| title | author | output | graphics | editor_options | ||||||||||||||
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Calibration |
James Mickley |
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true |
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This analysis calibrates the light and soil moisture sensors.
The light sensor is calibrated for PFD against a LiCor and compared to a Hobo, while the soil probes are calibrated against measured volumetric water content and compared to a Hobo.
This shows the calibration of the BH1750FVI light sensor against a LiCor LI-190R Quantum Sensor connected to a LiCor LI-250 Light Meter
Both were mounted at the same angle and height on a board, and taking readings every second.
Call:
lm(formula = umol ~ lux, data = light)
Residuals:
Min 1Q Median 3Q Max
-178.248 -37.350 -9.541 45.492 113.408
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.919e+01 9.603e+00 6.164 1.25e-08 ***
lux 1.675e-02 1.465e-04 114.378 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 56.45 on 108 degrees of freedom
Multiple R-squared: 0.9918, Adjusted R-squared: 0.9917
F-statistic: 1.308e+04 on 1 and 108 DF, p-value: < 2.2e-16
Call:
lm(formula = umol ~ lux + lux.squared, data = .)
Residuals:
Min 1Q Median 3Q Max
-203.442 -24.529 -1.738 38.084 100.974
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.239e+01 1.180e+01 1.899 0.0603 .
lux 1.893e-02 4.849e-04 39.047 < 2e-16 ***
lux.squared -1.898e-08 4.057e-09 -4.679 8.49e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 51.67 on 107 degrees of freedom
Multiple R-squared: 0.9932, Adjusted R-squared: 0.9931
F-statistic: 7817 on 2 and 107 DF, p-value: < 2.2e-16
Comparison between the linear and quadratic models
The best calibration is the quadratic model, presented here alone
Root mean square error between predicted values from the quadratic light model and PFD values from the LiCor. This gives a measure of accuracy.
mean.square root.mean.square
1 2597.424 50.96493
Graph showing the predicted values of PFD from the quadratic model graphed against the LiCor
Calibration of generic silver and gold soil moisture sensor probes with a datalogging scale, measuring water content of the soil every five minutes. The soil used for calibration was a rich loam from the Fenton Meadow. The data columns soil1 and soil2 are gold (ENIG) probes, while soil3 is a silver (HASL) probe.
Models using the data from the gold-plated soil moisture probe
Call:
lm(formula = vwc ~ gold, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.023981 -0.010827 0.001181 0.008224 0.044489
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.597e-01 5.311e-04 677.3 <2e-16 ***
gold -1.296e-05 2.850e-08 -454.6 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.01277 on 7678 degrees of freedom
Multiple R-squared: 0.9642, Adjusted R-squared: 0.9642
F-statistic: 2.067e+05 on 1 and 7678 DF, p-value: < 2.2e-16
The quadratic model is considerably better
Call:
lm(formula = vwc ~ gold + gold.squared, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.0154048 -0.0034169 -0.0000345 0.0035356 0.0142257
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.806e-01 7.129e-04 674.2 <2e-16 ***
gold -2.887e-05 8.951e-08 -322.5 <2e-16 ***
gold.squared 4.727e-10 2.633e-12 179.5 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.005603 on 7677 degrees of freedom
Multiple R-squared: 0.9931, Adjusted R-squared: 0.9931
F-statistic: 5.53e+05 on 2 and 7677 DF, p-value: < 2.2e-16
dAICc df
gold.quad 0.0 4
gold.lm 12654.2 3
The quadratic temperature-compensated model is better by AIC, but it doesn't add much, and doesn't eliminate the residual zig-zag pattern (see below).
Call:
lm(formula = vwc ~ gold + gold.squared + temp, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.0135034 -0.0027853 0.0007276 0.0033035 0.0138653
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.656e-01 1.323e-03 427.63 <2e-16 ***
gold -3.080e-05 7.480e-08 -411.72 <2e-16 ***
gold.squared 5.302e-10 2.204e-12 240.51 <2e-16 ***
temp -2.720e-03 3.844e-05 -70.74 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.00436 on 7676 degrees of freedom
Multiple R-squared: 0.9958, Adjusted R-squared: 0.9958
F-statistic: 6.106e+05 on 3 and 7676 DF, p-value: < 2.2e-16
dAICc df
gold.quad.temp 0.0 5
gold.quad 3853.1 4
gold.lm 16507.3 3
Models using the data from the silver (solder plated) soil moisture probe
Call:
lm(formula = vwc ~ silver, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.0180007 -0.0061523 0.0002036 0.0057225 0.0272827
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.341e-01 4.153e-04 1045.3 <2e-16 ***
silver -1.513e-05 2.002e-08 -755.6 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.007773 on 7678 degrees of freedom
Multiple R-squared: 0.9867, Adjusted R-squared: 0.9867
F-statistic: 5.71e+05 on 1 and 7678 DF, p-value: < 2.2e-16
Call:
lm(formula = vwc ~ silver + silver.squared, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.019434 -0.003896 0.000419 0.004251 0.014139
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.165e-01 1.288e-03 401.0 <2e-16 ***
silver -2.460e-05 1.440e-07 -170.9 <2e-16 ***
silver.squared 2.546e-10 3.846e-12 66.2 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.006202 on 7677 degrees of freedom
Multiple R-squared: 0.9916, Adjusted R-squared: 0.9916
F-statistic: 4.506e+05 on 2 and 7677 DF, p-value: < 2.2e-16
dAICc df
silver.quad 0.0 4
silver.lm 3466.7 3
Call:
lm(formula = vwc ~ silver + silver.squared + temp, data = .)
