Parameter Identification for Root Growth based on Soil Water Potential Measurements – An Inverse Modeling Approach

Parameter Identification for Root Growth based on Soil Water Potential Measurements – An Inverse Modeling Approach

Available online at www.sciencedirect.com Procedia Environmental Sciences 19 (2013) 574 – 579 Four Decades of Progress in Monitoring and Modeling of...

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Available online at www.sciencedirect.com

Procedia Environmental Sciences 19 (2013) 574 – 579

Four Decades of Progress in Monitoring and Modeling of Processes in the Soil-PlantAtmosphere System: Applications and Challenges

Parameter identification for root growth based on soil water potential measurements – an inverse modeling approach Kefeng Zhanga* a

Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Abstract In this study a strategy to calibrate process-based agro-hydrological models for water dynamics in the soil-crop system with soil sensor measurements was developed. An inverse problem was formulated to infer the root parameters based on the measured soil water potential at depths during crop growth. The root penetration down the soil profile is assumed to be driven by the accumulative daily mean air temperature, and root length density distribution in the soil profile is exponential. The forward agro-hydrological model for water dynamics in the soilcrop system was proposed by Yang et al. (J. Hydrol. 2009; 370:177-190). A micro-Genetic Algorithm was employed to infer the parameters. Results show that the predictions of soil water potential using the inferred values of root parameters agree fairly well with the measurements throughout the entire growing period, indicating that the deduced root parameters are credible and appropriate for the studied case. It follows that the strategy presented in the study enables accurate estimates of root parameters to be obtained from soil sensor measurements at various depths, and thus provides an effective way to calibrate models. © 2013 2013 The The Authors. Authors.Published Publishedby byElsevier ElsevierB.V B.V. © theScientific Scientific Committee conference. Selection and/or and/or peer-review peer-reviewunder underresponsibility responsibilityofofthe Selection Committee of of thethe conference Keywords: inverse analysis; SPAC system; soil water dynamics; root growth;

1. Introduction Process-based agro-hydrological models are becoming increasingly important in optimizing resources use in agriculture and in minimizing the environmental consequences. The techniques on modeling the soil-crop system have advanced greatly in the last few decades as a result of better understanding of soil and plant sciences and greater computing power. Many process-based agro-hydrological models for water

* Corresponding author. Tel.: 0086-574-88130254; fax: 0086-574-88130165. E-mail address: [email protected].

1878-0296 © 2013 The Authors. Published by Elsevier B.V Selection and/or peer-review under responsibility of the Scientific Committee of the Conference doi:10.1016/j.proenv.2013.06.065

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dynamics in such systems are now able to produce reliable results, given accurate inputs [1]. Focus is now shifting to find ways of calibrating models from measured data since parameters required by processbased agro-hydrological models are frequently difficult to obtain with certainty [1]. Great efforts have been made to infer model parameters for the soil-crop system using inverse modeling techniques. A large body of literature is available as how to infer the effective soil hydraulic properties based on laboratory experiments [2], field crop experiments [3] and field evaporation experiments [4,5]. Root processes are a key in controlling water dynamics in the soil-crop system, and accurate identification of root functional parameters is extremely difficult for field crops [6]. In particular, information of root length density distribution and root length in the soil profile is essential. Attempts should therefore be made to identify the parameters describing root growth and root length density distribution using the soil water measurements from different depths in the soil profile. Such approaches are now possible as soil sensors are more accurate and more widely adopted [7], and numerous optimization algorithms are readily available for the purpose of inverse modeling [8-10]. The main purpose of this study is to develop an inverse modeling strategy to identify root growth parameters based on soil water measurements gathered from various depths during growth, and to explore the feasibility of applying such an approach in field crops. 2. Materials and Methods 2.1. Inverse modeling procedure The forward agro-hydrological model proposed by Yang et al. [11] was used for simulating water dynamics in the soil-crop system. The root penetration down the soil profile in the model is assumed to be driven by the accumulative daily mean air temperature. Relative root length density declines logarithmically from the soil surface downwards [6].

