Probabilistic modeling of soil moisture dynamics in a revegetated desert area

Lei Huang ,ZhiShan Zhang,YongLe Chen

Shapotou Desert Research and Experiment Station,Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou,Gansu 730000,China

1 Introduction

Soil moisture plays an important role in the terrestrial water cycle as it is the key link between land hydrological and ecological processes,especially in revegetated desert areas.Changes in soil moisture directly affect the growth and survival of vegetation,however soil moisture dynamics is extremely complex.Due to the influence of different physical,chemical and biological processes,as well as uncertain variables in spatial and temporal scales such as precipitation,soil texture,topography,and temperature;changes in soil moisture dynamics exhibit a broad variability and stochastic properties (Schlesingeret al.,1996;Rodriguez-Iturbe,2000;Sherratt,2005;Rietkerk and Koppel,2008;Liuet al.,2011).Consequently,a probabilistic description of soil water exists to provide a productive framework for analysis,complementing the equilibrium based approach (Rodriguez-Iturbe,2000;Rodriguez-Iturbe and Porporato,2005;Liu and Zhao,2006).Eagleson’s pioneering work (1978) had developed a probabilistic method for modeling the dynamics of water transfer within a precipitation event,and proposed a probability density function through the mathematical expectation mode.Based on water losses from evapotranspiration and leakage with different schemes,Rodriguez-Iturbeet al.(1999) further refined the Eagleson model and improved the loss function of soil water,and then the steady-state probability distributions for soil moisture were analytically obtained.This probabilistic model provided an explicit linkage between temporal soil moisture dynamics and climate and vegetation processes,which had become an important milestone in ecohydrological studies (Liu and Zhao,2006;Panet al.,2008).Laioet al.(2001) further improved the calculation of evapotranspiration in the Rodriguez-Iturbe model,and provided a useful framework to analytically investigate the probabilistic structure of soil moisture and water balance in extremely arid regions.Subsequent models such as the Ridolfi (2003) and D’Odorico (2007) models were all derived from the Rodriguez-Iturbe model with different soil moisture probability density functions.These models confirm that soil moisture dynamics plays a central role in the ecosystem in terms of random fluctuations of climatic factors,soil characteristics,vegetation,and terrain conditions.Recent research has proven that the Rodriguez-Iturbe model has good applicability in various environment conditions (from arid to semi-arid environments,temperate to tropical climates) (Fernandezet al.,2001;Laioet al.,2001;Porporatoet al.,2002;Kumagaiet al.,2004).However,research on dynamics and probabilistic simulation of soil moisture in China are relatively weak.Huanget al.(2000) introduced a new equation for calculating transpiration and evaporation by means of the Eagleson stochastic dynamic water balance model,and simulated the rationing of the water balance factor and annual dynamic changes of soil moisture in an active layer according to characteristics of rainfall distribution in the loess plateau.Liuet al.(2007) simulated the stochastic dynamics of soil moisture in the Qilian Mountain grassland ecosystem at point scale.Wanget al.(2009) analyzed the dynamic and stochastic simulation of soil moisture in the Sichuan Basin hilly region.In arid desert regions,the stochastic model might have good application for researching soil moisture dynamics due to random rainfall.In this paper,we focused on the application of the Rodriguez-Iturbe stochastic soil moisture model in an arid artificial vegetation area based on long term continuous monitoring data of soil moisture.

2 Materials and methods

2.1 Experimental site description

This study was conducted in soil of the Water Balance Experimental Fields (WBEF),Shapotou Desert Experimental Research Station,Chinese Academy of Sciences.This station borders the Tengger Desert,China’s fourth largest desert located in the central part of West China (37°27′N,104°57′E;elevation:1,250 m).The climate at this site is characterized by abundant sunshine and low relative humidity.For the 46-year period from 1955 to 2000,minimum average monthly relative humidity was 33% in April,and the maximum was 54.9% in August.The elevation of this site is 1,330 m above sea level.Mean annual precipitation is 187 mm (according to meteorological records from 1956 to 2002),precipitation is mainly concentrated between June and September.Mean air temperature is 24.3 °C in July and-6.9 °C in January.The annual mean wind velocity is 2.6 m/s.The volumetric water content at a soil depth of 0-300 cm is on average 0.03-0.04 (VWC,m3/m3).Groundwater may exist,but located in deep underground,and is not viable for the maintenance of large areas of natural vegetation cover.Precipitation is usually the only source of freshwater to replenish soil water in this area (Shapotou Desert Experimental Research Station,Chinese Academy of Sciences,1995).The Water Balance Experimental Fields were revegetated withArtemisia ordosicaKrasch.andCaragana korshinskiFabr.under different group patterns since 1990,10m×10m quadrats were set in each vegetation community and three 3-m deep neutron moisture measurement tubes were embedded along the diagonal in each plot.

