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Published in Vadose Zone Journal 2:519-529 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

SPECIAL SECTION - ADVANCES IN MEASUREMENT AND MONITORING METHODS

Monitoring Temporal Development of Spatial Soil Water Content Variation

Comparison of Ground Penetrating Radar and Time Domain Reflectometry

J. A. Huisman*,a,b, J. J. J. C. Snepvangersa, W. Boutena and G. B. M. Heuvelinka

a Center for Geo-ecological Research (ICG), Institute for Biodiversity and Ecosystem Dynamics (IBED), Physical Geography, Universiteit van Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands
b Justus-Liebig University Giessen, Institute for Landscape Ecology and Resources Management, Heinrich-Buff-Ring 26-32, 35392 Giessen, Germany
* Corresponding author (sander.huisman{at}agrar.uni-giessen.de).

Received 7 February 2003.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
We compare the capability of ground penetrating radar (GPR) and time domain reflectometry (TDR) to assess the temporal development of spatial variation of surface volumetric water content. In the case of GPR, we measured surface water content with the ground wave, which is a direct wave between the sender and receiver through the upper centimeters of the soil. Spatial water content variation was measured on 18 d with GPR and TDR during a 30-d monitoring period. To ensure large fluctuations in the spatial water content variation, we created a heterogeneous pattern of water content by irrigation on 2 d. The temporal development of the spatial variation was studied by means of the variogram and interpolated water content maps. To compare GPR and TDR variograms, we estimated confidence intervals of the experimental variograms and the variogram model parameters with a jackknife approach and a first-order approximation of model parameter uncertainty. The results showed that the 95% confidence intervals of the GPR experimental variogram were one to two orders of magnitude smaller than the 95% confidence intervals of the TDR experimental variogram because of the larger number of GPR measurements. Consequently, the uncertainty in the variogram model parameters was also much lower for GPR, which meant that the temporal development of the fitted GPR variogram model parameters was easier to interpret. Furthermore, the larger GPR measurement volume resulted in a low spatial nugget variance of 1 x 10-6 to 1 x 10-9 (m3 m-3)2 because short distance variation was averaged. This meant that GPR accurately measured spatial correlation lengths, even in the case of low water content variation. Interpolated maps showing the increase of water content due to irrigation and the subsequent gradual drying of the soil were more accurate and reproducible for GPR. It was concluded that the noninvasive GPR measurements provide the means to accurately and consistently monitor the development of spatial water content variation in time.

Abbreviations: GPR, ground penetrating radar • TDR, time domain reflectometry


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
SURFACE WATER CONTENT is highly variable in both space and time. Variability of water content results from many processes acting over a range of temporal and spatial scales. Processes determining spatial water content variability include spatial heterogeneity of soil properties at scales from centimeters (Ritsema, 1999) to kilometers (Jackson and Le Vine, 1996), lateral water redistribution at scales of centimeters to tens or hundreds of meters under the influence of topography (Western et al., 1998), and water redistribution by vegetation (Bouten et al., 1992; Hupet and Vanclooster, 2002). Temporal variability of water content is often climatically determined; that is, the evaporation excess in the course of a year is a strong influence on the seasonal change of water content (Grayson et al., 1997). Furthermore, strong interactions between spatial and temporal variability have been reported. For example, Grayson et al. (1997) reported two preferred states of spatial water content patterns in a catchment situated in a temperate region of Australia. The wet state was dominated by lateral water movement leading to a strong spatial organization of water content along the drainage lines. The dry state was dominated by vertical fluxes, with only soil properties influencing the spatial pattern. Consequently, the spatial organization was much less pronounced in the dry state.

Measurements of the space–time variation of surface water content status over a range of scales (plots to continents) are desirable in many research fields. For example, a correct description of the evolution of antecedent water content patterns can improve simulations in event-based hydrological modeling (Merz and Plate, 1997). Similarly, knowledge of space–time water content patterns is of key importance in solute transport modeling because of the strong influence of water content on soil water fluxes (Ritsema and Dekker, 1998). Furthermore, the space–time variation of surface water content can be used to extract information about physical properties and processes within the entire vadose zone (e.g., Ahuja et al., 1993; Hoeben and Troch, 2000).