Rz

L( z )

Rz 0

e

max[0, ( az ( z / Rz )

T Tlag )k r ]

(1) (2)

where Rz is the rooting depth, Rz0 is the rooting depth at planting, T is the cumulative day degree, Tlag is the threshold of cumulative day degree for root growth, kr is the root growth rate, L is the relative root length density, and az is the shape parameter controlling root distribution down the profile. To identify the root parameters kr and az, the technique and corresponding software used in the study was a micro-GA, developed by Carroll [12]. Compared with a conventional GA, which normally requires a large population size and a large number of generations, the adopted micro-GA performs excellently for a small population size [12]. The inverse modeling procedures used in this study are similar with those for inferring soil hydraulic properties and crop coefficient as outlined by Zhang et al. [5,13]. 2.2. Experiments In order to test the developed inverse modeling technique, an experiment with Dutch white cabbage (cv. Eminence, Tozer seeds, UK) was carried out at Wellesbourne, UK (latitude: 52o12' N, longitude: 1o37' W) in a sandy loam soil [13]. The experimental design was a fully randomised block with five replicates. The plots were 5.0 x 2.0 m. The crop was transplanted on 29 April 2009 and harvested on 8

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September 2009. Soil water potential was measured at the depths of 10, 30, 50, 70 and 90cm using Watermark 200SS-v soil sensors (Irrometer Company, USA). Table 1 shows soil physical and hydraulic properties of the experimental soil profile [13]. The soil hydraulic properties were derived using the pedo-transfer functions proposed by Wösten et al. [14]. Table 1. Soil physical and hydraulic properties [13]

Topsoil (0 – 30 cm) Subsoil (30 cm – )

Clay (%) (<0.002mm)

Silt (%) (0.002 0.05mm)

Organic matter (%)

Bulk density (g cm-3)

(cm3 cm-3)

(cm3 cm-3)

(cm-1)

13.0

11.5

1.7

1.55

0.374

0.025

11.0

10.0

0.8

1.65

0.342

0.025

s

r

n

Ks (cm d-1)

0.07119

1.283

73.0

0.06173

1.346

174.8

Meteorological data used were measured on-site, approximately 100 m from the experimental site. The weather variables including maximum, mean and minimum air temperatures, total solar radiation, relative humidity, wind speed and rainfall were measured at daily intervals [13]. More detailed description of the experimental study can be found elsewhere[13]. 2.3. Model parameter values Three types of parameters are required for running the forward model: weather data, soil hydraulic properties and crop data. Weather data measured on the experimental site and the soil hydraulic properties shown in Table 1 were used in the simulations. The crop parameters include dates of planting and harvest, and dual crop coefficients for potential soil evaporation and plant transpiration from the FAO 56[15]. The rooting depth at planting Rz0 was 10cm, and the threshold of cumulative day degree for root growth Tlag was 400 doC[16]. The initial soil water content was 0.20, 0.21 and 0.24 cm3 cm-3 for the 0-30, 30-60, and 60-90cm soil layers, respectively [13]. 3. Results and Discussion By applying the proposed inverse modeling approach to the measured soil water dataset from the cabbage experiment, the root parameters kr and az were successfully deduced. The deduced values for kr and az were 0.000953 m d-1oC-1 and 3.55, respectively, which are close to 0.0012 m d-1oC-1 reported by Thorup-Kristensen [16] and 3.0 [13] for cabbage. This suggests that the proposed approach is capable of deducing root growth parameters from soil water measurements at depths for field crops reasonably. Figs. 1 and 2 show the overall comparison of soil water potential at various depths between and simulation and measurement, and detailed comparison at the 10cm, 30cm and 50cm depths. It is clear that the overall comparison of soil water potential between simulation and measurement is acceptable. The detailed comparison of soil water potential at various depths reveals that the simulated values follow the same pattern of measured soil water changes, and the produced values close to the measurements for the most of the growth period. However, clear discrepancies also exist. Generally the simulated soil water potential values are higher than the measured values in the event of drying soil, and at the deeper depths the decrease in simulated soil water potential is at a slower pace than that in the measured values during the dry spell in July. This might be attributed to the insufficient accuracy in soil hydraulic properties used in the simulations. It is widely reported that soil hydraulic properties are difficult to determine at the field scale [2-5].

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Sim ulated soil w ater potential (kPa) 0

-50

-100

-150

-200

Measured soil water potential (kPa)

0

-50

-100

-150

y = 1.0036x - 11.573 R2 = 0.6984

-200

Fig. 1. Comparison of soil water potential at various depths between simulation and measurement

27-Apr

17-May

06-Jun

Date 26-Jun

16-Jul

05-Aug

25-Aug

14-Sep

06-Jun

Date 26-Jun 16-Jul

05-Aug

25-Aug

14-Sep

06-Jun

Date 26-Jun 16-Jul

05-Aug

25-Aug

14-Sep

(kPa)

0 -60 -120

(a) 10cm

-180

27-Apr

17-May

(kPa)

0 -60 -120 -180

(b) 30cm

27-Apr

17-May

(kPa)

0 -25 -50

(c) 50cm

-75

Fig. 2. Comparison of soil water potential ( ) between simulation with inferred root growth parameter values and measurement at 10cm (a), 30cm (b) and 50cm (c) depths

