Correcting temperature sensitivity of ECH<sub>2</sub>O soil moisture sensors

Correcting temperature sensitivity of ECH2O soil moisture sensors

Introduction

In many natural and engineered soils, the output of ECH2O soil moisture sensors are sensitive to variations in the soil temperature. The temperature sensitivity is not caused by the ECH2O sensors themselves, which are almost perfectly insensitive to temperature changes, but rather the electrical characteristics of the soil, which can be quite sensitive to temperature changes. The ECH2O sensors measure volumetric water content (VWC) by measuring the dielectric permittivity (ε) of the bulk soil. ε in the soil is a complex quantity with both real (ε′) and imaginary (ε″) components. ε′ is the real dielectric permittivity of the soil constituents and has a negative correlation with temperature. ε″ is related to dielectric losses, and more importantly, electrical conduction through the soil.

The ability of a soil to conduct electrical current or electrical conductivity (EC) is related to VWC and the amount of free ions in the soil (solute content). The EC of a soil has a strong positive correlation to temperature. The opposing temperature sensitivities of the real and imaginary components of the dielectric permittivity can be thought of as opposing forces in the soil. In some soils, ε′ dominates, and an increase in temperature causes a decrease in the VWC measured by the ECH2O sensor. In other soils, ε″ dominates, and an increase in temperature causes an increase in the VWC measured by the ECH2O sensor. In some soils, the two components closely balance each other, and there is no apparent temperature sensitivity in the VWC measurement. Because of these complex interactions, it is impossible to determine a generic correction factor for temperature that can be applied to all soils.

The older ECH2O sensors (EC-10 and EC-20) operate at a low measurement frequency and are more strongly affected by ε″, meaning that there is often a positive relationship between temperature and measured VWC. The new generation of ECH2O sensors (EC-5, 5TM, 5TE) operate at a much higher measurement frequency and are much less affected by salts in the soil (ε″). With these sensors, the temperature sensitivity is generally small and can be either negative or positive. It should be noted that any ECH2O sensor buried at a depth of more than about 15 cm in the soil, or under a full vegetative canopy, will have little or no noticeable temperature sensitivity due to the very small diurnal fluctuations in soil temperature at these depths or under a closed canopy.

The three strategies described below for correcting the temperature sensitivity of ECH2O sensors are meant primarily for users who have sensors placed in the top 15 cm of the soil profile under a bare surface, or whose sensors otherwise undergo strong temperature cycling.

Strategy 1: multiple regression analysis

If temperature data are available at the same location as the ECH2O sensor (i.e., 5TM or 5TE sensor), then a multiple regression strategy can be used to relate the true VWC to the measured VWC and temperature data. The general goal is to construct a mathematical model (equation) of the form

Where VWCmeas is the VWC measured by the ECH2O sensor, Tsoil is the soil temperature at the location of the sensor, and C1 – C3 are empirical coefficients determined by multiple regression on field data. The steps below describe how to use the regression tool in Excel and co-located ECH2O sensor and temperature data to determine the values of C1 – C3 for a particular soil.

Requirements:

The requirement for this method is co-located temperature and ECH2O sensor output data in the soil that you wish to construct the correction model for. The data must have at least two (preferably three or more) 24-hour periods with no rain or irrigation events. For maximum effectiveness, the chosen 24-hour periods should have different average VWC that span the range from wet soil to dry soil (i.e., one 24-hour period with dry soil, one with moderately wet soil, and one with quite wet soil).

Method:

1. Identify three or more 24-hour periods to include in the data analysis (see Figure 1 for example). These periods should meet the following qualifiers:

1.1. no precipitation or irrigation in each 24-hour period

1.2. group of 24-hour periods spans the range of expected VWC

1.3. temperatures at beginning and end of 24-hour period are comparable

1.4. no anomalies present in the selected data

Figure 1. Example of three 24-hour periods chosen from a data set (shown under shaded boxes). The endpoints used for the linear interpolation example data shown in Figure 2 are indicated.

2. Interpolate VWC data between endpoints. To determine the non-temperature affected VWC of the soil during each 24-hour period, constant drainage/evaporation is assumed over the period, and VWC is interpolated as a straight line between the two endpoints of each 24-hour period. This is easily accomplished in Excel by plotting the VWC at the two endpoints on the Y-axis against time on the X-axis. Then, use the trendline function to draw the regression line between them (see Figure 2). The resulting linear equation is then applied to all of the time data in that 24-hour period to interpolate between the two endpoints. Often it is easiest to assign an arbitrary time scale to the data for this part of the correction instead of the time stamp your data acquisition system outputs. For example, if you are collecting data at 30-minute intervals, you would assign X-axis values of 1 to 49 during the interpolation routine, or values of 1 to 25 for hourly data (column A in Table 1). Note that this process must be repeated for each of the 24-hour periods.

