spatial soil moisture scaling structure during soil moisture experiment 2005

HYDROLOGICAL PROCESSESHydrol. Process. 25, 926–932 (2011)Published online 24 September 2010 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.7877

Spatial soil moisture scaling structure during Soil MoistureExperiment 2005

Minha Choi1* and Jennifer M. Jacobs2

1 Department of Civil and Environmental Engineering, Hanyang University, Seoul 133-791, Republic of Korea2 Department of Civil Engineering, University of New Hampshire, Durham, NH 03824, USA

Abstract:

Soil moisture state and variability control many hydrological and ecological processes as well as exchanges of energy andwater between the land surface and the atmosphere. However, its state and variability are poorly understood at spatial scaleslarger than the fields (i.e. 1 km2) as well as the ability to extrapolate field scale to larger spatial scales. This study investigatessoil moisture profiles, their spatial organization, and physical drivers of variability within the Walnut Creek watershed, Iowa,during Soil Moisture Experiment 2005 and relates the watershed scale findings to previous field-scale results. For all depths,the watershed soil moisture variability was negatively correlated with the watershed mean soil moisture and followed anexponential relationship that was nearly identical to that for field scales. This relationship differed during drying and wetting.While the overall time stability characteristics were improved with observation depth, the relatively wet and dry locationswere consistent for all depths. The most time stable locations, capturing the mean soil moisture of the watershed withinš0Ð9% volumetric soil moisture, were typically found on hill slopes regardless of vegetation type. These mild slope locationsconsistently preserve the time stability patterns from field to watershed scales. Soil properties also appear to impact stabilitybut the findings are sensitive to local variations that may not be well defined by existing soil maps. Copyright 2010 JohnWiley & Sons, Ltd.

KEY WORDS soil moisture; spatial organization; variability; time stability; physical properties

Received 2 April 2010; Accepted 19 August 2010

INTRODUCTION

Soil Moisture Experiments (SMEX) conducted to vali-date microwave remote sensing soil moisture productsprovide unique experimental datasets. These datasetsare the basis of a decade of scientific contributionsand have significantly enhanced our knowledge ofsoil moisture variability within satellite pixel foot-prints (Famiglietti et al., 1999; Mohanty and Skaggs,2001; Jacobs et al., 2004; Starks et al., 2006; Choiand Jacobs, 2007; Cosh et al., 2008). Three dominantfindings have emerged. First, soil moisture variabil-ity is strongly related to mean soil moisture. Second,topography and soil texture control the observed spatio-temporal persistence of soil moisture patterns. Finally,some sampling locations exhibit the ability to consis-tently capture the mean field or watershed scale soilmoisture.

Time stability (Vachaud et al., 1985) has been widelyused to analyse soil moisture and has demonstrated aconstancy of spatial soil moisture patterns. This findinghas practical value because it allows the number ofsoil moisture measurements to be minimized withoutconsiderable loss of information, thus reducing sampling

* Correspondence to: Minha Choi, Department of Civil andEnvironmental Engineering, Hanyang University, 17 Haengdang-dong,Seongdong-gu, Seoul 133-791, Republic of Korea.E-mail: [email protected]

costs (Fernandez and Ceballos, 2003; Brocca et al.,2010).

Despite a significant literature on soil moisture vari-ability and stability characteristics as reviewed by Broccaet al. (2009), few studies provide insights regardingwhich soil moisture characteristics are relevant at bothfield and watershed scales (Fernandez and Ceballos,2005; Famiglietti et al., 2008; De Rosnay et al., 2009;Brocca et al., 2010; Jacobs et al., 2010). Multi-scalestudies have generally found that the statistical prop-erties and time stability are relatively consistent acrossfield to watershed scales. The key question is: whatis the main physical driving force that results in thisconsistency. While the importance of vegetation, topog-raphy, and slope is well established at field-scale stud-ies (Mohanty and Skaggs, 2001; Jacobs et al., 2010),few of the multiple-scale studies have examined selectedphysical features. For example, Brocca et al.’s (2009)examination of three experimental sites (400–9000 m2)within a single region showed that contributing area andslope position were strong indicators of representativesoil moisture conditions. De Rosnay et al. (2009) alsoconcluded that slope position was an important indica-tor of time stability for their coarse textured sites. Todate, no multiple-scale study has considered the role ofvegetation, topography, and slope simultaneously.

