Regression relationships of air temperature and elevation along an elevation gradient in the Luquillo Experimental Forest (LEF), Puerto Rico

By: Eda C. Meléndez-Colom

0. General Information

0.0 Objective: Find regression relationships of air and soil temperature and elevation along an elevation gradient in the Luquillo Experimental Forest (LEF), Puerto Rico.

0.1 Abstract

The relationship between mean air temperature and elevation is a required parameter for some environmental models such as Zelig. Mean air and soil temperature measurements of 10 sites located along a windward elevation gradient from 153 to 1011 meters were used to develop relationships between mean air and soil temperature of and elevation. All sites were located in clearings receiving direct solar radiation except for one at Sabana, located beneath a closed canopy forest and closed to an open canopy pasture site. The regressions performed showed a linear relationship between both air and soil mean temperature and elevation. The equations Mean Air Temperature (in C) = 26.4 -(0.00558 * elevation in meters) and Mean Soil Temperature (in C) = 25.6 - (0.00543 * elevation in meters) best fit these relationships. Thus, we found that the lapse rate of the mean air temperature and elevation is an increase of 5.58 degrees Celsius for each kilometer increase in elevation and the lapse rate of the mean soil temperature and elevation is an increase of 5.43 degrees in Celsius for each kilometer increase in elevation. The equation that best fits the mean soil temperature - elevation relationship includes all the stations. In contrast, the best equation for the mean air temperature - elevation relationship excluded both station located at Sabana.

0.2 Location of sites. Measurements were done at 10 locations along a windward elevation gradient in the LEF. All sites, except the Sabana forest site (asf, ass) were in clearings that received direct solar radiation. The Sabana forest site was located beneath closed canopy forest that was adjacent to the open canopy site (asa, ssa). Table 1 shows the elevation at which the measurements where performed.

0.3 Data. The data files were obtained from the files compiled by the International Institute of Tropical Forestry (IITF) Ecosystem Group from February 1997 to January 1998. They recorded air and soil temperature at 10 locations along an elevation gradient in the LEF. Soil temperature was measured at a depth of 15-20 cm at each site with StowAway TidbiT XT temperature sensors. The air temperatures were measured at 1.3 above the soil surface with Optic Stowaway temperature sensors. The measurements were performed every 6 minutes and averaged by hour and month.

In this proyect we used the data that had been averaged by hour and month. These data sets were made accessible on the LUQ Long Term Ecological Research (LTER) Web site by the Forest Service, in collaboration with the LUQ LTER site Data Manager. Table 3 displays these data files.

For this project we calculated the max, min, and averages of the hourly and monthly data to create graphs, tables and ultimately select the regression that best discribes the relationships between temperature and elevation.

0.4 Methodology. The original data files structures were first merged and transformed into a single data file including the monthly mean data files from all stations for all months. The hourly data was also merged and transformed into a data set structure table for calculating summaries and preparing graphs. All the data manipulation was done using QPRO for windows (v6.0).

0.4.1 Graphs. Several graphs were first to get a general idea of what the relationship between the elevations and the temperatures may be. Three main sets of charts were prepared at this time: (1) charts showing the soil and air mean temperatures graphs by month for each station, (2) charts showing the averages of the mean soil and air temperatures graphs by elevation for each month, and (3) two charts showing all the hourly mean temperature by hour for air and soil. Other mean hourly data charts were prepared for data analysis: (1) charts of the hourly mean temperatures that show the graphs with the highest data points, the average of all, and the minimum data points, and (2) a set of 5 charts showing monthly and hourly temperature from all stations vs from non Sabana stations.

0.4.2 Analysis.

0.3.2.1 Hourly temperatures. To decide which mean hourly air temperature graphs exhibit most of the highest and lowest values, a table was prepared with all stations' air temperature data by hour. The higest, second highest, lowest, and second lowest values were colored, counted for each station and tabulated on the spreadsheet.

0.3.2.2 Monthly temperatures. An One Way ANOVA (the Kruskal-Wallis ANOVA on Ranks) was run on all the mean data points to detect the difference between the groups (temperature data columns by Month for all the air and soil stations), and for normality. The tests for normality did not pass and the results showed a difference between the groups. That is, the change in temperature, as elevation increases, varies from month to month. Some polynomial regressions were performed on some of the data groups resulting always that the best fitted curves were those of first order. Linear regressions were then run then on all data groups.

The linear regressions were run for each month three times for both the air and soil data. Each month group has a set of 6 different regressions, namely, three air temperatures-elevation regressions: one for all stations -"(a)2" equations-, another for all the non-closed-canopy forest stations (excluding SF)-"(9)3" equations-, and another for all non Sabana stations (excluding SF and SA), and three similar regressions between the soil temperatures and elevation.