There are many parameters in process-based agro-hydrological models. Amongst those are soil hydraulic properties, root growth parameters and crop coefficient, which are difficult to obtain at the field scale. Last decades, significant progress has been made in identifying soil hydraulic properties. However, less effort made has been made in identifying other parameters. Nowadays, automated soil sensors are becoming more accurate and affordable [7], and numerous optimization algorithms, traditional or evolutional, can be employed for inverse modeling [8-10]. Attempts should, therefore, be made to

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estimate other model parameters such as root functional parameters. Since parameter identifiability increases with reducing the number of parameters [9], the inverse modeling strategy could be two-staged. The identification of soil hydraulic properties could first be carried out using soil water measurements gathered from fallow soils, and upon this the identification of root growth parameters could be carried out using the data collected from the soil covered by crops where the soil hydraulic properties are already known. 4. Conclusions An inverse modeling approach to identify parameters describing root growth using soil water potential measurements at various depths in the soil profile is proposed. It has been demonstrated that deduced root parameters values for cabbage growth are reasonable, and the simulated soil water potential values at different depths using the deduced parameter values agree fairly well with the measured values. Although the proposed approach worked well for the studied case, more research is needed to demonstrate identifiability and robustness of the procedure. Acknowledgements The author is grateful to the financial support to carry out the work as part of the WaterBee project (Grant Agreement Number: 222440) funded by the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007-2013) under the Specific Programme “Capacities” (Research for the Benefit of SMEs). References [1] Bastiaanssen WGM, Allen RG, Droogers P, D’Urso G, Steduto P. Twenty-five years modeling irrigated and drained soils: State of the art. Agric. Water Manage. 2007;34:137–148. [2] Schmitz GH, Puhlmann H, Droge W, Lennartz F. Artificial neural networks for estimating soil hydraulic parameters from dynamic flow experiments. Eur. J. Soil Sci. 2005;56:19-30. [3] Jhorar RK, Bastiaanssen WGM, Feddes RA, Van Dam JC. Inversely estimating soil hydraulic functions using evapotranspiration fluxes. J. Hydrol. 2002;258:198-213. [4] Gómez S, Severino G, Randazzo L, Toraldo G, Otero JM. Identification of the hydraulic conductivity using a global optimization method. Agric. Water Manage. 2009;96:504-510. [5] Zhang K, Burns IG, Greenwood DJ, Hammond JP, White PJ. Developing a reliable strategy to infer the effective soil hydraulic properties from field evaporation experiments for agro-hydrological models. Agric. Water Manage. 2010;97:99–409. [6] Pedersen A, Zhang K, Thorup-Kristensen K, Jensen LS. Modelling diverse root density dynamics and deep nitrogen uptake–A simple approach. Plant Soil 2010;326:493-510. [7] Greenwood DJ, Zhang K, Hilton H, Thompson A. Opportunities for improving irrigation efficiency with quantitative models, soil water sensors and wireless technology. J. Agric. Sci. 2010;148:1–16. [8] Rao SS. Optimization: Theory and Application. Wiley Eastern Limited; 1984. [9] Hopmans JH, Šimunek J. Review of inverse estimation of soil hydraulic properties. In: Van Genuchten MTh, Leij FJ, Wu L, editors. Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media, University of California, CA; 1999, p. 634-659. [10] Abbaspour KC, Schulin R, van Genuchten MTh. Estimating unsaturated soil hydraulic parameters using ant colony optimization. Adv. Water Resour. 2001;24:827-841. [11] Yang D, Zhang T, Zhang K, Greenwood DJ, Hammond J, White PJ. An easily implemented agro-hydrological procedure with dynamic root simulation for water transfer in the crop-soil system: validation and application. J. Hydrol. 2009; 370:177-190. [12] Carroll DL. http://cuaerospace.com/carroll/ga.html; 1999.

Kefeng Zhang / Procedia Environmental Sciences 19 (2013) 574 – 579 [13] Zhang K, Hilton HW, Greenwood DJ, Thompson AJ. A novel use of soil sensor measurements and inverse modeling techniques for determining the FAO56 crop coefficients. Agric. Water Manage. 2011;98:1081-1090. [14] Wösten JHM, Lilly A, Nemes A, Le Bas C. Development and use of a database of hydraulic properties of European soils. Geoderma 1999;90:169-185. [15] Allen RG, Pereira LS, Raes D, Smith M. Crop evapotranspiration. Guidelines for computing crop water requirements. Irrigation and Drainage Paper 56. FAO, Rome; 1998. [16] Thorup-Kristensen K. Root growth and nitrogen uptake of carrot, early cabbage, onion and lettuce following a range of green manures. Soil Use Manage. 2006;22:29-38.

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