Figure 2. Linear interpolation between two endpoints of one 24-hour period (indicated in Figure 1). The X-axis is column A from Table 1, and the Y-axis is column E from Table 1. The linear equation was generated using the trendline function.

 

 ABCDEF
1Timescale for InterpolationTimeVWCmeasTVWC for InterpolationInterpolated VWC
218/6/2006 11:000.15417.360.1540.154
328/6/2006 12:000.15518.93=-0.0000833*A3+0.154
438/6/2006 13:000.15519.740.154
548/6/2006 14:000.15519.930.154
658/6/2006 15:000.15620.770.154
768/6/2006 16:000.15621.870.154
878/6/2006 17:000.15723.110.153
988/6/2006 18:000.15724.410.153
1098/6/2006 19:000.15725.010.153
11108/6/2006 20:000.15724.140.153
12118/6/2006 21:000.15623.260.153
13128/6/2006 22:000.15522.440.153
14138/6/2006 23:000.15421.580.153
15148/7/2006 0:000.15420.830.153
16158/7/2006 1:000.15420.160.153
17168/7/2006 2:000.15419.610.153
18178/7/2006 3:000.15319.030.153
19188/7/2006 4:000.15318.420.153
20198/7/2006 5:000.15217.870.152
21208/7/2006 6:000.15217.470.152
22218/7/2006 7:000.15117.070.152
23228/7/2006 8:000.15116.680.152
24238/7/2006 9:000.15116.450.152
25248/7/2006 10:000.15116.570.152
26258/7/2006 11:000.15217.270.1520.152
Table 1. Example of linear interpolation for a single 24-hour period. Note that the formula shown in cell F3 comes from the linear regression equation from Figure 2, and is applied to cells F3 to F25. Also note the arbitrary time scale in column A. This is often much easier to work with than the timestamp data from many data acquisition systems.

 

3. Combine all 24-hour periods and run a multiple regression. In Excel, this is easiest accomplished by pasting data from all 24-hour periods into the same columns (see Table 2). Then run the regression tool: Tools>Data Analysis>Regression. Select the interpolated VWC column from step 2 as the Y-variable (C2:C76 in Table 2), and measured VWC and Temperature as your X-axis variables (A2:B76 in Table 2). The regression tool will output several descriptive statistics and the multiple regression coefficients (see Table 3). The coefficients X Variable 1 and X Variable 2 are C1 and C2 in Equation 1 above, and the Intercept is C3. Note that X Variable 1 is the coefficient for the first (leftmost) column of the X-axis variable range (in this case measured VWC).

 

 ABC
1VWCmeasTInterpolated VWC
20.09825.420.0979583
30.09925.630.0979166
40.09926.870.0978749
50.128.580.0978332
60.10230.430.0977915
70.10332.270.0977498
80.10533.920.0977081
90.10635.230.0976664
100.10635.640.0976247
110.10635.640.097583
120.10735.680.0975413
130.10635.250.0974996
140.10534.390.0974579
150.10433.390.0974162
160.10332.40.0973745
170.10231.510.0973328
180.10230.670.0972911
190.10129.950.0972494
200.129.140.0972077
210.09928.280.097166
220.09927.430.0971243
230.09926.670.0970826
240.09826.030.0970409
250.09725.590.0969992
260.09725.410.0969575
270.15417.360.1539167
280.15518.930.1538334
290.15519.740.1537501
300.15519.930.1536668
310.15620.770.1535835
320.15621.870.1535002
330.15723.110.1534169
340.15724.410.1533336
350.15725.010.1532503
360.15724.140.153167
370.15623.260.1530837
380.15522.440.1530004
390.15421.580.1529171
400.15420.830.1528338
410.15420.160.1527505
420.15419.610.1526672
430.15319.030.1525839
440.15318.420.1525006
450.15217.870.1524173
460.15217.470.152334
470.15117.070.1522507
480.15116.680.1521674
490.15116.450.1520841
500.15116.570.1520008
510.15217.270.1519175
520.16719.540.1669583
530.16821.140.1669166
540.16822.310.1668749
550.16923.540.1668332
560.169250.1667915
570.1726.170.1667498
580.1726.650.1667081
590.1726.510.1666664
600.1725.830.1666247
610.16924.910.166583
620.16923.840.1665413
630.16822.840.1664996
640.16821.990.1664579
650.16721.330.1664162
660.16720.540.1663745
670.16619.760.1663328
680.16619.070.1662911
690.16618.510.1662494
700.16518.090.1662077
710.16517.660.166166
720.16517.440.1661243
730.16517.420.1660826
740.16517.650.1660409
750.16518.30.1659992
760.16619.560.1659575
Table 2. Combined data from three 24-hour periods, ready for multiple regression. With all 24-hour periods in the same columns, the multiple regression analysis will include data from all three days.