This paper extends the analysis of soil moisture vari-ability in SMEX02 Iowa fields (800 ð 800 m2) (Jacobset al., 2004; Choi and Jacobs, 2007) to the watershed

Copyright 2010 John Wiley & Sons, Ltd.

SPATIAL SCALING STRUCTURE OF SOIL MOISTURE 927

scale. The goal of this study was to determine if theSMEX02 field-scale findings are consistent at a water-shed scale. The soil moisture in the original SMEX02fields and eight additional fields was sampled during theSMEX05 experiment and analysed using statistical andtime stability methods (Cosh et al., 2009; Kabela et al.,2009).

DESCRIPTION OF THE STUDY AREAAND DATASET DURING SMEX05

The Walnut Creek watershed (¾100 km2) in Ames, Iowawas the site for intensive investigations of soil moistureand hydro-meteorological samples during SMEX02 andSMEX05 (Figure 1). The climate is nearly humid withan annual average rainfall of 835 mm, and the watershedis used for row crops including corns and soybeans.The topography is characterized by low relief and poorsurface drainage. The soils are loams and silt clay loamswith relatively low permeability. This study uses soilmoisture profile data measured daily during SMEX05,16 June 2002 to 3 July 2002 (i.e. 14 measurementdays), for three slope positions (i.e. hilltop, slope, andbottom), five depths (i.e. 0, 5, 10, 15, and 25 cm), andten fields in the Walnut Creek watershed (Figure 1 and

Table I). Approximate distances between measurementpoints within field and within Walnut Creek watershedare 100 and 2000 m, respectively. The soil textureclassification was verified in the field by visual inspectionand the percentages of sand and clay were obtained fromthe Iowa Soil Properties and Interpretations Database(Iowa State University, 1996).

Figure 1. Soil moisture sampling locations in the Walnut Creek watershedduring SMEX05

Table I. Geographic locations and field characteristics for the soil moisture sampling field in the Walnut Creek watershed, Iowa

Field Vegetation Latitude (N) Longitude (W) Altitude (m) Sand (%) Clay (%) Soil texture

WC10 (T) Corn 41Ð9769 93Ð6922 307 38 23 LoamWC10 (S) 41Ð9764 93Ð6922 306 33 23 LoamWC10 (B) 41Ð9759 93Ð6922 305 33 28 Loam

WC11 (T) Soybean 41Ð9754 93Ð6928 306 33 23 Silt clayWC11 (S) 41Ð9752 93Ð6928 305 20 31 Silt clayWC11 (B) 41Ð9749 93Ð6928 304 20 31 Silt clay


WC13 (T) Corn 41Ð9515 93Ð6900 320 33 23 Silt clayWC13 (S) 41Ð9515 93Ð6906 316 33 23 Silt clayWC13 (B) 41Ð9515 93Ð6911 307 20 31 Clay

WC15 (T) Soybean 41Ð9371 93Ð6598 317 33 28 LoamWC15 (S) 41Ð9370 93Ð6601 316 33 28 LoamWC15 (B) 41Ð9371 93Ð6605 315 33 28 Loam

WC22 (T) Corn 41Ð9472 93Ð6191 306 38 23 Silt and gravelWC22 (S) 41Ð9474 93Ð6191 304 38 23 Silt clayWC22 (B) 41Ð9480 93Ð6191 299 33 23 Silt clay

WC33 (T) Soybean 41Ð9731 93Ð6425 308 33 23 LoamWC33 (S) 41Ð9728 93Ð6425 306 20 31 LoamWC33 (B) 41Ð9724 93Ð6424 304 33 28 Loam

WC34 (T) Grass 41Ð9684 93Ð5813 286 33 23 Silt clayWC34 (S) 41Ð9681 93Ð5820 283 33 28 Silt clayWC34 (B) 41Ð9680 93Ð5823 282 20 31 Clay

WC44 (T) Soybean 41Ð9508 93Ð7115 325 33 23 Silt clayWC44 (S) 41Ð9509 93Ð7117 323 33 23 Silt clayWC44 (B) 41Ð9508 93Ð7123 321 20 31 Clay


T, S, and B within the parenthesis indicate top, slope, and bottom, respectively.