Currently, the only measurement technique that can potentially measure space–time variability of large regions with adequate spatial and temporal sampling density is remote sensing from either active or passive airborne platforms (Jackson et al., 1996; Famiglietti et al., 1999). However, to optimally use the large-scale remote sensing measurements, the transfer function between the measured response and water content needs to be known and understood. Accurate assessments of the spatial and temporal variability of water content within the radar footprint with typical pixel sizes in the range of hundreds of meters contribute to this understanding.

Unfortunately, studies on temporal and especially spatial variation of water content at the scale of hundreds of meters (hereafter referred to as field scale) show a wide variety of results (see the reviews in Western et al., 1998; Famiglietti et al., 1999). The accurate determination of field-scale spatial correlation in particular has proven to be difficult. Western et al. (1998) gave three possible reasons for the large differences in reported correlation lengths: (i) sampling density lower than correlation length, (ii) too few measurements for a reliable estimate of correlation length, and (iii) measurement error larger than water content variation. The first two points especially are typical problems of invasive, and therefore labor-intensive, water content measurement techniques with a small measurement volume, such as gravimetric sampling, capacitance measurements, and TDR. In this study, we tested GPR for measuring the temporal development of spatial variation of water content because potentially it does not suffer from these sources of errors. Ground penetrating radar is a noninvasive measurement technique that allows the acquisition of a large number of closely spaced measurements in a short time. In an equal time span, GPR can acquire 5 to 10 times more water content measurements than TDR. Furthermore, GPR has a larger measurement volume, which could be beneficial for accurately measuring spatial water content variation due to the averaging of small-scale variability.

The GPR technique is similar in principle to reflection seismics and sonar techniques. The radar produces high-frequency electromagnetic waves (MHz range), which are transmitted into the soil by a source antenna placed on the soil surface. The propagation velocity of these radar waves depends mainly on the soil permittivity, which is known to be strongly related to volumetric water content (Topp et al., 1980). Any subsurface contrast in dielectric properties will reflect part of the wave energy back to the surface. The reflected wave energy is then detected by the receiving antenna as a function of time (Davis and Annan, 1989). There are several methods to measure volumetric water content with GPR, including surface reflection (Chanzy et al., 1996), reflection from the groundwater table (van Overmeeren et al., 1997), and reflection from a soil horizon (Weiler et al., 1998), but here we focus on the velocity of the ground wave, which is the wave directly traveling from the source to the receiving antenna through the topsoil (Du and Rummel, 1994; Du, 1996). We use this particular wave because it is the only wave whose propagation distance is known a priori (e.g., the antenna separation); therefore, it is the only wave where the soil permittivity can be calculated from a single GPR measurement without knowledge of the depth of the reflecting layer. Furthermore, the ground wave can also be used in the absence of a clearly reflecting layer.

The aim of this study was to compare the capability of GPR and TDR to measure spatial variation in volumetric water content. In a previous paper (Huisman et al., 2002), the spatial water content variation measured with GPR and TDR on a single day were compared in detail. In this paper, the focus is on the temporal development of spatial water content variation. Therefore, we measured spatial variation of volumetric water content of a 60 by 60 m grassland with GPR and TDR on 18 d during a 30-d monitoring period. To ensure large fluctuations in spatial variation, we created a heterogeneous pattern of volumetric water content by irrigation on 2 d. The temporal development of spatial variation was studied by means of the variogram and interpolated water content maps.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 
Molenschot Dataset
We monitored surface volumetric water content of a pasture (60 x 60 m) located in Molenschot, in the south of The Netherlands (51°35' N and 4°52' E) for a period of 30 d. The soil was classified as a Plaggept according to U.S. soil taxonomy (Soil Survey Staff, 1975). The textural class of the topsoil was sandy loam as determined by grain-size analysis of 25 samples (66.5% sand, 30.2% silt, and 3.3% clay on average). Beneath the sandy loam there was a less permeable clay layer at the 0.9- to 1.0-m depth, which periodically caused water stagnation, as evidenced by gley mottles within the sandy loam from 0.75 to 0.90 m. Ditches bound the field on the north and east sides.