 

Regression Statistics 
Multiple R0.99954768
R Square0.999095565
Adjusted R Square0.999070442
Standard Error0.000916358
Observations75
Table 3. Summary output
 dfSSMSFSignificance F
Regression20.066787050.03339352539767.86622.6889E-110
Residual726.04592E-058.39711E-07
Total740.066847509
Table 4. ANOVA

 

 

 CoefficientStandard Errort StatP-valueLower 95%Upper 95%
Intercept0.0162392030.00135367711.996362647.70761E-190.0135406970.018937709
X Variable 10.9654945970.005510463175.21114111.83299E-960.9545096890.976479505
X Variable 2-0.0005621142.79704E-05-20.096776393.02271E-31-0.000617872-0.000506356
Table 5. Example output from Excel regression function. Shaded cells contain the information important for this analysis.

 

4. Construct a VWC correction model. Use the coefficients determined from the multiple regression in part 3 to construct a VWC correction model from Equation 1. In the case of the example data, the model would be

Equation 2

5. Apply the model to your raw data set, yielding corrected VWC. The temperature dependency in the corrected VWC data should be greatly reduced. In some instances, there will still be some apparent temperature dependence. Often the results can be improved by selecting data to input into the correction algorithm that more fully span the range of VWC encountered in the soil.

Figure 3. Example of temperature corrected data. Notice that with this method the VWC dynamics are preserved, but the temperature dependency is greatly reduced compared to the uncorrected data.

Strategy 2: once-per-day measurements or averaging

Soil moisture is reasonably conservative and does not change much in a day unless a precipitation or irrigation event occurs. So, if no temperature information is available, or if a simplified smoothing technique is preferred, using once-per-day water content measurement or designing a simple averaging technique is useful. Of course, this would wash out any hourly changes that might be of interest, but in our experience, we generally see very little temperature-related fluctuations in the water content data when there are multiple rain or irrigation events during a day, so these data would not need correction.

Implementing a once-per-day strategy involves selecting a time to use, culling and sorting the data, and checking to make sure the results fit the original data satisfactorily. We have chosen early morning hours (e.g., 2 AM) where temperature is near its minimum as our daily measurement. This reduces the likelihood of variation in the soil moisture data from changing daily high temperatures. To sort a dataset for 2 AM data, we use an “if” statement in Excel that only puts data into an adjoining column when it is 2 AM (Table 3). Once you have set up the formula for your worksheet, copy and paste so it covers all the date values and any water content columns you want to include. Next, use the sort command to collapse all the spaces in the data and sort your data by date. You should be left with a fraction of your original data that you can now graph against the full data to see the fit. Figure 4 shows that this method does a good job smoothing the data. Obviously, this technique will not preserve the high-frequency soil moisture dynamics, but the overall trends in soil moisture will remain.

Figure 4. Once-per-day smoothing and averaging of water content data. Original data courtesy of S. Tyler, J. Selker, and S. Assouline.

Data averaging is another way that you can smooth temperature cycling in the water content data. The advantage of this technique is that you can use the entire dataset instead of removing all but one reading per day. Implementing this technique is straightforward; simply make a new column for smoothed water content data and select the “Average()” function in Excel. For the data range, you must average an entire 24-hour period to remove the diurnal temperature cycle so the average function range in any given cell must include data from the past 12 hours and the next 12 hours. Data from the averaging are shown in Figure 4. From our analysis, this averaging technique did not appear to give better results than the once-per-day technique and, not surprisingly, tended to smooth large changes in water content.

Strategy 3: A calibration method using time series of field data that requires no laboratory experiments

See the following paper:

Saito, Tadaomi, Haruyuki Fujimaki, Hiroshi Yasuda, Koji Inosako, and Mitsuhiro Inoue. “Calibration of temperature effect on dielectric probes using time series field data.” Vadose Zone Journal 12, no. 2 (2013).  Article link.

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