Residuals:
Min 1Q Median 3Q Max
-0.0164454 -0.0030356 0.0007289 0.0036374 0.0134823
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 6.188e-01 1.722e-03 359.35 <2e-16 ***
silver -2.737e-05 1.172e-07 -233.60 <2e-16 ***
silver.squared 3.281e-10 3.128e-12 104.89 <2e-16 ***
temp -3.008e-03 4.138e-05 -72.68 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.004774 on 7676 degrees of freedom
Multiple R-squared: 0.995, Adjusted R-squared: 0.995
F-statistic: 5.088e+05 on 3 and 7676 DF, p-value: < 2.2e-16
dAICc df
silver.quad.temp 0.0 5
silver.lm 7486.2 3
Showing soil moisture probe values over time. There is some diurnal variation that is partially temperature-driven.
Adding temperature to the quadratic fit does improve things slightly, but the temperature range is only ~21-30 C, so it doesn't encompass the full temperature range outside
Root mean square error between predicted values from the gold probe quadratic model and measured VWC values from the scale. This gives a measure of accuracy.
mean.square root.mean.square
1 0.00604131 0.07772586
A graph of the calibration and formula using the quadratic model for the gold probe
Graph showing the predicted values of VWC from the quadratic model graphed against the actual VWC. Notably, the zig-zag pattern improves slightly in the temperature-compensated model, but it is far from eliminated.
R version 3.4.3 (2017-11-30)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1
Matrix products: default
locale:
[1] LC_COLLATE=English_United States.1252
[2] LC_CTYPE=English_United States.1252
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C
[5] LC_TIME=English_United States.1252
attached base packages:
[1] stats4 stats graphics grDevices utils datasets methods
[8] base
other attached packages:
[1] bindrcpp_0.2.2 bbmle_1.0.20 ggpmisc_0.3.0 cowplot_0.9.3
[5] forcats_0.3.0 stringr_1.3.0 dplyr_0.7.6 purrr_0.2.4
[9] readr_1.1.1 tidyr_0.8.0 tibble_1.4.2 ggplot2_3.0.0
[13] tidyverse_1.2.1
loaded via a namespace (and not attached):
[1] tidyselect_0.2.4 reshape2_1.4.3 haven_1.1.1
[4] lattice_0.20-35 colorspace_1.3-2 htmltools_0.3.6
[7] yaml_2.1.18 rlang_0.2.2 pillar_1.2.2
[10] foreign_0.8-69 glue_1.2.0 withr_2.1.2
[13] modelr_0.1.1 readxl_1.1.0 bindr_0.1.1
[16] plyr_1.8.4 munsell_0.4.3 gtable_0.2.0
[19] cellranger_1.1.0 rvest_0.3.2 codetools_0.2-15
[22] psych_1.8.4 evaluate_0.10.1 labeling_0.3
[25] knitr_1.20 parallel_3.4.3 broom_0.4.4
[28] Rcpp_0.12.16 polynom_1.3-9 scales_0.5.0
[31] backports_1.1.2 jsonlite_1.5 mnormt_1.5-5
[34] hms_0.4.2 digest_0.6.15 stringi_1.1.7
[37] numDeriv_2016.8-1 grid_3.4.3 rprojroot_1.3-2
[40] cli_1.0.0 tools_3.4.3 magrittr_1.5
[43] lazyeval_0.2.1 crayon_1.3.4 pkgconfig_2.0.1
[46] xml2_1.2.0 lubridate_1.7.4 assertthat_0.2.0
[49] rmarkdown_1.9 httr_1.3.1 rstudioapi_0.7
[52] R6_2.2.2 nlme_3.1-131 compiler_3.4.3