To ensure large fluctuations in spatial water content variation, we created a heterogeneous spatial pattern of water content by irrigation with four types of sprinklers (A–D) with different ranges and intensities. The monitoring period started on 16 August (Day 229) and ended on 14 Sept. 2000 (Day 258). We irrigated approximately one-third of the field early in the morning on Days 230 and 245 (0542 and 0400 h, respectively). Figure 1 shows the schematic irrigation pattern for the two irrigation days. Table 1 describes the irrigation duration and intensity for the four types of sprinklers. On Day 230, the high intensity sprinklers (B–D) irrigated for 1.75 h, whereas the low intensity sprinkler type A irrigated for 4 h. On Day 245, all sprinkler types irrigated for 4 h. The area and intensity of each sprinkler type was measured by determining the irrigation distribution around one sprinkler per sprinkler type with water collecting cups and assuming that all sprinklers of one type had the same irrigation characteristics. At some locations, the amount of irrigation was larger than the infiltration capacity, which resulted in ponding and subsequent overland flow (mainly close to sprinkler types C and D). The average irrigation on the entire site was 9.2 mm on Day 230 and 14.6 mm on Day 245.



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  		Fig. 1. Measurement locations for manual time domain reflectometry (TDR) measurements and ground penetrating radar (GPR) transects with a schematic representation of the imposed irrigation with four sprinkler types (marked A–D).

 

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  		Table 1. Description of four types of sprinklers (A–D) used in the irrigations on Days 230 and 245. Area and intensity of each type of sprinkler was determined with M cups during the experiment.

 
In the 30-d monitoring period we measured 18 water content maps with GPR and TDR. The minimum time interval between measurements was 4 h and the maximum time interval was 4 d. A meteorological station of 2-m height located in the southwest corner of the site provided climatic variables (i.e., precipitation, air temperature, relative humidity, wind velocity, and net radiation). Figure 2a shows the course of the daily precipitation during the experiment. It can be seen that the two irrigation days (marked with arrows) were closely followed by large precipitation events.



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  		Fig. 2. (a) Daily precipitation (arrows indicate irrigation events), (b) temporal development of spatially averaged volumetric water content (SWC) (m3 m-3), and (c) temporal development of total volumetric water content variance for ground penetrating radar (GPR) and time domain reflectometry (TDR). The 95% confidence interval in Fig. 2b is based on the standard error of the mean. Please note that the y axis scales are different for GPR and TDR in Fig. 2c.

 
Volumetric Water Content Measurements
We used a pulseEkko 1000 GPR system with a 200 V transmitter (Sensors and Software, Mississauga, ON, Canada) and broadband antennas with a center frequency of 450 MHz (in air) and a frequency bandwidth of 450 MHz (Davis and Annan, 1989). We measured 12 60-m transects (see Fig. 1) with a time window of 60 ns, a sampling rate of 60 ps (1000 sampling points per trace) and 16 stacks per trace. The transect measurements were made by placing the antennas on sleds with an antenna separation of 1.54 m and triggering the radar each 0.5 m with an odometer (121 measurements per transect). The southernmost transect was only 45 m because of the presence of the meteorological station in the southwest corner of the field. Therefore, the number of GPR measurements per day was 1422. We used REFLEX (Sandmeier Scientific Software, Karlsruhe, Germany) for standard data processing, including a "dewow" filter to remove low-frequency induction effects of the radar equipment and a down-trace averaging filter to remove noise.

The GPR refractive index, nGPR, was calculated for each measurement from the arrival times of the ground and air wave at the known antenna separation x (1.54 m) with

[1]
where c is the electromagnetic wave velocity in air (3 x 108 m s-1), v (m s-1) is ground wave velocity, and tGW (s) and tAW (s) are the arrival times of the ground wave and air wave, respectively. The arrival times of the air and ground wave were obtained by semiautomated time picking in REFLEX. The semiautomated procedure consisted of (i) picking a phase in the first measurement of each transect, (ii) using an automated phase-follow algorithm to find the same phase in the other measurements of the transect, and (iii) shifting the phase picks to the preceding zero-crossing. This procedure is only semiautomated because (i) the user needs to consistently pick the same phase for the air and ground wave for the first measurement of each transect and (ii) the results of the phase-follow algorithm need visual inspection. In the case of the air wave, we used the average arrival time per transect because the air wave was disturbed and not equally recognizable in each measurement because of interference with the sleds (see Huisman and Bouten, 2003).

