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## Introduction

In many natural and engineered soils, the output of ECH_{2}O soil moisture sensors are sensitive to variations in the soil temperature. The temperature sensitivity is not caused by the ECH_{2}O 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 ECH_{2}O 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 ECH_{2}O sensor. In other soils, ε″ dominates, and an increase in temperature causes an increase in the VWC measured by the ECH_{2}O 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 ECH_{2}O 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 ECH_{2}O 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 ECH_{2}O 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 ECH_{2}O 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 ECH_{2}O 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 *VWC _{meas}* is the VWC measured by the ECH

_{2}O sensor,

*T*is the soil temperature at the location of the sensor, and

_{soil}*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 ECH

_{2}O 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 ECH_{2}O 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

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.

A | B | C | D | E | F | |
---|---|---|---|---|---|---|

1 | Timescale for Interpolation | Time | VWCmeas | T | VWC for Interpolation | Interpolated VWC |

2 | 1 | 8/6/2006 11:00 | 0.154 | 17.36 | 0.154 | 0.154 |

3 | 2 | 8/6/2006 12:00 | 0.155 | 18.93 | =-0.0000833*A3+0.154 | |

4 | 3 | 8/6/2006 13:00 | 0.155 | 19.74 | 0.154 | |

5 | 4 | 8/6/2006 14:00 | 0.155 | 19.93 | 0.154 | |

6 | 5 | 8/6/2006 15:00 | 0.156 | 20.77 | 0.154 | |

7 | 6 | 8/6/2006 16:00 | 0.156 | 21.87 | 0.154 | |

8 | 7 | 8/6/2006 17:00 | 0.157 | 23.11 | 0.153 | |

9 | 8 | 8/6/2006 18:00 | 0.157 | 24.41 | 0.153 | |

10 | 9 | 8/6/2006 19:00 | 0.157 | 25.01 | 0.153 | |

11 | 10 | 8/6/2006 20:00 | 0.157 | 24.14 | 0.153 | |

12 | 11 | 8/6/2006 21:00 | 0.156 | 23.26 | 0.153 | |

13 | 12 | 8/6/2006 22:00 | 0.155 | 22.44 | 0.153 | |

14 | 13 | 8/6/2006 23:00 | 0.154 | 21.58 | 0.153 | |

15 | 14 | 8/7/2006 0:00 | 0.154 | 20.83 | 0.153 | |

16 | 15 | 8/7/2006 1:00 | 0.154 | 20.16 | 0.153 | |

17 | 16 | 8/7/2006 2:00 | 0.154 | 19.61 | 0.153 | |

18 | 17 | 8/7/2006 3:00 | 0.153 | 19.03 | 0.153 | |

19 | 18 | 8/7/2006 4:00 | 0.153 | 18.42 | 0.153 | |

20 | 19 | 8/7/2006 5:00 | 0.152 | 17.87 | 0.152 | |

21 | 20 | 8/7/2006 6:00 | 0.152 | 17.47 | 0.152 | |

22 | 21 | 8/7/2006 7:00 | 0.151 | 17.07 | 0.152 | |

23 | 22 | 8/7/2006 8:00 | 0.151 | 16.68 | 0.152 | |

24 | 23 | 8/7/2006 9:00 | 0.151 | 16.45 | 0.152 | |

25 | 24 | 8/7/2006 10:00 | 0.151 | 16.57 | 0.152 | |

26 | 25 | 8/7/2006 11:00 | 0.152 | 17.27 | 0.152 | 0.152 |

**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).

A | B | C | |
---|---|---|---|

1 | VWCmeas | T | Interpolated VWC |

2 | 0.098 | 25.42 | 0.0979583 |

3 | 0.099 | 25.63 | 0.0979166 |

4 | 0.099 | 26.87 | 0.0978749 |

5 | 0.1 | 28.58 | 0.0978332 |

6 | 0.102 | 30.43 | 0.0977915 |

7 | 0.103 | 32.27 | 0.0977498 |

8 | 0.105 | 33.92 | 0.0977081 |

9 | 0.106 | 35.23 | 0.0976664 |

10 | 0.106 | 35.64 | 0.0976247 |

11 | 0.106 | 35.64 | 0.097583 |

12 | 0.107 | 35.68 | 0.0975413 |

