Statistical analysis of carbon dioxide flux data

Question

I have been measuring flux of CO2 in (mmol m-2 d-1) from two different rivers and I now want to do a statistical analysis using IBM SPSS but I'm not sure where to start. One lake is showing negative flux, because the lake has acted like a sink for the CO2.

I have made a histogram first see how the data looks like, as you can see in the figure I’ve added additional data with label. As mentioned above, the negative values are from one lake and the positive values are from another lake

The labels show: what lake I have studied; what time I started the measurement and when I stopped measuring; the column daytime (1) describes when the sun is up and nighttime (2) describes when the sun is down; T_air oC and T_H2O describes describe the temperature in water and air during the measurement and FCO2 is a calculated variable of CO2 flux from its ppm to units of mmol m-2 d-1.

What I want to accomplish with the statistical analysis is first to understand how I should think before I start to analyzing;

• What leads to different values within each of the two lakes?
• What lead to different values between the two lakes? and
• What is the relationship between FCO2 and temperature?

Is there anyone who can come with some suggestion what statistically analysis I should use for each thing I want to accomplish? I have from somewhere I should use a one-way Anova but not sure where to start thinking.

Thank you for helping

Lake & Initial sampling (date and time) & Final sampling (date and time) & Daytime (1) nighttime (2) & T\_air oC & T\_H2O oC & FCO2\_mmol m-2 d-1 \\
Victoria & 2022-03-16 18:35 & 2022-03-16 20:18 & 1 & 4.5   & 4.5   & -2.29507 \\
Victoria & 2022-03-16 20:33 & 2022-03-16 22:15 & 2 & 4.35  & 4.35  & -2.48989 \\
Victoria & 2022-03-16 22:35 & 2022-03-17 00:16 & 2 & 4.22  & 4.22  & -2.52834 \\
Victoria & 2022-03-17 00:35 & 2022-03-17 02:18 & 2 & 4.02  & 4.02  & -2.4524  \\
Victoria & 2022-03-17 02:34 & 2022-03-17 04:13 & 2 & 4.12  & 4.12  & -2.47989 \\
Victoria & 2022-03-17 04:38 & 2022-03-17 06:15 & 1 & 4.36  & 4.36  & -2.18617 \\
Victoria & 2022-03-17 06:34 & 2022-03-17 08:16 & 1 & 5.35  & 5.35  & -1.86178 \\
Victoria & 2022-03-17 08:35 & 2022-03-17 10:17 & 1 & 6.07  & 6.07  & -2.42144 \\
Victoria & 2022-03-17 10:34 & 2022-03-17 12:18 & 1 & 7.44  & 7.44  & -2.52941 \\
Victoria & 2022-03-17 12:34 & 2022-03-17 14:17 & 1 & 8.16  & 8.16  & -2.21627 \\
Victoria & 2022-03-17 14:33 & 2022-03-17 16:19 & 1 & 7.97  & 7.97  & -2.55553 \\
Victoria & 2022-03-17 16:39 & 2022-03-17 18:17 & 1 & 7.52  & 7.52  & -2.0844  \\
Victoria & 2022-03-17 18:34 & 2022-03-17 20:17 & 1 & 7.54  & 7.54  & -2.43122 \\
Victoria & 2022-03-17 20:34 & 2022-03-17 22:17 & 2 & 8.06  & 8.06  & -1.96291 \\
Victoria & 2022-03-17 22:35 & 2022-03-18 00:18 & 2 & 7.41  & 7.41  & -1.54653 \\
Victoria & 2022-03-18 00:38 & 2022-03-18 02:18 & 2 & 7.60  & 7.6   & -1.591   \\
Victoria & 2022-03-18 02:35 & 2022-03-18 04:17 & 2 & 7.42  & 7.42  & -1.99879 \\
Victoria & 2022-03-18 04:36 & 2022-03-18 06:16 & 1 & 7.02  & 7.02  & -1.44514 \\
Victoria & 2022-03-18 06:35 & 2022-03-18 08:18 & 1 & 8.12  & 8.12  & -1.82221 \\