The regressions were tabulated with a subset of their most important parameters, and the data was plotted using SigmaStat (v1) and SigmaPlot (v3).

0.4.2.3 Soil vs air temperatures. Finally, a comparison was performed on the slopes and standard errors of the air and soil air temperature monthly curves for Feb to June 1997. The soil temperature data for the rest of the year was incomplete thus it was inaproppiate fro this comaprison. A table was created displaying the regression coefficients (first order) and its standard error for both the the air and soil temperature-elevation regressions all these months. The maximum value, the minimum value, and the range were calculated and displayed on the same table. The purpose is to check for the lapse rate and to compare the expected rate of change of the air and soil temperatures.

1.0 Graphs

1.1 Hourly Average Temperature. Mean air and soil temperature data for each time period (from midnight - 0 - to 11pm - 23 -) were ploted for all the stations. Two sets of two stations showing the lowest and the highest air (see Table 2 for details) and soil temperatures points were also ploted. The mean of the hourly average temperature for all stations is shown on these graphs. (Click on the image to view the corresponding chart.)

air temp  hourly average (all stations)			air temp hourly average (highest, avg, lowest)
soil temp  hourly average (all stations)			soil temp hourly average (highest, avg, lowest)

1.2 Monthly Temperature. Mean air and soil temperature data for each month was ploted in ascending order by elevation. ( Click on the image to view the corresponding chart.)

1.2.1 Air and soil mean monthly temperature by month. (Click on the image to view the corresponding chart.)

Feb 1997			Aug 1997
Mar 1997			Sep 1997
Apr 1997			Oct 1997
May 1997			Nov 1997
Jun 1997			Dec 1997
Jul 1997			Jan 1998

1.2.2 Air and soil mean monthly temperature by station. (Click on the image to view the corresponding chart.)

sf

sa

bi

g

y

uh

c

p

tc

sc

1.3 Monthly and Hourly temperature from all stations vs from non Sabana stations.

monthly mean temp All stations	monthly mean temp non Sabana stations	hourly mean temp All stations	hourly mean temp non Sabana stations	max, min, and avg monthly temp (both)

2.0 Results

2.1 Tables of functions. Tables 4 a and b show the air temperature-elevation and soil temperature-elevation linear regressions. The parameters R, Rsqr, PRESS, power, Std. Error of Estimate, Std Error of Constant, and Std. Error of Coefficient for each regression are also shown. The probability of being wrong in concluding that there is a true association between the variables, P, is <.00001 for all regressions.

Table 4a shows linear regressions between elevation and air temperature. Table 4b shows those between elevation and soil temperature.

The analysis and the selection of the best curves are discused on section 3.1 bellow.

2.2 Graphs. The results from the annual average air-elevation and soil-elevation regressions were ploted. The following table displays the graphs for these regressions. (The graphs are displayed when clicking on the equation).

Figure 1 shows the ranges and averages from all the stations.

Figure 1. Descriptive parameters of the 10 air temperature stations.

2.3. Comparisons between air and soil temperatures. The coeficients and their standard errors for the monthly curves were tabulated to observe the difference between the air-elevation relationship and the soil-elevation relationship. Only the curves from the months of February to June 1997 were used for this comparison since other months have incomplete record. Table 6 shows this comparison.

The highest regressions coefficients, which are a measure of how much does the temperature changes for a change of 1 m in the elevation in this case, were mostly shown by the air temperature-regression equations. The 3 soil temperature-elevation equations for the month of March, the one for all stations for the month of April, and the ones for the non Sabana stations for the month of Feb and June have greater regression coefficient than the corresponding air temperature-elevation regression coefficient.

The average slope for all the air temperature-elevation equations for these months is 5.898 ^OC/km for the all stations regressions, and 6.548 ^OC/km for the regressions excluding the SF station, and 5.99 ^OC/km for the ones excluding the two Sabana stations.

The average slope for all the air temperature-elevation equations for the month from February to June is 5.874 ^OC/km for the all stations regression, 6.028 ^OC/km for the regressions excluding the SF station, and 6.172 ^OC/km for the regressions excluding the Sabana stations.

2.4 Highest and lowest hourly air temperature. On Table 8, all the non Sabana hourly mean air tempearture can be observed by the hour. These are the averages of all the hourly mean temperatures for all the twelve months. The highest numbers values are colored with dark red, the second highest with light red, the lowest with dark blue and the second lowest with light blue. The averages for all hours and all months are also displayed.

The lowest mean air temperatures were recorded at the cloud forest's stations, both the SC (1011 m) and the TC (988 m), with an equaly number of highest values on the average during the 24 hours period. The short cloud forest showed the highest values during the afternoon and evening hours (from 1 to 8pm) and the tall cloud forest had the highest air temperature during the evening and night hours (from 6pm to 5am). The palm forest data was the highest during the morning hours (7am to 12md). The lowest temperatures (18.9 to 18.2 C) were recorded at the cloud forest stations from 6pm to 6am.