13 | 0.106 | 35.25 | 0.0974996 |

14 | 0.105 | 34.39 | 0.0974579 |

15 | 0.104 | 33.39 | 0.0974162 |

16 | 0.103 | 32.4 | 0.0973745 |

17 | 0.102 | 31.51 | 0.0973328 |

18 | 0.102 | 30.67 | 0.0972911 |

19 | 0.101 | 29.95 | 0.0972494 |

20 | 0.1 | 29.14 | 0.0972077 |

21 | 0.099 | 28.28 | 0.097166 |

22 | 0.099 | 27.43 | 0.0971243 |

23 | 0.099 | 26.67 | 0.0970826 |

24 | 0.098 | 26.03 | 0.0970409 |

25 | 0.097 | 25.59 | 0.0969992 |

26 | 0.097 | 25.41 | 0.0969575 |

27 | 0.154 | 17.36 | 0.1539167 |

28 | 0.155 | 18.93 | 0.1538334 |

29 | 0.155 | 19.74 | 0.1537501 |

30 | 0.155 | 19.93 | 0.1536668 |

31 | 0.156 | 20.77 | 0.1535835 |

32 | 0.156 | 21.87 | 0.1535002 |

33 | 0.157 | 23.11 | 0.1534169 |

34 | 0.157 | 24.41 | 0.1533336 |

35 | 0.157 | 25.01 | 0.1532503 |

36 | 0.157 | 24.14 | 0.153167 |

37 | 0.156 | 23.26 | 0.1530837 |

38 | 0.155 | 22.44 | 0.1530004 |

39 | 0.154 | 21.58 | 0.1529171 |

40 | 0.154 | 20.83 | 0.1528338 |

41 | 0.154 | 20.16 | 0.1527505 |

42 | 0.154 | 19.61 | 0.1526672 |

43 | 0.153 | 19.03 | 0.1525839 |

44 | 0.153 | 18.42 | 0.1525006 |

45 | 0.152 | 17.87 | 0.1524173 |

46 | 0.152 | 17.47 | 0.152334 |

47 | 0.151 | 17.07 | 0.1522507 |

48 | 0.151 | 16.68 | 0.1521674 |

49 | 0.151 | 16.45 | 0.1520841 |

50 | 0.151 | 16.57 | 0.1520008 |

51 | 0.152 | 17.27 | 0.1519175 |

52 | 0.167 | 19.54 | 0.1669583 |

53 | 0.168 | 21.14 | 0.1669166 |

54 | 0.168 | 22.31 | 0.1668749 |

55 | 0.169 | 23.54 | 0.1668332 |

56 | 0.169 | 25 | 0.1667915 |

57 | 0.17 | 26.17 | 0.1667498 |

58 | 0.17 | 26.65 | 0.1667081 |

59 | 0.17 | 26.51 | 0.1666664 |

60 | 0.17 | 25.83 | 0.1666247 |

61 | 0.169 | 24.91 | 0.166583 |

62 | 0.169 | 23.84 | 0.1665413 |

63 | 0.168 | 22.84 | 0.1664996 |

64 | 0.168 | 21.99 | 0.1664579 |

65 | 0.167 | 21.33 | 0.1664162 |

66 | 0.167 | 20.54 | 0.1663745 |

67 | 0.166 | 19.76 | 0.1663328 |

68 | 0.166 | 19.07 | 0.1662911 |

69 | 0.166 | 18.51 | 0.1662494 |

70 | 0.165 | 18.09 | 0.1662077 |

71 | 0.165 | 17.66 | 0.166166 |

72 | 0.165 | 17.44 | 0.1661243 |

73 | 0.165 | 17.42 | 0.1660826 |

74 | 0.165 | 17.65 | 0.1660409 |

75 | 0.165 | 18.3 | 0.1659992 |

76 | 0.166 | 19.56 | 0.1659575 |

**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 R | 0.99954768 |

R Square | 0.999095565 |

Adjusted R Square | 0.999070442 |

Standard Error | 0.000916358 |

Observations | 75 |

**Table 3.**Summary output

df | SS | MS | F | Significance F | |
---|---|---|---|---|---|

Regression | 2 | 0.06678705 | 0.033393525 | 39767.8662 | 2.6889E-110 |

Residual | 72 | 6.04592E-05 | 8.39711E-07 | ||

Total | 74 | 0.066847509 |

**Table 4.**ANOVA

Coefficient | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
---|---|---|---|---|---|---|

Intercept | 0.016239203 | 0.001353677 | 11.99636264 | 7.70761E-19 | 0.013540697 | 0.018937709 |

X Variable 1 | 0.965494597 | 0.005510463 | 175.2111411 | 1.83299E-96 | 0.954509689 | 0.976479505 |

X Variable 2 | -0.000562114 | 2.79704E-05 | -20.09677639 | 3.02271E-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

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.

## 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.

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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