The sampling volume of water content measurement with the ground wave is determined by the antenna separation, the width of the antenna, and the sampling depth. Unfortunately, the depth of influence of the ground wave is not yet well defined. Du (1996) suggested that the influence depth is approximately one-half of the wavelength. Sperl (1999) reported that the depth of influence was indeed a function of wavelength, but from a modeling exercise he concluded that the influence depth is about 0.145{lambda}1/2. The results of Sperl (1999) do not contradict those of Huisman et al. (2001), who found no systematic differences between GPR measurements based on the ground wave (225 and 450 MHz) and TDR measurements with a 0.1-m-long probe. However, their results were based on volumetric water content measurements for different soil types, presumably with relatively homogeneous water content profiles with depth, and did not include a comparison with TDR probes of different lengths. In a comparison of ground wave data and gravimetric water content measurements at 0 to 0.10, 0.10 to 0.20, and 0 to 0.20 m, Grote et al. (2003) found that water content measurements obtained using 450-MHz and 900-MHz data showed the highest correlation with the soil water content values averaged over the 0- to 0.20-m range. Clearly, the zone of influence of the ground wave as a function of antenna frequency is not yet well understood, and further research on this important topic is required. For more information on the use of the ground wave for volumetric water content measurements, the reader is referred to Huisman et al. (2003). For more information on the GPR methods used in this study, the reader is referred to Huisman et al. (2002).

We collected TDR measurements at 216 locations, 156 locations on a 5 by 5 m grid and 60 nested locations to estimate short distance variation (diamonds in Fig. 1). We used a Tektronix 1502 cable tester (Beaverton, OR) and a single 0.1-m-long three-wire probe (Heimovaara, 1993) inserted vertically into the soil. We used a 0.1-m probe because water content measurements with these probes corresponded well with GPR measurements, based on the ground wave velocity measurements in Huisman et al. (2001). The TDR refractive index of the soil was calculated according to

[2]
where {Delta}ts (s) is the travel time of the electromagnetic signal in the soil obtained with the travel time analysis presented in Heimovaara and Bouten (1990) and L is the length of the probe obtained with the calibration procedure described in Heimovaara (1993).

We determined a site-specific calibration between refractive index and volumetric water content ({theta}) by simultaneous weight and TDR measurements on 14 soil samples taken from the topsoil in 0.1-m-high and 0.05-m-diameter stainless-steel rings (Herkelrath et al., 1991). The known volume of the rings allowed conversion of the measured weight loss to volumetric water content. We used the empirical calibration equation proposed by Herkelrath et al. (1991) because it is one of the few models that ensures equal weighing of dry and wet areas in heterogeneous samples. The resulting calibration equation is

[3]
with an R2 of 98.7% and a standard error of 0.012 m3 m-3. Huisman et al. (2001) showed that there was little difference between GPR and TDR calibration equations for measurements made with 225 and 450 MHz antennas. Therefore, we also used Eq. [3] to convert nGPR to volumetric water content.

Geostatistical Analysis
The semivariance between measurements at locations x and x + h is defined as

[4]
where E signifies expectation, and h is the distance separating x and x + h. The function relating semivariance to h is the variogram. Spatial correlation manifests itself in the variogram by a monotonic increase from the origin with increasing h. The variogram as expressed in Eq. [4] must be estimated from the data, and this is done by fitting a variogram model to the experimental variogram computed from the data according to

[5]
where N(h) is the number of pairs of observations separated by a distance h and z(xi) denotes an observation at location xi. Different types of variogram models can be fitted to the experimental variogram. In this study we used the spherical model

[6]

The nugget variance c0 [(m3 m-3)2] represents short distance variation and measurement error. The variogram range a (m) describes the correlation length. In the spherical model, the semivariance between two measurements becomes constant at distances larger than the variogram range, where the sill variance c0 + c [(m3 m-3)2] is reached. To ensure that the variograms reached a stable sill variance, the Molenschot data required detrending with a second-order polynomial trend plane in the x–y coordinates. To not disturb the comparison between GPR and TDR, we detrended the GPR and the TDR measurements with the same trend plane calculated from the GPR measurements.

