Understanding Spatio-temporal Patterns of Soil Moisture at the Field Scale

Agricultural and Biosystems Engineering

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Agricultural and Biosystems Engineering

6-2007

Understanding Spatio-temporal Patterns of Soil

Moisture at the Field Scale

Lingyuan Yang

Iowa State University

Amy L. Kaleita

Iowa State University, [email protected]

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An ASABE Meeting Presentation Paper Number: 072108

UNDERSTANDING SPATIO-TEMPORAL PATTERNS OF

SOIL MOISTURE AT THE FIELD SCALE

Lingyuan Yang, Graduate Research Assistant

Department of Agricultural & Biosystems Engineering, Iowa State University

Amy Kaleita, Assistant Professor

Department of Agricultural & Biosystems Engineering, Iowa State University

Written for presentation at the

2007 ASABE Annual International Meeting

Sponsored by ASABE

Minneapolis Convention Center

Minneapolis, Minnesota

17 - 20 June 2007

Abstract. Spatial patterns of soil moisture across a field seem to exhibit some degree of temporal

stability, which has been proved to be related to such invariant attributes as topography and soil characteristics. However, how these patterns and locations might be predicted from these attributes is not well understood. Motivated by a desire to understand these relationships, the objective of this study is to determine how elevation relates to underlying stable and consistent moisture patterns. The characteristics of temporal stability of soil moisture across the field have been analyzed during the 2004 and 2005 growing seasons for a 10-ha field near Ames, IA. Ordinary Kriging (OK) and kriging with external drift (KED) have been used as interpolation tools to estimate the spatial pattern of soil moisture across the field in each observing date. Temporally stable locations can be used to accurately predict the field mean soil moisture. Also, kriging predictions of soil moisture on un-sampled locations using OK and KED have no significant differences in the predicted soil moisture surfaces, but on their standard error of prediction.

Introduction

Soil moisture is one of the important components of hydrological processes, as well as that of biochemical and geomorphological processes and crop growth. It exerts a major influence on runoff generation, erosion, soil evaporation, plant transpiration, solute transport, and land-atmosphere feedback interaction. Soil moisture is highly variable in space and time, so characterizing its spatio-temporal variability is very important for understanding and modeling the above processes. Numerous studies have focused on capturing the spatial variability of soil moisture across the study area (Crave and Gascuel-Odoux, 1997; Grayson and Western, 1998; Famiglietti et al., 1999). These studies were conducted at different spatial scales (1 m2 to a few km2), at different temporal scales (few days to few years), in a variety of hydrologic and climatic conditions (Hupet and Vanclooster, 2002), and with different measurement techniques (e.g. in

situ techniques and remote sensing). Studies of spatial variation of soil moisture using

ground-based measurements require detailed and accurate information, which can be time- and resource-consuming to generate with in situ techniques. Remote sensing gives the average spatial pattern of soil moisture over a large area known as a footprint, in which only predominant soil and vegetation types are usually used for calibration purposes (Mohanty and Skaggs, 2001). It also requires some form of groundtruthing using in situ techniques which is known as validation to convert the remotely sensed signal into a soil moisture estimate. But the

interpretation and validation of the remotely sensed signal is hampered by the high spatial variability of soil moisture (Cosh et al., 2004; Western et al., 2004), as well as by the mismatch in scales between satellite footprints and a ground sample (Western and Blöschl, 1999), the latter is usually 8-10 orders of magnitude smaller than the former. Therefore, to overcome these problems, approaches are needed to accurately estimate the soil moisture within remote

sensing footprint from only limited ground-based measurements.

Many studies have indicated that the spatial pattern of soil moisture in an area is persistant over time, which is referred as temporal stability (Kachanoski and De Jong, 1988). Vachaud et al. (1985) first introduced the concept of temporal stability as a particular location to maintain its soil wetness condition (wetter than the area mean, drier than the area mean, or close to the area mean) across the study area. He indicated that particular sites in the field always displayed mean behavior while others always represented extreme values. When the relative soil moisture ranked, certain sites always showed the same relative wetness, i.e. the temporal fluctuations of those particular sites were the same as that of the field average. For some sites, not only were the temporal fluctuations the same as the field average, but the actual soil moisture values were also the same. Grayson et al. (1998) concluded that temporal stability of the complete soil moisture pattern did not exist in the 10.5-ha studied catchment, and identified particular temporally stable sites (CASMM Sites: Catchment Average Soil Moisture Monitoring Sites) which represented the mean areal moisture content, instead of the complete soil moisture pattern throughout the entire studied area. Using the temporally stable site information, sampling schemes can be made more efficient by reducing the number of monitoring sites, while maintaining the accuracy of the network based estimate (Jacob et al., 2004; Cosh et al., 2006). Most of temporal characteristics are found on watershed or transect scales. Additional studies on the field scales are still needed (Kaleita et al., 2007).

