis at MT of 1500 kpa, according to Klute (1986). Both Richards (1949) and Stevenson (1982) have shown that determining UW on a pressure plate has some limitations. To avoid variability in bulk density due to handling, the four replications of each medium were packed in rigid aluminum cylinders 2.2 cm tall by 7.6 cm diameter. Packing and handling techniques were as similar as possible to those used with the larger cylinders, and were adjusted to give similar bulk densities. To validate the model, means of moisture retention data were compared both to points of corresponding MT on the nonlinear curve, and to model predictions using the 7.6 cm aluminum cylinder as the container. The cylinder was chosen so that the moisture retention curve could be tested on the same media samples from which data were collected. Also, because the container was a cylinder rather than a frustrum of a cone or pyramid, both the nonlinear function and the container model could easily be tested against the means. When more complicated geometry was encountered, only the container model was used. 3. Results and Discussion 3.1. Moisture characteristic curves and nonlinear model predictions Means of moisture retention data and nonlinear curves for the 3 media are in figure 2. Parameter values, mean square errors and coefficients of determination for the nonlinear function (table 1) indicate that the function accurately described the moisture retention properties of each medium between zero and 30 kpa. This is consistent with data from Milks (1986). Precision of data about means was partially determined by their standard errors (SE) (table 2). All SE s for collected data were very small (0.1 to 0.7), indicating that laboratory precision for media preparation and handling was good. The largest absolute residuals (observed minus predicted) for the means vs regression predictions occurred for MT at 30 kpa for 3 media, but the differences barely exceeded one percent. This difference reflected the fact that the means at 30 kpa were not the true 70

100 80 1 Peat: 1 Vermiculite 3 Pine bark: 1 Peat: 1 Sand Percent Volume 60 40 20 1 Soil: 1 Sand: 1 Peat 0 0.0 0.5 1.0 1.5 2.0 2.5 Pressure, log(kpa) Figure 2 - Moisture characteristic data and nonlinear regression curves for three media. asymptotic residual water content, so the equation predicted values slightly higher than observed. Where accuracy at higher MT levels is desired, data collected at higher MT should be used so as to give a better estimate of the true asymptotic residual (Van Genuchten and Nielsen, 1985). Table 1 - Parameter values, mean square errors (MSE) and coefficients of determination (r 2 ) for the nonlinear function(θ = Θ r + (Θ s -Θ r )/[1+(αh) n ] m ) for 3 media. Model Parameters Medium Θ s Θ r α n m MSE r 2 1 peat:1 vermiculite 86.9 31.9 0.9 3.3 1.2 1.3 0.999 3 bark:1 peat:1 sand 70.5 22.7 3.4 1.1 1.0 1.3 0.999 1 soil:1 peat:1 sand 54.6 15.4 5.2 0.8 1.0 3.0 0.997 3.2. Equilibrium capacity variables model Accuracy of the ECV model predictions was also very high (table 2). For all three substrates, the largest difference between predicted and observed values residual) was 2.0 percent. The data clearly indicate the model s ability to predict container capacity. This procedure reduces the measurement errors associated with the fill and drain methods commonly used in determining CC (Hillel, 1980). If CC predictions are accurate, then calculating the difference between measured TP and predicted CC gives 71

an equally accurate prediction of air space. 3.3. Unavailable and available water determinations Percent moisture standard errors (0.34 to 0.39) were small for all media, again evidence of laboratory precision. The volume percent moisture remaining at 1500 kpa, was low for the soil-based substrate (8.5%), but very high for the peat- and bark-based media (24.1% and 21.5%, respectively). These data are consistent, however, with over 100 other soilless media tested (not shown) where UW ranged from 20 to 40 percent by volume. These high values indicate the necessity of including 1500 kpa measurements in any model that attempts to describe plant available water. CC and UW were then used to calculate AW. Since UW varies considerably among media and is independent of CC, available water cannot be satisfactorily determined from CC alone. Table 2 - Mean observed water content with their mean standard errors (SE), pre dicted percent water volume and Equilibrium Capacity Variable Model (ECV) predictions for a 7.6 cm (height, diameter) container for three media at four tensions. Treatment 0 kpa 0.4 kpa 5 kpa 30 kpa 1 peat : 1 vermiculite Observed 86.9 76.2 39.9 31.9 Mean SE 0.7 0.5 0.1 0.2 Predicted 86.9 75.6 38.9 3.7 ECV 86.9 74.7 37.9 33.2 3 bark : 1 peat : 1 sand Observed 70.5 58.7 28.8 22.7 Mean SE 0.5 0.3 0.3 0.2 Predicted 70.5 58.4 27.9 24.3 ECV 70.5 58.0 27.2 23.9 1 soil : 1 peat : 1 sand Observed 54.6 52.0 21.2 15.4 Mean SE 0.6 0.6 0.5 0.4 Predicted 54.6 52.6 21.0 16.5 72