Meaningful comparison of different experimental variograms and associated variogram model parameters is difficult without knowledge of the magnitude of their uncertainty. In this study, we use the jackknife method presented by Shafer and Varljen (1990) to estimate the confidence limits on the experimental variogram. Following Shafer and Varljen (1990), we partition the entire dataset of size n into g subgroups of size m such that n = gm. Let {gamma}(h)all be the experimental variogram estimated from the entire dataset and let {gamma}(h)j be the experimental variogram estimated from all the data remaining after removing the jth partition, nj = (g - 1)m. Partition-dependent estimates Jj[{gamma}(h)] are then calculated according to

[7]

The final jackknife estimate J[{gamma}(h)] of the experimental variogram is

[8]

The partition jackknife estimates, Jj[{gamma}(h)], may be used to construct confidence intervals about the jackknife estimate of the experimental variogram. The variance, {sigma}2J(h), of the jackknife estimate is estimated by

[9]

We used ±2 times {sigma}J(h) to approximate the 95% confidence interval of the experimental variogram.

In the case of TDR we used the classical jackknife where data re-use is maximized by requiring that the number of partitions, g, equals the number of data; that is, g = n and m = 1. The classical jackknife estimate is then based on sequentially deleting a single data point and recomputing the experimental variogram. In the case of GPR, the classical approach was too computationally intensive because of the size of the dataset. Therefore, we investigated the stability of {sigma}J(h) as a function of g to determine the optimum number of partitions, as was suggested by Shafer and Varljen (1990). The objective is to minimize g, thereby maximizing computational efficiency, while maintaining a stable estimate of {sigma}J(h). This approach resulted in g = 20, which meant that the GPR jackknife estimate was based on sequentially deleting blocks of 70 data points and recomputing the experimental variogram.

The variogram model was fitted to the experimental variogram with a weighted least squares (WLS) procedure. The WLS procedure takes into account the uncertainty of each point in the experimental variogram, in our case approximated by the jackknife variance {sigma}J2(h). The goal of the WLS procedure is to minimize

[10]
where {theta} represents the model parameters to be estimated, {Sigma}-1 is the inverse of the variance–covariance matrix of the experimental variogram, {Gamma} is the vector of the experimental variogram values at lags h and {Gamma}({theta}) is a vector with variogram model values at these lags. In this study, the diagonal of {Sigma} was filled with {sigma}2J estimates for each lag, and the nondiagonal elements were set to zero because the covariances between the lags were unknown. The WLS optimization algorithm was based on the Nelder–Mead simplex direct search method.

The uncertainty of the variogram model parameters can be approximated by the variance-covariance matrix of the inversion (Tarantola, 1987; Woodbury and Sudicky, 1991; Pardo-Iguzquiza and Dowd, 2001a)

[11]
where S is the K x M Jacobian or sensitivity matrix for which the ijth element is [Sij] = {partial}{gamma}(hi)/{partial}{theta}j, K is the number of experimental variogram lags, and M is the number of variogram model parameters. S is evaluated for the optimized WLS estimates of the model parameters.

There are two drawbacks to the method used here. First, the covariance between the lags of the experimental variogram is neglected in the WLS and the approximation of Cm. A complete evaluation of {Sigma} including the lag covariances was presented by Pardo-Iguzquiza and Dowd (2001b). Unfortunately, the evaluation is computationally exhaustive for GPR because the number of calculations is of the order n4. However, a complete evaluation of {Sigma} for the TDR datasets, where n is much smaller, showed that the model parameter uncertainty was not consistently different when covariances were included in Eq. [10]. Second, the optimization in Eq. [10] is nonlinear, and therefore, the posterior error distribution is potentially non-Gaussian. The implication is that the variances in Cm are hard to interpret in terms of confidence intervals. Possible solutions of this problem, such as Markov Chain Monte Carlo methods for parameter uncertainty assessment (e.g., Kuczera and Parent, 1998; Vrugt et al., 2002) are beyond the scope of the present study. Despite these provisos, we believe that the presented method provides a first estimate of uncertainty and is certainly useful in a comparison of experimental and modeled variograms, as in this study.

Interpolated water content maps were obtained by universal kriging on a 1 by 1 m grid. We used universal kriging because this interpolation scheme allows the inclusion of trends. To compensate for the difference in support (measurement volume) between GPR and TDR, we used point kriging for the GPR measurements and block kriging for the TDR measurements. In block kriging we consider a finite (block) support, with the size of the measurement volume of GPR, and estimate the mean volumetric water content of these blocks. The interpolations were done with GSTAT (Pebesma and Wesseling, 1998). For more information on geostatistical interpolation the reader is referred to the textbooks of Goovaerts (1997) and Webster and Oliver (2001).