Victoria & 2022-03-18 08:33 & 2022-03-18 10:17 & 1 & 8.97  & 8.97  & -2.30534 \\
Victoria & 2022-03-18 10:34 & 2022-03-18 12:18 & 1 & 11.63 & 11.63 & -1.49893 \\
Victoria & 2022-03-18 12:37 & 2022-03-18 14:17 & 1 & 10.75 & 10.75 & -2.20711 \\
Victoria & 2022-03-18 14:38 & 2022-03-18 16:18 & 1 & 11.57 & 11.57 & -1.80309 \\
Victoria & 2022-03-18 16:41 & 2022-03-18 18:17 & 1 & 8.66  & 8.66  & -1.67234 \\
Victoria & 2022-03-18 18:37 & 2022-03-18 20:15 & 1 & 6.18  & 6.18  & -1.3983  \\
Victoria & 2022-03-18 20:37 & 2022-03-18 22:17 & 2 & 5.02  & 5.02  & -1.32119 \\
Victoria & 2022-03-18 22:34 & 2022-03-19 00:17 & 2 & 4.50  & 4.5   & -1.45022 \\
Victoria & 2022-03-19 00:34 & 2022-03-19 02:17 & 2 & 4.74  & 4.74  & -1.49234 \\
Victoria & 2022-03-19 02:35 & 2022-03-19 04:18 & 2 & 4.75  & 4.75  & -1.16388 \\
Victoria & 2022-03-19 04:35 & 2022-03-19 06:18 & 1 & 4.34  & 4.34  & -0.87719 \\
Victoria & 2022-03-19 10:33 & 2022-03-19 12:17 & 1 & 13.33 & 13.33 & -1.04391 \\
Victoria & 2022-03-19 12:34 & 2022-03-19 14:18 & 1 & 11.86 & 11.86 & -1.15754 \\
Victoria & 2022-03-19 14:37 & 2022-03-19 16:18 & 1 & 14.32 & 14.32 & -1.3017  \\
Victoria & 2022-03-19 16:35 & 2022-03-19 18:18 & 1 & 7.77  & 7.77  & -1.41987 \\
Victoria & 2022-03-19 18:33 & 2022-03-19 20:18 & 1 & 5.49  & 5.49  & -1.20405 \\
Victoria & 2022-03-19 20:35 & 2022-03-19 22:16 & 2 & 4.92  & 4.92  & -1.29523 \\
Victoria & 2022-03-20 08:34 & 2022-03-20 10:13 & 1 & 13.10 & 13.1  & -2.09114 \\
Victoria & 2022-03-20 10:34 & 2022-03-20 12:16 & 1 & 12.37 & 12.37 & -1.80007 \\
Victoria & 2022-03-20 12:32 & 2022-03-20 14:18 & 1 & 12.81 & 12.81 & -1.55716 \\
Victoria & 2022-03-20 14:34 & 2022-03-20 16:17 & 1 & 15.58 & 15.58 & -1.86034 \\
Victoria & 2022-03-20 16:34 & 2022-03-20 18:17 & 1 & 9.39  & 9.39  & -1.90103 \\
Victoria & 2022-03-20 18:33 & 2022-03-20 20:18 & 1 & 5.44  & 5.44  & -1.53041 \\
Victoria & 2022-03-20 20:35 & 2022-03-20 22:14 & 2 & 4.67  & 4.67  & -1.79374 \\
Victoria & 2022-03-20 22:37 & 2022-03-21 00:17 & 2 & 4.48  & 4.48  & -1.01154 \\
Denveer  & 2022-03-29 21:55 & 2022-03-29 23:35 & 2 & 4.44  & 4.44  & 2.853022 \\
Denveer  & 2022-03-29 23:56 & 2022-03-30 01:35 & 2 & 3.51  & 3.51  & 2.15667  \\
Denveer  & 2022-03-30 01:56 & 2022-03-30 03:34 & 2 & 2.38  & 2.38  & 2.231913 \\
Denveer  & 2022-03-30 03:54 & 2022-03-30 05:35 & 2 & 2.16  & 2.16  & 1.759635 \\
Denveer  & 2022-03-30 05:53 & 2022-03-30 07:35 & 1 & 3.7   & 3.7   & 1.001419 \\
Denveer  & 2022-03-30 07:56 & 2022-03-30 09:35 & 1 & 7.8   & 7.8   & 0.960555 \\
Denveer  & 2022-03-30 09:53 & 2022-03-30 11:35 & 1 & 9.98  & 9.98  & 1.991259 \\
Denveer  & 2022-03-30 11:56 & 2022-03-30 13:34 & 1 & 10.25 & 10.25 & 1.517868 \\
Denveer  & 2022-03-30 13:51 & 2022-03-30 15:34 & 1 & 10.2  & 10.2  & 1.821623 \\
Denveer  & 2022-03-30 15:53 & 2022-03-30 17:35 & 1 & 9.63  & 9.63  & 1.741887 \\
Denveer  & 2022-03-30 17:54 & 2022-03-30 19:35 & 1 & 6.38  & 6.38  & 2.141064 \\
Denveer  & 2022-03-30 19:55 & 2022-03-30 21:35 & 2 & 4.96  & 4.96  & 2.685757 \\
Denveer  & 2022-03-30 21:56 & 2022-03-30 23:35 & 2 & 4     & 4     & 2.923715 \\
Denveer  & 2022-03-30 23:52 & 2022-03-31 01:11 & 2 & 3.54  & 3.54  & 3.316899 \\
Denveer  & 2022-03-31 01:52 & 2022-03-31 03:34 & 2 & 2.99  & 2.99  & 1.681422 \\