The highest temperatures were recorded at the three non Sabana stations with the lowest elevations, Bisley (BI) at 290 m, Gate (G) at 350 m , and the Yokaho station (Y) at 484 m. The BI station showed the highest during the afternoon and evening hours (from 3pm to 11pm at night) and during 2am to 4am. The G station showed the highest air temperatures during early morning from midnight to 8am. The Y station showed the highest air temperature values from 9am to 2pm. The highest temperatures (30 to 29.7 C) were recorded at the Yokahu station from 9am to 2pm.

3.0 Analysis

3.1 Regression that fits the best.

3.1.1 Definition of the best equation. I defined the best equation as the regression whose parameters show the optimum values for most of the selected parameters emphasizing on the PRESS and the standard error of estimate. Both parameters gave the same rank of equations except for the months of August and December. (Click here for more details).

3.1.2 Best equations for the soil tempearture data. Only the data for the months from February to June 1997 was considered for this analysis since the other months have missing data. For the soil data, the regression including all stations are the best for all months and for the annual data. All the parameters for the equations including all stations did best when compared to the parameters from the equations from the equations excluding SF only, and from the equations excluding both, SA and SF.

3.1.3 Best equations for the air temperature data. The mean air temperature data equations do not exhibit the same properties as the equations of the mean soil temperature case. For this case, the best parameters values vary among the months and annual regressions. (Click here for more details).

3.2 Selected equations. In order to do a projection analysis we selected the equations that do best according to the above anlysis.

The equation presenting annual mean air temperature - elevation relationship for all non Sabana stations was selected for this analysis.

The equation presenting annual mean soil temperature - elevation relationship for all stations was selected for this analysis.

The following table displays the selected equations for air and soil, the graphs of the projected against the actual values, and the data of the former graphs.

(Click on the name of the equation to see the graph of the original regression, on the image to see the graph of the actual against the projected value, and on the "Data Points" to see the actual and projected data.)

Table 9. Best air and soil regressions.

BEST REGRESSION EQUATIONS FOR MEAN AIR AND SOIL TEMPERATURES (IN CENTIGRADES) AND ELEVATION (IN METERS)	ACTUAL VS PROJECTED GRAPHS	DATA SET OF THE ACTUAL VS PROJECTED GRAPHS
Airtemp=26.4-(0.00558*elevation)		DATA POINTS
soitemp=25.6-(0.00543*elevation)		DATA POINTS

3.3 Hourly mean air temperature measurents summary.

The hourly data presents a wide range of fluctuation during the day. The following table shows the max, min, and ranges of the temperature for all the stations. Table 10 shows the mean air temperature fluctuations (max, min, and range) for all stations.

4.0 Conclusions. For these set of stations (located along a windward elevations gradient -from 153 to 1011 meters of elevation- sites receiving direct solar radiation and measured at 1.3 m above the soil surface):

4.1 Monthly temperature.

The mean air temperature data decreases linearly with elevation with an approximate rate of 5.58 degrees Celsius for each kilometer increase in elevation (the lapse rate). The mean soil temperature data also increses linearly with an approximate rate of 5.43 degrees Celsius for each kilometer meter increase in elevation.

4.2 Hourly temperature.

The hourly mean air temperature shows its peak during the mid day hours from 9am to 2 pm in the lowest elevations at sites exposed to the direct sunlight and its lowest values at the highest elevations from 6pm to 6am. The equations for these hourly data display a normal-like distribution curves for all stations with peaks varying from 11am to 2pm. The station located at the Palm forest at 901 m of elevation appear to be right skewed and has the peak value at 2pm. Hourly mean air temperature-elevation regressions should be run to confirm these observations. The highest daily variation was recorded at the Yokahu station at 484 m of elevation and the smallest was recorded at the Sabana Forest at 153 m. The highest diurnal variation (from 6am to 6pm was recorded at the Sabana pasture at 153 m of elevation and the two smallest were recorded at the Gate at 350 meters of elevations and at the Sabana Forest at 153 meters.

4.3. Soil vs air mean temperatures.

The rates of change of temperature for each meter of elevation do not differ if we consider the regression for all the stations. If we consider the non-open-canopy stations only the rates differ approximately by .51. That is, the air temperature increase will be .51 degrees in Celsius greater than the soil temperature for each increase of 1 meter in elevation. When we excledes the Sabana stations this difference lowers to .16 degrees.

Mean air temperature data are in general higher than the mean soil temperature at the same site. The gaps between these temperatures seems to be wider for the month of April, and it seems to be the least in February. Complete monthly soil and air temperaturs records should be taken to veruify this.