The stable pattern of spatial variability of soil moisture has been correlated with relatively time-invariant properties such as topography. A number of studies demonstrated that the influence of relative elevation on the distribution of soil moisture (Famiglientti et al, 1998). Relative elevation is often correlated with various soil and topographic attributes that may influence soil water redistribution (e.g. specific contributing area, clay content). Krumbach (1959), Henninger et al.

(1976), Hawley et al. (1983), Robinson and Dean (1993) and Nyberg (1996) all found that moisture content is inversely proportional to relative elevation.

Geostatistics, which is based on the theory of regionalized variables (Goovaerts, 1997), is more and more used to characterize the spatial soil moisture pattern (Vachaud et al., 1985; Nyberg, 1996; Brocca et al., 2007), because it allows one to capitalize on the spatial correlation between neighboring observations to predict attribute values at unsampled locations. Besides providing a measure of prediction error (kriging variance), a major advantage of kriging over simpler

methods is that the sparsely sampled observations of the primary attribute can be

complemented by secondary attributes that are more densely sampled (P. Goovaerts, 2000). The objectives of the study are: 1) to explore the characteristics of the temporal stability of soil moisture in the field scale; 2) to apply geostatistical approaches for incorporating elevation into the spatial interpolation of soil moisture across a field during the growing season.

Location and Methods

Soil moisture data was collected across a working 10-ha corn-soybean rotation field, Brooks Field, just southeast of Ames, IA, during the 2004 and 2005 growing seasons. There are a total of 25 days (from mid-May to early July) in 2004 and 30 days (from early-May to Mid-August) in 2005 of data available for analysis. Three volumetric moisture content readings for 0-6 cm depth were taken using a Theta probe moisture meter at each of 78 locations which include 42 regular grid nodes with a 50-m interval and two transects with a 5-m interval. Elevation data was obtained from much denser grids (2-m interval) in the same field. Because of the data capacity of programming, the elevation data was refined to 4-m interval. The locations are given as UTM Easting and Northing, and the unit of soil moisture data is volumetric water content (%) and unit of elevation data is meter. Sampling locations for soil moisture and elevation are shown in Figure 1.

The surface soil moisture dataset was analyzed using the methods provided by Vachaud et al. (1985) to determine the temporal patterns of soil moisture throughout the whole field the monitoring period. The mean relative difference

1

1

m i ij j

m

δ

δ

=

=

∑

and its standard deviation

1/ 2 1

( )

1

m ij i i j

m

δ

δ

σ δ

=

⎡

−

⎤

= ⎢

⎥

−

⎢

⎥

⎣

∑

⎦

will be calculated, where,

j ij ij j

θ θ

δ

θ

−

= ,

θ

_ij is the moisture at the ith

location on the

j

th sampling occasion,

θ

_j is the field average of all

θ

_ij on the

j

th sampling

occasion, and m is the total number of sampling occasions. Locations with

δ

_iclose to zero

indicate sites having an average soil moisture close to field mean, whereas other locations

with

δ

_ihigher or lower than zero are over- or under-estimating the field mean, respectively.

442700 442800 442900 4 6 4 72 0 0 46 47 3 0 0 4 64 74 00 4 6 4 7 5 0 0 Easting (UTM) No rthing (UTM ) Surface inlet

Surface moisture sampling locations

Figure. 1 Soil Moisture Sampling Locations at Brooks Field. The contour lines represent elevation in meters. The stars represent sampling locations.

Analysis

Data description

Time series of soil moisture in Brooks Field in 2004 and 2005 (Figure. 2) show field mean soil moisture data differ from each other with respect with two growing seasons and the observing dates in each growing season. In both seasons, the data sets captured both dry and wet days, as well as the drying processes of the field after precipitation.