2.2 Data collection

Volumetric soil moisture data at 40 cm and 60 cm were measured with a neutron probe (CNC503DR,Beijing Nuclear Security Nuclear Instrument Co.,Ltd.),and the 20-cm soil moisture was measured with TDR300 (Spectrum Technologies,Plainfield,IL).Soil moisture was measured half a month from April of 2008 to December of 2011.Precipitation parameters such as frequency and mean depth were collected from the Shapotou weather station (1991-2011).Other parameters such as soil porosity,plant water stress point and field capacity were obtained from Wanget al.(2007),Porporatoet al.(2002) and other publications.All statistical analyses were conducted using Matlab7.0 (The MathWorks,Natick,MA,USA) and the Origin7.0 software(OriginLab,Northampton,MA,USA).

2.3 The probabilistic soil moisture dynamic model

Under conditions where there are no lateral contributions,the soil moisture balance equation at a point was expressed as:

wherenwas soil porosity,Zris root zone depth (mm),tis time (d);sis relative soil moisture (0≤s(t)≤1),ands=θ/nwith θ referred to the volumetric soil moisture content (VWC,%),andR(t) is precipitation (mm/d).We idealized the occurrence of rainfall as a series of point concentrations in continuous time arising in a Poisson process.Each rainfall event was assumed to have a random depth,characterized by an exponential probability density function.E[s(t),t] is evapotranspiration (mm/d),andL[s(t),t] is deep percolation from root depth (mm/d).From Equation(1),we can see that the input to soil moisture balance is rainfall,and the output is evapotranspiration plus leakage,and they are all dependent on soil moisture.The loss from evapotranspiration is assumed to increase linearly as a function ofsuntil the moisture reaches a thresholds*,above which evapotranspiration takes place at a maximum valueη,when soil moisture exceeds soil field capacitys1.Here we represent leakage loss by an exponential growth starting at soil field capacitys1and reaching the saturated hydraulic conductivitykats=1.The dependence of evapotranspiration losses on soil moisture is summarized in Equation(2):

The solution to stochastic rainfall forcing in Equation(1)is meaningful only in probabilistic terms.The probability density function that reflects soil moisture intensity at a certain range could be derived from the Chapman-Kolmogorov forward equation for the process under mathematical analysis.The probability density function is given as Equation(3):

Detailed description of the formula’s construction can be found in Rodriguez-Iturbe (1999).The goal of this study refers to its applicability in the Shapotou desert area.

3 Results

3.1 Soil moisture dynamics

As presented in Figure 1,soil moisture at 20 cm,40 cm and 60 cm varied basically along with precipitation,with nearly the same interannual change trends.The fluctuation of soil moisture in the surface 20 cm was relatively large because it was more susceptible to the influence of meteorological factors,e.g.,precipitation,especially in the precipitation concentrated period (Jul.-Sep.).There was a 3-5 day time lag between the 40 cm and 60 cm soil moisture dynamics and precipitation.Soil moisture was different between different months,from January to March the dynamics showed minor changes,because the temperature was relatively low and vegetation growth had not yet begun and precipitation was rare at that time.As temperatures rose,the soil began to thaw in March,and snow in the topsoil started to melt which led to an immediate increase in soil water content.In May and June,soil moisture was maintained at a high level due to increased precipitation,but as temperatures continued to rise and plant transpiration and soil evaporation were enhanced,total losses of soil moisture gradually increased,thus soil moisture content began to decline.From September to December,as temperatures decreased and vegetation growth ceased,soil moisture began to gradually increase.From the aforementioned factors,it can be concluded that surface soil moisture is influenced by meteorological and vegetation factors,but deep soil moisture does not have a significant correlation (Heet al.,2010;Zhanget al.,2011).

Figure 1 Soil moisture dynamics in different layers in 2008-2011

3.2 The probability distribution of soil moisture

Figure 2 shows the probability distribution of soil moisture in different layers in 2008-2011,and we find that the histogram of the soil relative to water probability distribution in the soil active layer (0-60 cm) shows a single peak curve.The maximum relative soil moisture at 0-20 cm wass=0.035,and the peak width was about 0.02-0.065,wider than those in other soil layers;there was another aggregated distribution ats=0.06.The peak position of relative soil moisture in 20-40 cm soil layer was lower than in 0-20 cm soil layer,at abouts=0.026 and the peak width was relatively narrow,approximately between 0.02 and 0.05.Peak value in 40-60 cm soil layer wass=0.025 and width was approximately between 0.02 and 0.04.It can also be seen from the figure that the peak width distributions of relative soil moisture in different layers were not completely continuous,they had a multi-peak curve in the topsoil moisture,but the peak position at different layers and the width of the peak did not show significant differences.However,as presented in Figure 2,the peak width of soil moisture distribution was wider in the surface because of increased uncertain fluctuations.

Figure 2 The probability distribution of soil moisture in different layers

3.3 Numerical simulations

Parameters were obtained through research publications(Porporatoet al.,2002;Wanget al.,2007) and all parameter values are listed in Table 1.The soil active layer depths ofZr(cm) were 20 cm,40 cm and 60 cm respectively.