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 REFERENCES
 
Figure 2b shows the temporal development of the mean field volumetric water content measured with GPR and TDR and the 95% confidence interval based on the standard error of the mean for both methods. The precipitation, including the two irrigation days (marked with arrows), is shown in Fig. 2a. Clearly, the temporal development of mean water content is dominated by the large precipitation events on Days 232 through 234 and Day 246, but the irrigation events on Days 230 and 245 can also be recognized as small peaks in the mean water content. The temporal development of the mean field water content measured with GPR and TDR is reasonably similar. The mean difference between GPR and TDR is 0.004 m3 m-3, and the root mean squared difference is 0.015 m3 m-3. The fairly large root mean square difference is caused by the significantly lower temporal variation in mean water content measured with GPR as compared with TDR, which could indicate that the effective sampling depth of GPR is somewhat larger than the 0.1-m sampling depth of TDR, as was also suggested by Grote et al. (2003). Again, it seems that further research on the GPR sampling volume is of crucial importance.

Figure 2c shows the temporal development of the spatial variance of volumetric water content measured with GPR and TDR. Note that the water content variance measured with TDR is about three times as high as the variance measured with GPR (different y axis) due to the different measurement volume of both methods. As expected, the spatial variance of water content is highest directly after the two irrigation events because we created a heterogeneous water content pattern.

Figure 3 shows a selection of the experimental variograms with 95% confidence intervals and the modeled variograms for GPR and TDR. The experimental variograms of GPR (top row) have much narrower confidence intervals than the experimental variograms of TDR (bottom row). The main reason for this higher confidence is the larger number of pairs in each variogram lag for GPR. Note especially the narrow confidence intervals for short separations (<5 m) in the case of GPR as compared with those of TDR at these separations. This illustrates the benefit of GPR, which allows closely spaced measurement, compared with an invasive measurement technique such as TDR, which requires an extra measurement effort to determine short distance variation (i.e., clustering of observations). The relatively large increase in GPR semivariance between 5 and 6 m visible for Day 229 and 230 is an artifact of the data acquisition. All measurements with separations <5 m are from the same transects, whereas larger separations also contain data pairs from different transects. Apparently, the within-transect water content variation is somewhat smaller than the between-transect variation. Most likely, this artifact was introduced because the GPR measurements were acquired, processed, and analyzed transect by transect.



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  		Fig. 3. Variograms of volumetric water content (m3 m-3) measured with ground penetrating radar (GPR) (top row) and time domain reflectometry (TDR) (bottom row) for four selected days. Please note that the y axis scales are different for GPR and TDR.

 
The temporal development of the modeled variogram parameters is given in Fig. 4 for GPR (left column) and TDR (right column). The 95% confidence intervals of each model parameter obtained from the covariance matrix of the inversion Cm are also shown. Figure 4c and 4d show the temporal development of the sill variance, which shows similar behavior as the spatial variance of water content despite detrending of the data. The narrow confidence intervals of GPR resulted in accurate estimates of the sill variance, whereas the large uncertainty in the experimental variogram of TDR resulted in a large uncertainty in the TDR sill variance. The lower bound of the 95% confidence is below zero on several occasions for TDR, indicating that the posterior error distribution is not normally distributed and that the confidence intervals should be interpreted with care.



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  		Fig. 4. (a,b) Temporal development of daily precipitation, including irrigation, (c) sill variance for ground penetrating radar (GPR), and (d) time domain reflectometry (TDR), (e) variogram range for GPR and (f) TDR, and (g) nugget variance for GPR and (h) TDR. Please note that the y axis scales are different for GPR and TDR in Fig. 4c and 4d and Fig. 4g and 4h.

 
The sill variance was lowest for saturated conditions. The large precipitation events on Days 232 through 234 completely saturated the soil and reduced the sill variance to a minimum of 1.4 x 10-4 (m3 m-3)2 for GPR and 6.0 x 10-4 (m3 m-3)2 for TDR at Day 236 [spatial variance was reduced to 3.3 x 10-4 (m3 m-3)2 and 8.3 x 10-4 (m3 m-3)2, respectively]. In the drying period from Day 236 to 245 the variance increased steadily; this was more pronounced for GPR. An increase in variance with decreasing volumetric water content close to saturation was also reported by Famiglietti et al. (1999), Western et al. (1998), and Hupet and Vanclooster (2002) but contradicts results found by others (e.g., Famiglietti et al., 1998). In our opinion, low variability of volumetric water content close to saturation can be expected for small reasonably homogeneous fields, such as in this study, simply because of the upper limit provided by the saturated volumetric water content. Differential drying due to microtopography, spatial patterns in root water uptake, and drainage may increase spatial variation in surface water content.