2004 0.00 2.00 4.00 6.00 8.00 10.00 134 139 144 149 154 159 164 169 174 179 184 189 Day of Year P re c ip ita ti on (i n c h ) 10.00 15.00 20.00 25.00 30.00 35.00 M ean V S M ( % )

Precipitation Mean Soil Moisture

2005 0.00 2.00 4.00 6.00 8.00 10.00 129 138 148 158 168 178 188 198 208 218 228 Day of Year P re c ipi ta ti on ( inc h) 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 M ean V S M ( % )

Precipitation Mean Soil Moisture

Figure. 2 Mean volumetric soil moisture with one standard deviation error bars in 2004 & 2005, the dates have been converted to days of year.

Temporal stability of soil moisture

Locations with negative mean relative difference underestimated the field average soil moisture, and locations with positive ones overestimated the field average. It’s notable that the ranges of mean relative moisture vary between two data sets (shown in Figure 3). The ranges of the mean relative soil moistures for Brooks field are from -17.0 to 28.4% in 2004 and from -18.3 to 25.8% in 2005, respectively. In general, the standard deviations vary from 3.0 to 11.4% in 2004, and 4.4 to 15.5% in 2005. The results indicate that soil moisture at some sites behaves consistently

(has small error bars) over time, where

δ

i _{approximated to zero with small error bars. In the}

Brooks field, the points 77, 61, 7, 59, 27, 99 in 2004 could be considered as the suitable sites to represent the field mean, and points 15, 85, 87, 89 in 2005 could be considered as the suitable sites to represent the field mean.

To characterize the value of field mean prediction using such stable points, all the stable

were used individually to predict the field average soil moisture content in both seasons. The result indicates that the time stable locations provide accurate prediction of the field mean with low variability (as shown in figure 4), which proved that the temporally stable locations can predict the field mean soil moisture well.

2004 77 61 7 59 27 99 -40 -20 0 20 40 M ea n R eal ti v e D if fe ren ce % 2005 87 85 83 15 -40 -20 0 20 40 M ean R el at iv e D ifferen ce %

Figure. 3 Ranked mean relative difference with one standard deviation error bars for the year of 2004 & 2005 in Brooks Field, respectively.

If a region exhibits time stable characteristics, selection of stable sampling points offers an efficient alternative to random sampling of many points (Jacobs & Mohanty, 2004). It is obvious that the temporally stable locations in two growing seasons are different from each other (Figure 3). It may not be sufficient to use the stable sites from only one year data, for the purpose of using temporally stable locations to capture the field mean average soil moisture conditions. Moreover, the mean relative difference for all the data in both season (Figure 5) indicated that the temporally stable locations in each season do not behave consistently in the two

consecutive growing seasons. Exploring the combination of the temporally stable locations from different growing seasons may provide more useful information in the future.

Field Mean vs. Stable sites- 2004&2005 14 18 22 26 30 34 14 18 22 26 30 34 Field M ean VSM (% V/V) T im e -s ta b le s ite V S M (% V /V ) Site 05_13 Site 05_83 Site 05_85 Site 05_87 Site 04_7 Site 04_27 Site 04_59 Site 04_61 Site 04_77 Site 04_99

Figure. 4 Comparison of field mean soil moisture content with sampling location using the most stable locations in 2004 & 2005. Dashed lines represent +/- 2% and +/-4%.

-30 -20 -10 0 10 20 30 40 m ean r e la ti ve d if fe re n ce ( % )

Figure 5. Ranked mean relative difference with one standard deviation error bars for all the observing dates in both seasons in Brooks Field

Quantifying spatial variability of soil moisture

In order to quantify the spatial variability across the field, the semivariogram of the spatially distributed data is required. The semivariogram measures the average dissimilarity between data separated by a certain distance. The estimated semivariogram for a given dataset is described by the equation:

[

]

∑

=

+

−

=

( ) 1

)

(

)

(

)

(

2

1

)

(

h N

h

u

z

u

z

h

N

h

α α α

γ

(1)

where

γ

( )h is the empirical semivariogram, N(h) is the number of pairs of data locations

which are separated by the distance

h

, and

z

(

u

_α

)

is the data value at location

u

_α.