Denveer  & 2022-03-31 07:55 & 2022-03-31 09:35 & 1 & 10.4  & 10.4  & 1.361125 \\
Denveer  & 2022-03-31 13:58 & 2022-03-31 15:34 & 1 & 12.34 & 12.34 & 0.734101 \\
Denveer  & 2022-03-31 15:55 & 2022-03-31 17:35 & 1 & 8.69  & 8.69  & 0.947828 \\
Denveer  & 2022-03-31 17:54 & 2022-03-31 19:35 & 1 & 6.6   & 6.6   & 0.512018 \\
Denveer  & 2022-03-31 19:53 & 2022-03-31 21:35 & 2 & 4.82  & 4.82  & 1.261292 \\
Denveer  & 2022-04-01 06:04 & 2022-04-01 07:35 & 1 & 4.9   & 4.9   & 1.77807  \\
Denveer  & 2022-04-01 09:54 & 2022-04-01 11:34 & 1 & 7.73  & 7.73  & 1.738892 \\
Denveer  & 2022-04-01 12:02 & 2022-04-01 13:22 & 1 & 9.9   & 9.9   & 1.109685 \\
Denveer  & 2022-04-01 13:51 & 2022-04-01 15:35 & 1 & 9.06  & 9.06  & 1.232822 \\
Denveer  & 2022-04-01 15:56 & 2022-04-01 17:36 & 1 & 8.57  & 8.57  & 0.857767 \\
Denveer  & 2022-04-01 17:56 & 2022-04-01 19:34 & 1 & 4.62  & 4.62  & 1.44003  \\
Denveer  & 2022-04-01 19:53 & 2022-04-01 21:36 & 2 & 2.78  & 2.78  & 2.121573 \\
Denveer  & 2022-04-01 22:04 & 2022-04-01 23:24 & 2 & 2.9   & 2.9   & 2.611131 \\
Denveer  & 2022-04-02 00:01 & 2022-04-02 01:36 & 2 & 1.99  & 1.99  & 1.989111 \\
Denveer  & 2022-04-02 01:56 & 2022-04-02 03:36 & 2 & 1.6   & 1.6   & 1.889324 \\
Denveer  & 2022-04-02 03:56 & 2022-04-02 05:35 & 2 & 1.51  & 1.51  & 1.239421 \\
Denveer  & 2022-04-02 05:54 & 2022-04-02 07:34 & 1 & 2.73  & 2.73  & 0.908215 \\
Denveer  & 2022-04-02 07:58 & 2022-04-02 08:48 & 1 & 4.94  & 4.94  & 0.72762  \\
Denveer  & 2022-04-02 10:04 & 2022-04-02 11:26 & 1 & 11.35 & 11.35 & 0.634685 \\
Denveer  & 2022-04-02 13:59 & 2022-04-02 15:37 & 1 & 9.45  & 9.45  & 0.851654 \\
Denveer  & 2022-04-02 15:54 & 2022-04-02 17:38 & 1 & 8.7   & 8.7   & 1.322688 \\
Denveer  & 2022-04-02 17:58 & 2022-04-02 19:38 & 1 & 6.64  & 6.64  & 1.169257 \\
Denveer  & 2022-04-02 19:54 & 2022-04-02 21:39 & 2 & 5.25  & 5.25  & 1.483866 \\
Denveer  & 2022-04-02 22:00 & 2022-04-02 23:40 & 2 & 4.87  & 4.87  & 1.363993 \\
Denveer  & 2022-04-03 00:04 & 2022-04-03 01:36 & 2 & 4.78  & 4.78  & 1.777732 \\
Denveer  & 2022-04-03 02:00 & 2022-04-03 03:40 & 2 & 4.8   & 4.8   & 1.488471 \\
Denveer  & 2022-04-03 03:56 & 2022-04-03 05:40 & 2 & 4.54  & 4.54  & 0.842322 \\
Denveer  & 2022-04-03 05:57 & 2022-04-03 07:41 & 1 & 5.12  & 5.12  & 1.25267  \\
Denveer  & 2022-04-03 07:58 & 2022-04-03 09:40 & 1 & 7.82  & 7.82  & 1.638629 \\
Denveer  & 2022-04-03 10:02 & 2022-04-03 11:42 & 1 & 10.2  & 10.2  & 1.543532 \\
Denveer  & 2022-04-03 11:59 & 2022-04-03 13:42 & 1 & 11.4  & 11.4  & 1.734148 \\
Denveer  & 2022-04-03 14:02 & 2022-04-03 15:42 & 1 & 10.1  & 10.1  & 2.221091 \\
Denveer  & 2022-04-03 16:01 & 2022-04-03 17:20 & 1 & 9.2   & 9.2   & 2.092675 \\
Denveer  & 2022-04-03 19:59 & 2022-04-03 21:43 & 2 & 6.69  & 6.69  & 2.461853 \\
Denveer  & 2022-04-03 22:03 & 2022-04-03 23:38 & 2 & 6.34  & 6.34  & 3.361063 \\
Denveer  & 2022-04-04 00:01 & 2022-04-04 01:43 & 2 & 6.36  & 6.36  & 4.282346 \\
Denveer  & 2022-04-04 02:02 & 2022-04-04 03:45 & 2 & 7.02  & 7.02  & 5.178646 \\
Denveer  & 2022-04-04 04:08 & 2022-04-04 05:45 & 1 & 7     & 7     & 1.177135 \\
Denveer  & 2022-04-04 06:08 & 2022-04-04 07:44 & 1 & 6.58  & 6.58  & 1.053295 \\
Denveer  & 2022-04-04 08:07 & 2022-04-04 09:24 & 1 & 6.74  & 6.74  & 1.20853