Figure 4e and 4f show the temporal development of the variogram range measured with GPR and TDR. For both methods, the introduction of large-scale volumetric water content structures by irrigation (sprinkler type A) on Days 230 and 245 increased the fitted variogram ranges. At first sight, there are large differences in the fitted variogram ranges for GPR and TDR. However, the large uncertainty for the TDR ranges indicates that the differences are not significant for most days. The large confidence intervals for Days 234 and 235 for TDR are caused by the nugget/sill ratio of 1 at these days, which means that the range becomes undefined (often taken as zero). A nugget/sill ratio close to 1 indicates that the sum of measurement error and short distance variation make up a large part of the total water content variation. Figure 4g and 4h compare the GPR and TDR nugget variance. The GPR nugget variance is very low because of the larger measurement volume, which averages short distance variation. The remaining GPR nugget is in the order of 0.001 to 0.003 m3 m-3, which is close to the reproducibility of water content measurements reported by Huisman and Bouten (2003). Generally, it can be concluded that the modeled variogram parameters determined from GPR measurements are more reliable than the parameters determined from TDR measurements for two reasons: (i) low uncertainty in the GPR experimental variograms and (ii) low GPR nugget/sill ratio, which avoids inaccurate and uncertain variogram range estimates.

Figure 5 shows the interpolated volumetric water content maps measured with GPR, and Fig. 6 shows the interpolated volumetric water content maps measured with TDR. There is a general agreement between the GPR and TDR maps. For example, both series of maps indicate that the southwest corner is driest. However, there are also some striking differences between the water content maps measured with GPR and TDR. The difference in appearance between TDR maps is caused by the day to day variation in the modeled variogram parameters. In the case of the nugget variograms of Days 233 and 234, the interpolated water content maps are very smooth (i.e., only the water content trend is visible), whereas other interpolated maps appear spotted due to the small variogram range of <5 m, which singles out individual measurements because the TDR grid separation was 5 m. The water content maps measured with GPR have a more coherent appearance because of the consistency of the fitted GPR variograms.



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  		Fig. 5. Interpolated volumetric water content maps (m3 m-3) based on ground penetrating radar (GPR) measurements.

 


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  		Fig. 6. Interpolated volumetric water content maps (m3 m-3) based on time domain reflectometry (TDR) measurements.

 
The large-scale features of the water content pattern created by irrigation can clearly be recognized in the water content maps measured with GPR (Days 230 and 245 in Fig. 5). The drying of the soil after irrigation was nicely captured in the water content maps of Days 231 and 232. On Day 245, even the west boundary of the imposed zigzag line (a relatively small feature, see Fig. 1) can be recognized. There are also numerous persistent small-scale features in Fig. 5, which are probably caused by small-scale heterogeneities in topography or soil texture.

In contrast, the heterogeneous water content pattern created by irrigation can hardly be recognized in the TDR maps. Of course, this is partly because of the lower number of TDR measurements and the inherent smoothing of kriging. For example, Snepvangers et al. (2002) showed that the interpolation of the TDR measurements could be improved with the more elaborate technique of spatial-temporal kriging with external drift, which allows the inclusion of extra process information such as net precipitation. Nevertheless, it should be remembered that the time to acquire the water content maps was approximately equal for GPR and TDR; that is, the higher number of GPR measurements is not associated with a larger measurement effort.