Semivariograms for each data were computed, and subsequently a model was fitted to each date’s results according to the least square technique. The variogram properties for each data are shown in table 1. Spherical models were used to describe all the semivariograms. The spherical model with range a is described by the equation:

⎪⎩

⎪

⎨

⎧

₋

_≤

=

otherwise

a

h

if

a

h

a

h

h

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,

0

:

,

)

(

5

.

0

5

.

1

)

(

3 (2)

The ordinary kriging has been used to estimate the soil moisture contents at the unsampled location u as a linear combination of neighboring observations:

∑

=

=

( ) 1 *

)

(

)

(

)

(

u N OK OK

u

u

z

u

z

α α α

λ

with

(

)

1

) ( 1

=

∑

= u N OK

u

α α

λ

(4)

Ordinary kriging weights

λ

OK_α

(

u

)

are determined such as to minimize the estimation

variance,

Var

{

z

*OK

(

u

)

−

z

(

u

)

}

, while ensuring the unbiasedness of the estimator,

{

z

*

(

u

)

− u

z

(

)

}

=

0

E

_OK (Goovaerts, 2000).

Aside from dates 5/18/2004, 6/2/2004, 6/8/2004, 6/14/2004, 7/7/2004, the ranges of most of the models are within115 to 155 meters (shown in figure 6). All dates are similar in semivariogram shape, most being well-described by a simple spherical model. Most of the semivariograms reach a maximum around 150 m before dipping and fluctuating around a sill value, which can be found in semivariograms in 2005 as well (Figure 7). The so-called “hole effect” typically reflects pseudo-periodic or cyclic phenomena (Journel and Huijbregts, 1978, p. 403). Here, the hole effect relates to the existence of two lowest spots in the field (Figure 1) which creates two high-valued areas of soil moisture. Ordinary kriging using the spherical models has predicted the soil moisture at the field as well as the associated kriging standard errors as shown in table 2.

Figure 6. Semivariograms of soil moisture with fitted spherical models in 2004.

Figure 7. Semivariograms of soil moisture in 2005

Now, consider the situation where the soil moisture data are supplemented by elevation data available at all estimation grid nodes.

Kriging with an external drift (KED) uses the secondary information (elevation in this case) to derive the local mean of the primary attribute z, then performs simple kriging on the

corresponding residuals:

[

]

∑

=

−

=

−

( ) 1 * * *

)

(

)

(

)

(

)

(

)

(

u N KED SK KED KED

u

m

u

u

z

u

m

u

z

α α α α

λ

(5)

where

m

_KED*

(

u

)

=

a

₀*

(

u

)

+

a

₁*

(

u

)

y

(

u

)

, y(u) represents the elevation at location u in this case, and

) ( ), ( ) ( ) ( ) ( 1 * u u z u u z KED u N KED KED α α α α

λ

λ

∑

=

= is the kriging weights. Table 1 has summarized the

regression coefficients used in this study. The correlation coefficients R2 vary from day to day.

Most of them are around 0.4, some of them are smaller than 0.4 (for example, 0.1 for date 5/18/2004, and 0.22 for date 6/14/2004). There is no relationship between elevation and soil moisture wetness conditions. Besides elevation, there are also undoubtedly other attributes such as soil type, vegetation, and other topographic indices may have impact on the spatial distribution of soil moisture across the field. Nonetheless, while elevation may not explain the entire variability of the spatial patterns of the soil moisture, it does explain a large portion on

most dates. Overall, soil moisture and elevation has the highest correlation (R2=0 .54) than any

single day.

Table 1. Summary of the regression coefficients between soil moisture and elevation

Date

a

₁*

a

*0 R 2 Date

a

₁*

a

*0 R 2 5/17/2004 -1.99 645.58 0.39 6/14/2004 -0.98 336.51 0.22 5/18/2004 -0.78 273.50 0.10 6/17/2004 -1.33 445.86 0.35 5/19/2004 -1.78 585.31 0.42 6/18/2004 -1.48 489.96 0.34 5/20/2004 -1.82 596.10 0.40 6/22/2004 -2.09 686.64 0.41 5/21/2004 -1.69 552.19 0.37 6/23/2004 -2.32 753.65 0.46 5/28/2004 -3.48 1119.5 0.52 6/25/2004 -1.80 589.42 0.41