Answer 1

As you don't seem to have a lot of background in exploring data of this kind and ultimately modeling it with multiple regression, I'll walk you through some steps. I don't use SPSS so I'll illustrate with R. I suspect that this can be done similarly in SPSS.

You made a good start by looking at the histogram of FCO2 values. Next, extend that to looking at a set of critical predictors and all their pairwise associations. Looking at all of your data together is a good way to proceed.

I took your data, removed the \\ end-of-line markers and extra spaces, kept the "&" field separators, and read them into a data frame, the format that R uses. I changed the field/column names to shorter versions.

lakeData <- read.table("lakeData.txt",sep="&",header=TRUE)
names(lakeData) <- c("Lake","startTime","stopTime","DayNight","airTemp","waterTemp","FCO2")

Note that the air and water temperature values are all the same, so we only have to deal with one of them

all.equal(lakeData$airTemp,lakeData$waterTemp)
## [1] TRUE

Make sure that "Lake" is treated as a categorical variable. The first value in alphabetical order, "Denveer," will be the reference level. Put the date/time data into a useful internal format. Extract the actual hour:minute values from each with a tool from the hms package in R. As the HM values (expressed here in seconds) are really continuous around the clock, also express them as angles from 0 to $2 \pi$ to simplify later analysis.

lakeData$Lake <- factor(lakeData$Lake)
lakeData$startTime <- as.POSIXct(lakeData$startTime)
lakeData$stopTime <- as.POSIXct(lakeData$stopTime)
library(hms)
lakeData[,"HM"] <- as_hms(lakeData$stopTime)
lakeData[,"timeAngle"] <- 2 * pi * as.numeric(lakeData$HM)/(24*60*60)

Histograms and pairwise associations

Now, examine the pairwise associations of some critical variables. The following requires you to first define a couple of helper functions, adapted from the help page for the standard R pairs() function, shown at the end of this answer.

pairs(lakeData[,c(7,1,2,5,8)],diag.panel=panel.hist, lower.panel=panel.cor,cex.cor=2,cex=1)

This is a type of "pairs plot." The plots along the diagonal are histograms of each of these 5 variables. The first is pretty much the histogram of FCO2 values you showed. Note the break in startTime values: some are in early to mid March, others in late March into April. The airTemp values are distributed from below 2 to over 14 degrees C. The sampling times within each day, the "HM" values in seconds past midnight, are reasonably uniform.