The simulation of Equation(1)was based on the algorithm of Kim and Jang (2007),firstly the equation was transformed into a finite difference equation,then the parameters and original data were substituted into the Rodriguez-Iturbe soil moisture model,finally the soil moisture Probability Density Function (PDF) was exported in Figure 3.Results show that peak position and peak width of soil moisture PDF in the active layer (0-60 cm) were consistent with observations,basically reflecting the probability distribution characteristics of soil moisture.As presented in Figure 3,20 cm soil moisture reached a maximum ats=0.03 ands=0.04,indicating that soil moisture content was almost distributed in this range,and a minor peak ats=0.06 also means another aggregated soil moisture distribution.The probability distribution of soil moisture curve was smoother at 40 cm and 60 cm,mainly due to the fact that relative surface soil moisture was more stable with increased soil depth.The simulated results also prove that the Rodriguez-Iturbe model has a good applicability in revegetated desert areas,and could well simulate soil moisture statistical characteristics.

Table 1 Parameters of the probabilistic soil moisture dynamic model

Figure 3 The probability distribution of soil moisture at (a) 20 cm,(b) 40 cm,(c) 60 cm from Rodriguez-Iturbe model

4 Conclusions and discussions

Soil moisture dynamics is the core of water-controlled ecosystems,and is a hotspot for difficult ecohydrology research.Extensive research on soil moisture and numerous models have been developed in an attempt to study soil moisture dynamics and its response to climatic and vegetation processes.There has been a buildup of empirical models from statistical forecasting methods between agro-meteorological factors and soil moisture (Kanget al.,1994);using soil water balance equation to estimate soil moisture conditions (Liu and Sun,1999);establishing soil water dynamics model based on Darcy’s law and continuous equation (Xuet al.,1999);founding time series models extracted from the soil moisture time series cycle and dynamic optimization simulation (Liuet al.,2004);setting up artificial neural network models for soil moisture prediction(Zhouet al.,2005),as well as micro soil moisture models based on large scale microwave remote sensing technology(Zhanet al.,2004).Each of these models has its merits and drawbacks,e.g.,water dynamics model had definite physical meaning and wide range of applications,but on a large scale,soil heterogeneity and too many parameters limited its application.However,some empirical models have a very good application in certain areas,but as the region and climate changed,the model became restricted.

Compared with the aforementioned traditional soil water dynamics model,the main advantage of the stochastic model was that it had grasped the key character of various stochastic factors.The probability density function was used to describe soil moisture distribution,but did not determine accurate soil moisture.However,it was an efficient means in some areas with limited soil moisture data but relatively abundant rainfall (Liuet al.,2007).In arid desert regions,the main source of soil water is rainfall which has strong temporal and spatial heterogeneity and randomness (Holt,2008),causing sizable random characteristics in the dynamics of soil moisture (Rodriguez-Iturbe and Porporato,2005),especially for surface soil moisture content.The results in our study have shown that soil moisture peak at 20 cm are wider than others,and the distribution curve jumps to a certain extent.In deeper soils,the peak width of soil moisture probability distribution is smaller at 40 cm and 60 cm because soil moisture is relatively stable at this level,which reflects the distribution characteristics of soil moisture properties.Our conclusions have proven that the Rodriguez-Iturbe model has good application character in revegetated desert areas and soil moisture statistical characteristics are well simulated.The difference from other stochastic soil moisture models is that the Rodriguez-Iturbe model assumes that there is an approximate linear relationship between evapotranspiration and soil moisture.Calculation and simulation of this model was relatively simple,the parameters in this model had definite physical meaning and were easy to measure.The Laio soil moisture dynamic model had been widely used in recent literature (Liuet al.,2007;Wanget al.,2009),in which soil evaporation was divided into two parts,evapotranspiration under soil water stress and non water stress,deep percolation was considered to have an exponential relationship with soil moisture content.However,the Rodriguez-Iturbe model with simple forms and perspicuous expressions could also provide an effective way for design and calculation of average soil moisture content and soil water balance (Panet al.,2008).Obviously,from Figure 1 we can conclude that precipitation was the key environmental factor affecting soil moisture dynamics,besides representing as the main input term in the stochastic model,precipitation depth and frequency were the main driving force of soil moisture content (Chenet al.,2012).Other factors such as vegetation canopy interception and soil active layer depth also had significant effects (Laioet al.,2001).From Figures 2 and 3,with increasing soil active layer depth,soil moisture probability distribution diagrams show a meaningful tendency from multi-peak to single peak,indicating that soil moisture content in the surface was easily influenced by random factors than that in deeper layers.Although the stochastic model was a useful tool for soil moisture probability distribution description,it could not predict the specific content of soil moisture.Also,the dynamics of soil moisture,in turn,had a significant impact on vegetation (Zhuet al.,2011).Therefore,a coupled eco-hydrological model taking into account random soil moisture,vegetation types and distribution characteristics should be established in the future,in order to study the plants’ adaptation mechanisms and response to soil moisture dynamics.This will not only enhance our understanding of the relationship between plants and water,but also provide suggestions on ecosystem management in arid regions.

This work was supported by the Key Orientation Project of Chinese Academy of Sciences (KZCX2-EW-301-3),Talented Young Scientist Fund of the Cold and Arid Regions Environmental and Engineering Research Institute,CAS(51Y251971) and National Natural Scientific Foundation of China (41101054,41201084).

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