Copyright 2010 John Wiley & Sons, Ltd. Hydrol. Process. 25, 926–932 (2011)

928 M. CHOI AND J. M. JACOBS

Slope positions (hilltop, slope, and bottom) weredetermined using a mobile Global Positioning Systemcoordinate instrument in each field. Soil moisture datawere collected using theta probes (Dynamax Inc., Hous-ton, TX, USA). The theta probe measures the averagedielectric constant using 6 cm long tines. For subsurfacemeasurements, an auger was used to extract soil to thetop of the required soil depth and the theta probe waspushed into the undisturbed soil until the tines were fullycovered. In this study, the theta probe soil moisture mea-surements are referred to by the top depth (e.g. 0–6 cmis 0 cm, 5–11 cm is 5 cm).

METHODS

Statistical moments were calculated daily to examinethe statistical characteristics. Probability plot correlationcoefficient (PPCC) tests were conducted to test thenormality of the soil moisture measurements. Thetime stability concept originally proposed by Vachaudet al. (1985) was used to characterize a time-invariantassociation between the spatial location and statisti-cal parametric values of a given soil property. Thewatershed mean soil moisture (�j,t), the mean rela-tive difference (υi,j), the variance of the relative differ-ence [��υ�2

i,j], and the root mean square error (RMSE)of mean relative difference for each sampling point(Vachaud et al., 1985; Jacobs et al., 2004) were definedas

�j,t D 1

nj,t

nj,t∑iD1

�i,j,t �1�

υi,j D 1

nt

nt∑tD1

�i,j,t � �j,t

�j,t�2�

��υ�2i,j D 1

nt � 1

nt∑tD1

(�i,j,t � �j,t

�j,t� υi,j

)2

�3�

RMSEi,j D [υ2i,j C ��υ�2

i,j]1/2 �4�

where t is the number of dates, j is the number of fields,i is the number of sample points within field j at timet, �i,j,t is the volumetric soil moisture (VSM) at locationi in field j and time t.

Analysis of variance (ANOVA) was employed to deter-mine whether differences exist among time stabilitystatistics based on topographic, soil, and vegetation siteproperties (Johnson and Wichern, 2002). When signifi-cant differences were identified, Tukey’s Honestly Sig-nificant Difference (HSD) test was employed to identifywhich pairs were significantly different. Unlike a t-test,the HSD considers the suite of all pairwise compar-isons and indicates which pairs are significantly different(Helsel and Hirsch, 2002).

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30 35 40 45

Mean Soil Moisture (%)

Coe

ffici

ent o

f Var

iatio

n

0 cm5 cm15 cm25 cm0-31cm

WC 11_SMEX02

(b)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30 35 40 45


Coe

ffici

ent o

f Var

iatio

n

0 cm5 cm15 cm25 cm0-31cm

e) WC 13_SMEX02

(c)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30 35 40 45


Coe

ffici

ent o

f Var

iatio

n

0 cm5 cm10 cm15 cm25 cm0-31 cm

WC_SMEX05

Figure 2. Relationships between volumetric soil moisture and the coeffi-cient of variation during SMEX02 and SMEX05

RESULTS AND DISCUSSION

Spatial statistics, mean, standard deviation, and coeffi-cient of variation (CV) were calculated for each sam-pling period. Figure 2 shows the relationship betweenthe mean soil moisture and the coefficient of variationduring SMEX02 and SMEX05. An exponential relation-ship, CV D A expB�j,t described the relationship betweenmean soil moisture and spatial variability (Table II). Themean soil moisture and the coefficient of variation had astrong negative relationship. These negative relationshipsare consistent with previous results from 18 different soilmoisture field experiments (Choi et al., 2007) as wellas the 36 000 ground-based soil moisture measurementsacross scales during the Southern Great Plains 1997



Table II. Regression relationship between the coefficient of vari-ation and the mean soil moisture observed for the different soildepths: CV D A expB� , where CV is the coefficient of variation,A and B are the parameters, and � is the watershed mean soil

moisture

Depth (cm) A B R2

0 0Ð87 �0Ð055 0Ð805 2Ð08 �0Ð085 0Ð9310 2Ð45 �0Ð089 0Ð9215 2Ð86 �0Ð091 0Ð9125 8Ð15 �0Ð124 0Ð900–31 1Ð99 �0Ð086 0Ð93

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-5 -4 -3 -2 -1 0 1 2 3 4 5

∆ mean soil moisture (%)