Figure 7 shows the increase of volumetric water content due to irrigation. These water content increase maps were obtained by subtracting the water content map of Day 244 from the three maps measured at Day 245. The increase of water content measured with GPR (top row) is consistent. The drying of the soil after irrigation in the course of Day 245 is visible. The mean difference of water content measured with GPR decreased from 0.018 m3 m-3 at Time 245.47 via 0.016 m3 m-3 at Time 245.64 to 0.014 m3 m-3 at Time 245.81. The water content increase maps measured with GPR also agree on smaller details, such as the U-shaped increase pattern of the large sprinkler located at coordinates (15, 45) and the position of the zigzag line. The increase of water content measured with TDR is less consistent and shows less detail. Especially the resulting map for Time 245.64 seems incongruous. The mean increase of water content measured with TDR varied from 0.014 m3 m-3, via 0.030 to 0.015 m3 m-3. The lack of consistency in the water content increase maps measured with TDR as compared with GPR cannot be blamed on the difference in sampling density for GPR and TDR, as the inconsistencies in the TDR maps are much larger than the uniform grid spacing of 5 by 5 m. This was also confirmed by calculating the water content increase maps measured with GPR with the same number of measurements as the TDR maps (results not shown). Therefore, the high reproducibility of spatial patterns measured with GPR is attributed to the positive effect of using a larger measurement volume, which averages short distance variation and leads to a lower sensitivity to small-scale effects.



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  		Fig. 7. Increase of volumetric water content (m3 m-3) due to irrigation measured at three times on Day 245 with ground penetrating radar (GPR) (top row) and time domain reflectometry (TDR) (bottom row).

 

   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
REFERENCES
 
We evaluated the capability of GPR and TDR to measure the temporal development of spatial water content variation during a 30-d monitoring period. We created a heterogeneous water content pattern by irrigation with different sprinkler types on 2 d. The temporal development of the mean field water content was reasonably similar for GPR and TDR, although GPR measured less temporal water content variation. As expected, the temporal development of the field water content variance showed that GPR measured less variation than TDR because of the larger measurement volume. For both methods, the water content variance increased with decreasing mean water content.

To compare GPR and TDR variograms, we assessed confidence intervals for the experimental variograms and the variogram model parameters. The confidence intervals of the experimental variogram were much smaller for GPR than for TDR because of the larger number of GPR measurements. The small confidence intervals of the experimental GPR variograms also resulted in reliable variogram model parameters. For the TDR measurements, these model parameters were much less reliable despite the relatively large sample size of 216 TDR measurements. Furthermore, the small measurement volume of TDR resulted in a high TDR nugget variance, which led to unreliable estimates of correlation length when the nugget variance was a substantial part of the sill variance. Comparison of the uncertainty in the modeled variogram range for GPR and TDR showed that the apparently large differences in variogram range were not significant for most days. This indicates the usefulness of reporting confidence intervals for experimental variograms and fitted variogram model parameters. Despite the approximations in the assessment of the confidence intervals, we feel that it should be common practice to report uncertainty measures, especially when the variogram model is not only used in interpolation but is also used as a summary of spatial or temporal structure. This would help in the comparison of different studies (or methods) and the evaluation of the significance of measured temporal changes in spatial variation.

The interpolated water content maps of GPR and TDR showed the same general behavior, but differed strongly in details. The TDR maps were dominated by fluctuations in the fitted TDR variogram model parameters (especially the range parameter), which changed the appearance of the interpolated TDR maps from spotted in the case of variogram ranges below the grid separation to smooth in the case of high nugget variances and long variogram ranges. The GPR maps were much more consistent. This was confirmed by calculating water content increase maps for the irrigation, which clearly showed the high reproducibility of spatial patterns of water content measured with GPR.

It can be concluded that GPR is an attractive alternative to other measurement techniques for monitoring temporal development of spatial water content variation at the field scale. It provides reliable estimates of spatial variation of surface water content both in terms of variogram model parameters and interpolated water content maps. Ground penetrating radar allows the quick acquisition of large datasets with closely separated measurements because measurements can be made while "on the move." Furthermore, the larger GPR measurement volume averages short distance variation and reduces the nugget variance to the reproducibility of the GPR analysis, which was found to be high. Of course, the use of GPR restricts the range of measurable water content patterns to those that are larger than the measurement volume. If small-scale water content variation (<1.5 m) is of importance, then the use of one of the traditional measurement techniques, such as TDR, is more appropriate.


   ACKNOWLEDGMENTS
 
NWO-ALW grants 750-19-804 (J.A. Huisman) and 809-32-003 (J.J.J.C. Snepvangers) financially supported this study. We thank S.C. Dekker, M. van der Gulik, B. Jansen, K. Raat, M. van der Velde, A. Visser, P. de Willigen, and especially L. de Lange for assistance during the fieldwork period.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 REFERENCES
 




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