In this section, results from comparisons of data from 2018 and 2019 will be presented.
The purpose of this is to get an overview of the difference in the data sets between the two years, and to use that information to evaluate the influence of increased grass height in a broad perspective. As mentioned in section 3.4, the weather situation in the two years was very different. Section 3.5 explained how this influences the use of the data from 2018. The time period between 11/7 12:00 and 15/9 13:00 will be used when evaluating data from 2018 and comparing data directly between 2018 and 2019, as explained in section 3.5.
4.2.1 Difference in temperature over uncut and cut grass
Mean and standard deviation are statistical tools that can be used to get an overview of the data and the data’s dispersion. The mean and standard deviation of the difference in temperature at 2 m between U and C in the period 11/7 12:00 and 15/9 13:00 in 2018 and 2019 are given in table 4.3. The mean values are 0.0◦C. The standard deviation is 0.1◦C in 2019, while it is 0.2◦C in 2018.
Table 4.3: This table presents the mean and standard deviation of the difference in temperature between the measuring instruments over uncut and that over cut grass, (TU−TC), at 2 m in the time period between 11/7 12:00 and 15/9 13:00 in 2018 and 2019.
Year Mean [◦C] Standard deviation [◦C]
2018 0.0 0.2
2019 0.0 0.1
4.2.2 Test statistics to evaluate how different the years were
The two-sample KS and MWU tests are used to decide if two data sets are from the same sample, i.e. whether they are significantly different or not. The tests were presented in section 3.6. A sufficiently small p-value lets you conclude on a given significance level that the samples are different. The chosen significance level in this thesis was 95%, which means that a p-value of 5%=0.05 is needed to reject the null-hypothesis,H0. The results from the KS and MWU tests are given in table 4.4.
The null-hypothesis for the tests in row a and b in table 4.4 was that there was no significant difference in the difference between temperature measured at 2 m and 1.25 m between the two locations U and C in 2019 (row a) and 2018 (row b). If there was a difference between T2m and T1m, the influence by surface properties reach higher than what is assumed by WMO. This means that if there was a difference between
Table 4.4: The table presents test statistics from KS (Kolmogorov-Smirnov) tests and MWU (Mann-Whitney U) tests on data from the test site. U is the location with uncut grass under it and C the location with cut grass under it. 2m and 1m represents the measuring instruments mounted at 2 m and 1.25 m respectively.
Input x Input y KS test p-value WMU test p-value a (T2m−T1m)U, 2019 (T2m−T1m)C, 2019 8.23·10−5 6.85·10−5
(T2m−T1m) in two different locations, the surface properties at one location influenced the air at 1.25 m temperature to a higher degree than at the other location. The p-values in row a have an order of magnitude of -5, and one can then say that the data sets with (T2m−T1m) with data from U and C were significantly different from each other in 2019.
When using data from 2018 instead, the p-values for the two tests were 0.125 and 0.203, which are larger than 0.05. These test statistics are in row b. It can therefore be said with 95% significance that (T2m−T1m)U and (T2m −T1m)C were different in 2019, but not in 2018. In addition, due to the very low p-values in row a and the relatively high p-values in row b, H0 is rejected at all common significance levels for 2019 and fails to be rejected for 2018.
In row c and d in table 4.4, the data sets with the difference between temperature measured at U and C at a specific height, is compared between 2018 and 2019. The null-hypothesis is therefore that there was no difference between (TU−TC) at a specific height between the two years. In row c, data from 2 m are compared and in row d, data from 1.25 m are compared. The p-values in row c are much smaller than 0.05, both having an order of magnitude of -23. This means that the data sets consisting of (TU −TC)2m in 2019 and 2018 can be said to have been significantly different from each other according to the KS and MWU tests. The p-values in row d have orders of magnitude of -10 and -5, and the same can therefore be said for the difference in temperature at 1.25 m, (TU−TC)1m, between the two years.
In row e and f, the data sets consisting of (T2m −T1m) at a specific location is compared between the two years. The null-hypothesis is therefore that there was no significant variation in the difference between temperature measured at 2 m and 1.25 m at a specific location between 2018 and 2019. It is shown in row e that the p-values are 0.115 and 0.531 when doing this test on data sets from U. This means that it cannot be concluded on a 95% level, or any common significance level, that there was a difference between the temperature profile from 1.25 m up to 2 m at U between 2018 and 2019.
In row f, the results from comparing the (T2m−T1m)C values from 2018 and 2019 are shown. The p-values from running the KS and MWU tests on these two data sets are 0.003 and 0.094. In the KS test,H0 is rejected on a 95% significance level, while it fails to be rejected in the WMU test. 0.094 is below 0.10, which means that H0 would have been rejected on a 90% significance level. This means that according to the KS test, it can be concluded on a 95% significance level that there was a difference between the temperature profile from 1.25 m up to 2 m at C between 2018 and 2019.