100 90 80 1 Peat: 1 Vermiculite 3 Bark: 1 Peat: 1 Sand Air Space Available Water Unavailable Water Percent Volume 70 60 50 40 30 20 1 Soil: 1 Peat: 1 Sand 10 0 15 10 48 273 648 15 10 48 273 648 15 10 48 273 648 Container ECV 54.6 51.1 20.3 16.2 Figure 3 - Equilibrium capacity variables for combinations of 3 media and five containers. Total porosity = air space + available water + unavailable water, container capacity = available water + unavailable water. Containers: 15 = 15 cm pot, 10 = 10 cm pot, 48 = bedding plant cell (48 cells/tray), 273 = plug cell (273 cells/tray), 648 = waffle plug cell (648 cells/tray). 3.4. Substrate/container combinations The adaptability of the model is demonstrated in Figure 3, which shows volumes of AS, AW and UW for the 3 media. TP is the sum of AS, AW and UW (the top of each bar). CC is the sum of AW and UW and can be read as the value at the top of the AW portion of each bar. Each medium was mathematically placed into 5 containers: a waffle plug cell (648 cells per flat), a 273 plug (273 cells/flat), a bedding plant cell (48 cells/flat), a 10 cm and a 15 cm standard plastic container. TP and UW are medium-specific and do not vary across containers. However, CC and AS are greatly affected by container parameters. These data demonstrate the need to consider both medium and container size when describing air and water values. The same trends across container size appeared in all media, the degree of change in AS and CC being affected by the nature of moisture retention patterns. In summary, air and water content of horticultural substrates can be predicted given: 1) a substrate moisture retention curve, 2) an estimate of unavailable water (such as the 1500 kpa data), and 3) a mathematical function for container geometry. Once mathematically described, the substrate data can be applied to any container with one major assumption: the bulk density of the substrate does not change from container to con- 73

tainer. In fact, this is a major limitation to the current ECV model. Compensation for bulk density must be made at the moisture characteristic curve level, ie separate curves for each bulk density. Further work on the relationship of bulk density on the moisture characteristic curve is needed to incorporate a function to compensate for this problem. References Bilderback, T. E. and W. C. Fonteno. 1987. Container Modeling. J. Environ. Hort. 5(4): 180-182. Brooks, R. H. and A. T. Corey. 1964. Hydraulic properties of porous media. Colo rado State Univ., Hydrology Paper No. 3. Bunt, A. C. 1961. Some physical properties of pot-plant composts and their effect on growth. Plant and Soil 13:322-332. De Boodt, M. and O. Verdonck. 1972. The physical properties of the substrates in horticulture. Acta Hort. 26:37-44. Hillel, D. 1980. Fundamentals of soil physics. Academic Press, New York. Karlovich, P. T. and W. C. Fonteno. 1986. The effect of soil moisture tension and volume moisture on the growth of Chrysanthemum in three container media. J. Amer. Soc. Hort. Sci. 111:191-195. King, L. G. 1965. Description of soil characteristics for partially saturated flow. Soil Sci. Soc. Am. Proc. 29:359-362. Klute, A. 1986. Water retention: laboratory methods. In Amer. Soc. of Agron. Mono graph No. 9, Revised. Methods of Soil Analysis, Part 1. Physical and Mineralogical Methods. Milks, R. R. 1986. Culture and water relations of Pelargonium x hortorum Bailey Ringo Scarlet as seedlings established with limited root volumes. PhD. Diss., N. C. State Univ., Raleigh. Richards, L. A. 1949. Methods of measuring soil moisture tension. Soil Sci. 68:95-112. Stevenson, D. S. 1982. Unreliabilities of pressure plate 1500 kilopascal data in predict ing soil water contents at which plants become wilted in soil-peat mixes. Can. J. Soil Sci. 62:415-419. Van Genuchten, M. T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898. Van Genuchten, M. T. and D. R. Nielsen. 1985. On describing and predicting the hy draulic properties of unsaturated soils. E. G. S.; Annales Geophysicae. 3:615-628. White, J. W. and J. W. Mastalerz. 1966. Soil moisture as related to container capacity. Proc. Amer. Hort. Sci. 89:758-765. 74