Now look at the off-diagonal plots at the upper right. They show the pairwise associations among these 5 critical variables. The numbers in the corresponding positions at the lower left are the pairwise correlation coefficients.

Look at the Lake:startTime pair. All of the earlier startTime values were for "Victoria"; all the later ones for "Denveer." That means that you won't readily be able to distinguish a trend over calendar time from a difference associated with Lake. That's emphasized in the FCO2:startTime pair. There's a clear hint of an increase of FCO2 with time in the earliest observations (those from Lake Victoria), at least. The startTime:airTemp pair also shows some association at least for the measurements at earlier values of startTime.

The airTemp:HM pair shows the diurnal variation of airTemp evaluated over all of the 99 observations. That's part of what you attempted to capture with your binary "daytime/nighttime" variable, but it's generally best to keep continuous predictors continuous. Based on the Lake:airTemp pair, it seems that typical airTemp values differ between the two Lakes.

Stop and think

Your attempt to distinguish between the two lakes is unfortunately confounded by the systematic difference in calendar dates of sampling. That's a fundamental problem with a study like this. One could argue from the FCO2:startTime plot that most of the difference in FCO2 values is just due to the dates of the samples. A skeptical reviewer of your study will be sure to point that out, however you try to account for that confounding by statistical analysis.

Multiple regression

When there are several predictors affecting a continuous outcome of interest, multiple linear regression can be a useful approach, as another answer suggests. That tries to account for effects of all of the predictors at once, moving beyond pairwise associations. That is more difficult, however, when the predictors are correlated as they are in this study.

You have 99 observations. To avoid overfitting, you can typically consider about 1 predictor per 10-20 observations: about 6 predictors here. Here's an example incorporating major predictors.

The angular predictor of time of day is modeled with separate sin and cos terms to account for how it wraps around (at midnight in these data). It looked like the association of FCO2 and startTime differed between the two Lakes, so there's an interaction term to allow for that possibility. This models the association of FCO2 with startTime as linear within each Lake; you might do better if you use a non-linear regression spline for startTime. I also transformed the startTime values into days since the first sample, to simplify interpretation of some coefficients. You might make different choices, based on your understanding of the subject matter.

lakeData[,"sampleDay"] <- (lakeData$startTime - min(lakeData$startTime))/(60*60*24)
lm1 <- lm(FCO2 ~ Lake + sampleDay + Lake:sampleDay + airTemp + sin(timeAngle)+cos(timeAngle),data=lakeData)
summary(lm1)
some lines omitted
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)             1.012680   0.833337   1.215   0.2274
LakeVictoria           -3.991721   0.858045  -4.652 1.10e-05
sampleDay               0.003145   0.052393   0.060   0.9523
airTemp                 0.099420   0.038228   2.601   0.0108
sin(timeAngle)          0.284655   0.114615   2.484   0.0148
cos(timeAngle)          0.692550   0.142666   4.854 4.92e-06
LakeVictoria:sampleDay  0.215383   0.095978   2.244   0.0272


Residual standard error: 0.6356 on 92 degrees of freedom
Multiple R-squared:  0.896,  Adjusted R-squared:  0.8892
F-statistic: 132.1 on 6 and 92 DF,  p-value: < 2.2e-16

This model captures nearly 90% of the variance among your FCO2 values, as shown by the "R-squared" values. The coefficients are the changes in FCO2 per unit change in the corresponding predictor, with all other predictors assumed constant. Interpreting these coefficient values is tricky, however, particularly with the interaction term.

The coefficient for LakeVictoria is the difference in FCO2 from that for the reference Lake, "Denveer," with other predictors held constant at baseline values, for example with sampleDay = 0. Lake Victoria thus seems to have a lower FCO2 than Lake Denveer.

Remember, however, that there was no overlap in sampleDay values between the two lakes--Denveer had no samples taken until sampleDay = 13, so there must be some caution interpreting that baseline difference. Playing with predictions from this model suggests that extrapolations for Lake Victoria out to the last sampleDay at Lake Denveer lead to higher predicted FCO2 for Victoria than for Denveer at that date.