4.2.3 The difference in temperature at three heights
In figure 4.3, the differences between temperature at U and C at the three heights 2 m, 1.25 m, and 0.55 m are plotted as box and whisker plots. In figures 4.3a and 4.3b, the
hourly temperature difference from 2018 and 2019 are shown respectively. Figure 4.3a shows that the interval of the (TU −TC) values at 1.25 m and 0.55 m were [-0.8◦C, 1.5◦C] and [-1.0◦C, 2.3◦C] in 2018. Figure 4.3b show that these intervals were reduced to [−0.6◦C, 1.0◦C] and [-1.0◦C, 1.4◦C] in 2019. Additionally, the interval of the box for the (TU−TC) values at 1.25 m is reduced by 0.1◦C from 2018 to 2019. This means more values were contained within a smaller range in the data set for 2019. In appendix C, box and whisker plots of the diurnal variation of the difference in temperature in 2018 are shown. These plots further demonstrate that the variation in the (TU −TC) values was larger for all heights in 2018 than in 2019.
(a) (b)
Figure 4.3: These plots show box and whisker plots of the difference in temperature measured over uncut grass (U) and cut grass (C) at three heights above the ground: 2 m, 1.25 m, and 0.55 m. (a)displays the difference in temperature in 2018, while(b)displays the difference in temperature in 2019. For 2018, the data set is from 11/7/2018 12:00 until 15/9/2018 13:00. For 2019, the data set is from 23/5/2019 00:00 until 30/10/2019 12:00.
Table 4.5 presents the percentage of data points of the value (TU −TC) that are in the ranges±0.2◦C,±0.3◦C,±0.4◦C, and±0.5◦C for the three heights, 2 m, 1.25 m, and 0.55 m, in both 2018 and 2019. The percentage numbers in the table demonstrates that more (TU−TC) values are closer to 0.0◦C in 2019 than in 2018, just like what was seen in figure 4.3.
Table 4.5: This table displays the percentage of data points that are within a given interval for the difference in temperature between the location with uncut (U) and cut (C) grass. ±0.4◦Cis the combined expanded uncertainty for the difference in temperature between the two locations, U and C, in this experiment at 2 m. ±0.5◦C is the combined expanded uncertainty for this difference at 1.25 m and 0.55 m. For 2018, the data set is from 11/7/2018 12:00 until 15/9/2018 13:00. For 2019, the data set is from 23/5/2019 00:00 until 30/10/2019 12:00.
Box and whisker plots give a deeper understanding of the spread of the data. Plotting the diurnal difference in temperature measured over uncut (U) and cut (C) grass is useful to evaluate the development of this value. A thorough explanation of box and whisker plots was given in section 3.7. These kinds of plots will be presented in this section for the three heights and for different weather conditions.
4.3.1 Overview
The diurnal difference in hourly temperature at 2 m between U and C in 2019 is evaluated in figure 4.4. For all hours of the day, the boxes (containing at least 50% of the data) are within the [-0.1◦C, 0.2◦C] interval. Furthermore, the median values are either 0.0◦C or 0.1◦C for all hours of the day. No whiskers are outside of the [-0.4◦C, 0.5◦C] interval.
The largest positive outlier is 0.9◦C and the largest negative outlier is−0.8◦C.
Figure 4.5 shows the same as figure 4.4, but for 1.25 m instead. Just like the plot of the diurnal difference in temperature between U and C at 2 m, all the hours’ boxes are within the [-0.1◦C, 0.2◦C] interval, and all whiskers are within the [-0.4◦C, 0.5◦C]
interval. The main difference between the difference in temperature at these two heights is the amount of, and the pattern in, the outliers in the plot for (TU−TC) at 1.25 m.
The outliers are more in number and there is an indication of a diurnal pattern. The largest negative and positive (TU−TC) values at 1.25 m were−0.6◦C and 1.0◦C.
Figure 4.6 shows the same as figures 4.4 and 4.5, but for 0.55 m. There are more and larger outliers for the difference in temperature between U and C in this plot than in figures 4.4 and 4.5. The largest negative and positive (TU−TC) values at 0.55 m were
−1.0◦C and 1.4◦C. This indicates that the temperature measurements at 0.55 m were more affected by the ground than the measurements at 2 m and 1.25 m. This is in line with the theory presented in section 2.4. However, the boxes for all hours are within the [-0.1◦C, 0.2◦C] interval, just like for the difference in temperature at 1.25 m and 2 m.
Contrary to the results from the comparison of the instruments at 1.25 m, no obvious diurnal pattern was found in this plot for 0.55 m.
Additionally, similar analyses were performed separately for the temperature data at 2 m in the months June-October. The plots can be found in appendix D. No significant difference between the months could be detected. Median differences ranged from -0.1◦C to +0.1◦C, and the boxes (containing at least 50% of the data) were all within the interval [-0.2◦C, 0.2◦C], with only a few exceptions. The mean values of the hourly