∆ C

V

0 cm5 cm10 cm15 cm25 cm0-31 cm

Figure 3. Slope change (delta symbol, �) of the coefficient of variation(CV) versus change of the mean soil moisture

and 1999 (SGP97 and SGP99), SMEX02, and SMEX03(Famiglietti et al., 2008). While Famiglietti et al. (2008)found that the best fit A and B parameter values increasedas aggregation scale increased, our results indicate that,the best fit A and B parameter values are intermediatebetween those determined for the two field-scale stud-ies conducted during SMEX02 for all depths (Choi andJacobs, 2007).

Several previous studies reported spatial organizationof the soil moisture differed during drying and wettingcycles (Bell et al., 1980; Famiglietti et al., 1998, 1999;Hupet and Vanclooster, 2002). Our day-to-day differencesfor mean soil moisture and the coefficient of variation (thedifferences were calculated values at t � 1) reveal thatthe soil moisture variability changes were much largerand more variable during the drying process than duringthe wetting process (Figure 3). This result supports thefindings of Manfreda et al. (2007) who indicated thatspatial organization of the soil moisture was affecteddifferentially by drying and wetting processes as wellas mean soil moisture values. Bell et al. (1980) andFamiglietti et al. (1998) found that variance decreasedwith drying, while Famiglietti et al. (1999) and Hupet and

Vanclooste (2002) pointed out opposite patterns. Peters-Lidard and Pan (2002) suggested that variance increaseswith drying if the mean soil moisture is between porosityand field capacity, while variance decreases with dryingif the mean soil moisture is drier than field capacity.

Famiglietti et al. (1999) postulated that spatial distri-bution of the transpiration and runoff processes are phys-ical drivers that influence the spatial variability of thesoil moisture associated with initial distribution of thesoil moisture and heterogeneity of the land surface prop-erties. Mechanistically, our findings reflect evaporativeforcings, which are typically more spatially homogeneousthan precipitation at a watershed scale (Mahmood andHubbard, 2003; Nordbotten et al., 2006). Ivanov et al.’s(2010) modelling study results, which showed that hys-teresis effects driven by vegetation states tend to reduceheterogeneity of the initial states due to rainfall, is notborne out in our current observational study. However,our results are limited to the characteristics of the tworainfall events observed during SMEX05.

The PPCC test results showed that the normal andlognormal distributions were appropriated for 90 and92% of the datasets. This was somewhat higher thanprevious field-scale values where normal and lognormaldistributions were appropriate for 83 and 77% of thedatasets, respectively (Choi and Jacobs, 2007). It hasbeen suggested that this phenomenon occurs becausethe heterogeneity of local scale soil properties is lesspronounced as spatial scales increase. As spatial scale isincreased, most of the soil moisture variability is likelyto be averaged out and normally distributed (Western andBloschl, 1999; Fernandez and Ceballos, 2005; Broccaet al., 2010).

Figure 4 shows the time stability patterns for alldepths. The most time stable points represent the water-shed mean soil moisture for all depths within š0Ð9%VSM. As soil depths increased, the mean relative differ-ences decreased with the average RMSE decreasing from26Ð6 to 14Ð4% VSM from the surface to a depth of 25 cm.Most locations maintained their stability without regardto soil depths (Figure 4g). Surface soil moisture spatialpatterns are strongly related to those in the subsurfacelayers (Jackson, 1980; Arya et al., 1983; Fernandez andCeballos, 2003; Choi and Jacobs, 2007). These patternsare likely due to similar physical controls such as soilproperties and topography for these depths. Several pre-vious studies found that time stability patterns were verysimilar in even different scales and different regions (Fer-nandez and Ceballos, 2003; Brocca et al., 2009, 2010).Fernandez and Ceballos (2005) and Brocca et al. (2010)pointed out that the most time stable locations can pre-dict mean soil moisture values with low average RMSE(<2Ð5%) of the mean relative difference across scales.