There is an evident increase of FCO2 with airTemp, about 0.1 flux unit per degree. This is assumed to be the same for both Lakes, as there was no Lake interaction coefficient involving airTemp. Was that a reasonable assumption?

The sin and cos terms nicely picked up a diurnal variation in FCO2, but this acts to counteract the otherwise expected change of FCO2 with airTemp during the day. In the pairs plot, note how much flatter the FCO2 values are through the day (FCO2:HM plot), versus the strong diurnal variation of airTemp. So if higher current airTemp leads to higher FCO2, then a flat FCO2 through the day means there has to be some counterbalancing diurnal effect. Does that make sense biologically? Maybe current airTemp isn't what matters?

The sampleDay coefficient isn't so simple as it might seem, because sampleDay is involved in an interaction with Lake. In this case it's the change in FCO2 per extra day of sampling date for the reference level of Lake, or Lake Denveer. For that Lake, there seems to be no influence of sampleDay on FCO2 levels.

The LakeVictoria:sampleDay interaction coefficient is the difference between Victoria and Denveer (the reference value of Lake) in the association of sampleDay with FCO2. There thus does seem to be an increase of FCO2 with later sampling date for Lake Victoria, unlike for Lake Denveer. You need to think about the underlying biogeochemistry to determine what might be going on here; I worry that there were some rapid seasonal changes during the early samples at Victoria that had stabilized by the time samples were taken at Denveer.

It's important to do quality control to see how well the model fit the data and the underlying assumptions. I did that with plot(lm1) as a start, not shown here. There seem to be 2 outlying data points, the 2 highest ones on your histogram, but otherwise the model seemed OK with even a reasonably normal distribution of the residuals, the differences between the observed values and those predicted by the model. Without knowledge of the subject matter it's hard to know whether those apparent outliers represent a technical measurement failure or a failure of the model.

The lack of overlap between sampling dates from the two lakes showed up (via car::vif(lm1)) as a very high "variance inflation factor" (VIF) for each of Lake (45) and sampleDay (34). The VIF is an estimate of how unreliable your coefficient values might be due to correlations among the predictors. Those values (well over the rule of thumb of 10 or so for a "high" VIF) emphasize the potential problem posed by this experimental design.

Summary

One could argue from the multiple regression results that all of those predictors play roles in determining FCO2. Although the result shows a highly "statistically significant" difference between Lakes Denveer and Victoria, the lack of overlap in sampling dates during what might be a change of season requires care in interpretation.

For planning future studies, it's a good idea to include the data analysis approach as part of the planning. Then you can see problems in the experimental design, like this lack of overlap between Lakes in sampling dates, and alter your experimental design accordingly.

To learn more about this type of data analysis, see suggestions for books on this page and this page, among others on this site. Frank Harrell's course notes and book on "Regression Modeling Strategies" are particularly helpful, although they might assume a bit more background in statistics than you currently have. Working with a local experienced colleague and statistician would be very helpful and could help you avoid a lot of blind alleys along your path to becoming a more experienced data analyst.

---

Code for helper functions:

panel.hist <- function(x, ...)
 {
     usr <- par("usr"); on.exit(par(usr))
     par(usr = c(usr[1:2], 0, 1.5) )
     h <- hist(x, plot = FALSE)
     breaks <- h$breaks; nB <- length(breaks)
     y <- h$counts; y <- y/max(y)
     rect(breaks[-nB], 0, breaks[-1], y, col = "cyan", ...)
 }
panel.cor <- function(x, y, digits = 2, prefix = "", cex.cor, ...)
 {
     usr <- par("usr"); on.exit(par(usr))
     par(usr = c(0, 1, 0, 1))
     r <- abs(cor(x, y))
     txt <- format(c(r, 0.123456789), digits = digits)[1]
     txt <- paste0(prefix, txt)
     text(0.5, 0.5, txt, cex = cex.cor )
 }

Answer 2

to find out what causes the difference between the two lakes, you could use a regreesion analysis like a GLM or a Multiple Linear Regression (but check the prerequisits for the latter). Therebey, you could model the flux in dependency of different environmental variables (e.g., temperature, but you could add other environmental variables if you measured some, too).

Greetings Jan