6/1/2004 -2.28 740.06 0.41 6/28/2004 -1.93 629.63 0.42 6/2/2004 -2.44 790.58 0.47 6/29/2004 -1.97 640.62 0.40 6/3/2004 -2.11 686.07 0.43 6/30/2004 -2.17 704.41 0.40 6/4/2004 -2.22 720.88 0.53 7/6/2004 -1.47 492.66 0.47 6/7/2004 -2.12 688.16 0.45 7/7/2004 -1.74 572.57 0.42 6/8/2004 -1.68 548.59 0.30 7/8/2004 -1.71 561.11 0.41 6/9/2004 -2.22 717.45 0.47 Overall -7.46 2340.70 0.54

Kriging with external drift has the interpolation results and the associated kriging standard errors shown in table 2.

The two interpolation tools have little difference with respect to the predicted field mean soil moisture (shown in table 2), but slight difference with respect to the mean kriging standard errors. The results indicated that OK has smaller mean kriging standard error than KED except the dates of 5/17/2004 (KED has smaller value), 5/28/2004 (same), 6/2/2004 (same), 6/22/2004 (same).

Table 2 Comparison of the predicted field mean soil moisture (Mean SM) and kriging standard error (Mean kriging SD) using OK and KED, respectively

Mean SM Mean kriging

SD Mean SM Mean kriging SD Date OK KED OK KED Date OK KED OK KED 5/17/2004 22.95 23.12 2.38 0.00 6/14/2004 29.53 29.64 1.49 1.79 5/18/2004 28.81 29.43 1.75 2.52 6/17/2004 28.46 28.54 1.66 1.80 5/19/2004 27.05 27.34 1.60 2.19 6/18/2004 25.41 25.55 1.84 2.03 5/20/2004 24.49 24.76 2.00 2.32 6/22/2004 30.02 30.02 1.55 1.55 5/21/2004 22.26 22.65 2.01 2.35 6/23/2004 25.97 25.97 1.64 1.64 5/28/2004 29.10 29.10 2.44 2.44 6/25/2004 26.22 26.53 1.33 1.91 6/1/2004 26.48 26.42 1.74 2.40 6/28/2004 24.57 24.90 1.38 1.91 6/2/2004 26.47 26.47 1.59 1.59 6/29/2004 23.45 23.75 1.55 2.28 6/3/2004 25.34 25.57 1.48 2.39 6/30/2004 22.54 22.95 2.29 2.64 6/4/2004 24.75 24.87 1.71 2.11 7/6/2004 31.51 31.68 1.02 1.41 6/7/2004 23.26 23.69 1.49 2.24 7/7/2004 27.72 27.77 1.52 1.73 6/8/2004 22.83 23.18 2.12 2.42 7/8/2004 24.57 24.80 1.74 2.01 6/9/2004 23.38 23.35 1.54 2.04

Conclusion

Temporal stability analysis of soil moisture data in two consecutive growing seasons for Brooks field revealed that there are locations in the field consistently representing the field mean soil moisture in each growing season. And these temporal stable locations have proved to predict the field mean soil moisture very well. However, the stable locations are different from each other in two seasons, so the information of stable locations from only one season is not sufficient for the efficient sampling plan to capture the field average moisture conditions. Also, there’s no clear indication for these stable locations behave consistently in the two consecutive growing seasons. Therefore, future work is necessary for testing if the combination of the stable locations from more than one season will provide more useful information.

The relationship between moisture patterns and the elevation was investigated for the field. The results indicated that the elevation explain as a large portion of the spatial variability of the soil moisture for most of the observing dates, as well as the overall spatial pattern for the growing season. There are also other invariant attributes like soil type, vegetation and other topographic indices having impact on the moisture patterns.

Geostatistical technologies, variogram analysis and kriging interpolation, were also used to explore the spatial moisture patterns only in 2004 growing season. The result indicated that taking denser elevation data as secondary information to predict the spatial pattern of soil moisture across the field (KED) have little difference on the field mean soil moisture from the ordinary kriging without considering any supplemented information, but the kriging standard deviations are a little bit larger than the original process.

In the future, more studies will be done to find out the mechanism about the relationship

between temporal stability of soil moisture across the field and the invariant attribute such as the elevation as well as the scale on which the relationship are exerted.

Acknowledgements

This research has been sponsored by the Iowa State University University Research Grant Program and by the NASA Terrestrial Hydrology Program.

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