An ANOVA analysis (Table III) showed significantdifferences among the time stability characteristics basedon topographic position, soil texture, and percentage ofsand and clay classes but not for the given vegetationtypes. Tukey’s HSD test (Table IV) indicated that low



Figure 4. Rank ordered mean relative difference with standard deviation error bars, root mean square error, and mean volumetric soil moisture contentfor (a) 0 cm, (b) 5 cm, (c) 10 cm, (d) 15 cm, (e) 25 cm, (f) 0–31 cm, and (g) mean relative differences for all depths where field ID is ordered by

0–31 cm depth ranking

lying locations had significantly different time stabil-ity characteristics than hill slope and hilltop locations.Also, the time stability characteristics of clay were verydifferent from all other soil types. These time stabilitypatterns for soil texture (clay) and low lying areas canbe explained by the low soil hydraulic conductivities andthe slow drainage, respectively, both of which serve toretain soil water (Mahmood and Hubbard, 2003).

Figure 5 demonstrates how these findings might beused to select time stable sites a priori. Low lying areasand clay soil are unlikely to be time stable because theyare typically wetter than the watershed average. While thehilltops and hill slope time stability was not significantlydifferent, hilltop locations are consistently drier thanthe average for all depths. Mechanistically, low lyingareas tend to receive infiltrated water. However, hilltop



Table III. ANOVA analysis for the mean relative difference forthe 0–31 cm depth

Feature f-value (mean relative difference (MRD))

Topography 12Ð0647ŁŁŁ

Soil texture 6Ð6374ŁŁ

Sand (%) 4Ð6456Ł

Clay (%) 4Ð7063Ł

Vegetation 1Ð0750 (NS)

NS, non-significant.Ł , ŁŁ , ŁŁŁ Significant at the 0Ð05, 0Ð01, and 0Ð001 probability levels,respectively.

locations will dry quicker due to rapid drainage duringrainfall events (Famiglietti et al., 1998; Qiu et al., 2001).The mild slopes in the SMEX02 fields also preserved thetime stability patterns (Jacobs et al., 2004) and suggestthat the local slopes are good indicators of stability fromfield to watershed scales. This is consistent with other

Table IV. Tukey’s HSD test for the mean relative difference ofthe 0–31 cm depth

Sand (%) Topography

20 33 38 Bottom Slope Hilltop

— NS Ł — ŁŁ ŁŁŁ

— — NS — — NS— — — — — —

Clay (%) Soil texture

23 28 31 Clay Silt clay Loam Silt and gravel

— NS Ł — ŁŁ ŁŁ ŁŁ

— — NS — — NS NS— — — — — — NS

— — — —

NS, non-significant.Ł , ŁŁ , ŁŁŁ Significant at the 0Ð05, 0Ð01, and 0Ð001 probability levels,respectively.

Figure 5. Average of the mean relative difference with 95% confidence interval bars ordered by (a) topography and (b) soil texture for differentdepths



regions’ findings that time stability patterns are preservedin sites with average topography and vegetation (Broccaet al., 2009).

One difference between the field and watershed scalesis that soil texture appears to have greater importance atthe watershed scale than the field scale. This may be duein part to differences in soil characterization. While thisstudy classified soil texture by site, the SMEX02 studyobtained soil texture data from a soil database (Iowa StateUniversity, 1996). Because soil texture may be affectedby agricultural management practices, the importance ofsoil texture might be difficult to assess without site-specific data and explains one of the difficulties inidentifying soil moisture variability patterns affected byauxiliary data quality such as soil texture (Western et al.,1998).

CONCLUSIONS

For the Iowa Walnut Creek watershed, a strong rela-tionship exists between the watershed- and the field-scale soil moisture variabilities. Soil moisture variabilitydecreases exponentially with increasing mean soil mois-ture. This study’s best fit equations have parametersthat are bounded by those found for the two SMEX02field-scale studies. Time stable locations were also foundpreferentially on hill slopes at depths ranging from nearsurface to 31 cm for both scales. At the watershed scale,time stable locations can be used to estimate watershedscale mean soil moisture within š0Ð9% VSM and pro-vide good estimates of watershed soil moisture for allsoil depths. For both of these SMEX studies, the role ofsoils, topography, and vegetation were investigated. Ofthese both soil properties and topography were identifiedas important physical drivers across scales.

ACKNOWLEDGEMENTS

Support for this study was provided by a NASA grant(NNG04GL60G) and NSF grant (NSF-EAR-0337277).The authors wish to thank Dr Michael Cosh and Dr RamRay for their field data collection efforts.

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spatial soil moisture scaling structure during soil moisture experiment 2005

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