MT303 Experiment E4



MT23E Experiment E2

Measurement of Sensible Heat Flux (H) by the Eddy Correlation Method

OBJECTIVES

To measure the vertical sensible heat flux H in the surface layer by the eddy correlation method, and investigate the effect of sampling error and instrument response on the accuracy of the measured mean flux.

BACKGROUND AND THEORY (see section 7 of MT23E Keynotes)

At any height Z within the surface layer, the sensible heat flux [pic] can be estimated from a measured value of the eddy-covariance between vertical velocity (w) and temperature (T). In mathematical terms this is expressed as

[pic] , (1)

where [pic], [pic], and the over-bar indicates a time-average over the period of measurements. If the measurement is made close to the surface in a near constant-flux layer, then [pic] provides an estimate of the surface sensible heat flux H. Given measurements of Rn and G, the surface latent heat flux [pic] may then be estimated assuming the SEB equation

[pic] . (2)

In order to obtain an accurate estimate of H it is necessary to sample w and T simultaneously at frequent intervals (typically at least once every second), using fast response instruments. For a fixed period of measurement, the measurement accuracy will then depend on

1. The calibration accuracy of the instruments

2. The frequency of sampling

3. Instrument lag.

Increasing the frequency of sampling should lead to a more accurate estimate of H. However, the accuracy is then limited by the time-response characteristics of the instruments. In this experiment we investigate both effects by a) sub-sampling the data and b) filtering the data to simulate the effect of using slower-response instruments. All the necessary calculations are performed using a specially designed EXCEL workbook.

APPARATUS AND METHOD

Vertical velocity is sensed by a Gill propeller anemometer with axis pointing upwards. Temperature is sensed by a fine-wire platinum resistance thermometer (PRT). Both instruments are at a height of 3 m. Data are logged automatically by a computer located in the field site hut. The logging is carried out using a program called GENLOG which is already installed on the computer. In order to run GENLOG, the sampling rate, required number of data points and output file name must be supplied.

THE EXPERIMENT

Familiarise yourself with the equipment. Note which direction the vertical anemometer rotates for updraughts and downdraughts. Check that the computer in the hut is on and that the prompt on the screen says

C:\USERS\LAB\MT23E>

If this is not the case, consult a demonstrator.

As an initial test, run the programme for 3 minutes at a rate of 2 samples per second or 2 Hz(. The syntax for the program command is:

GENLOG

The output file name should end in the extension .DAT. Thus, for a 3 minute trial at 2 Hz, you should type

GENLOG 2 360 test.dat

Press the Enter key (() to start the program running. After 3 minutes, a message should appear showing that the data have been collected. Check that the file TEST.DAT has been created by typing

DIR (

This lists the contents of the MT23E directory (folder) and TEST.DAT should be there. You can check the contents of the file by typing

EDIT TEST.DAT (

The collected data should appear on the screen in the following format:

data collection started 25/02/2001 06:49.04.50 at 10.000Hz

Sample No,time/secs,Chan0,Chan1,Chan2,Chan3,Chan4,Chan5,Chan6,Chan7,

0, 0.000,0.186,0.125,0.000,4.150,0.371,-0.784,-2.388,-3.408,

1, 0.555,0.183,0.115,0.005,4.152,0.400,-0.579,-2.100,-3.289,

2, 1.055,0.198,0.125,-0.015,4.157,0.383,-0.537,-2.017,-3.254,

The 1st column gives the sample number and the 2nd column gives the sample time. Scroll to the end of the file to check that 360 data values (0 to 359) were collected and check that the interval between successive samples is 0.5 s.

Column five contains the output voltage from the upward pointing propeller (measuring w). You should be able to see that the w column has relatively small numbers which switch between positive and negative.

The 6th column contains the PRT output. This is volts and the recorded numbers should be between 3 and 5.

Having satisfied yourself that the instruments are working and GENLOG is giving sensible output, you are ready to start the IOP.

Some minutes before the IOP type in the appropriate command to sample at 2 Hz for 20 minutes (to generate 2400 data values). The filename should be the date in 6 digit format followed by .DAT. For example the output file name for the 16th June, 2003 would be 160603.DAT and your command line would be

GENLOG 2 2400 160603.DAT

DO NOT PRESS ENTER (() YET. Check with a demonstrator that the command line has been correctly typed before starting the IOP. The ENTER key (() should be pressed when the signal is given to start the IOP.

During the IOP you should make general observations of the weather (including screen measurements) and also note the timing of any significant changes. You should also spend a few minutes observing the behaviour of the propeller anemometer. It should be approximately true that the total transport of air upwards is equal to the total transport of air downwards. (Why is this?). As a rough check you can try to observe the time the propeller spends rotating one way compared with the time it spends rotating the other way. You can devise your own system for doing this but record your observations in a notebook.

At the end of the IOP copy the data file onto a floppy disk, e.g. using the command

COPY 160603.DAT a: (

and then take the floppy to 1L61 to carry out the analysis.

ANALYSIS

Preliminary analysis

From your observations of the rotation of the anemometer, estimate the total time for which the anemometer was experiencing (a) an updraught and (b) a downdraught. What is the average time period for (a) updraughts, (b) downdraughts? Record your calculations in your notebook.

Now follow these instructions carefully.

Log onto one of the computers in Room 1L61 using

username: metpc

password: metpc

In Internet Explorer, go to



Right-click on MT23E2.xls, go to Save target as and save it in your home directory. Then copy your data on the floppy (A drive) into your home directory. You can now run the program MT23E2.xls from your home directory.

When the spreadsheet is loaded, go to the sheet named Process. You will notice that there are a number of buttons on this sheet. These call macros which run the spreadsheet operations automatically. This minimises the amount of data manipulation you have to do within the spreadsheet.

To load your data and calculate a value for H from your full data set, click on the button marked Load data. In the dialogue box which appears, give the name of your data file without the .dat extension (e.g. for the file 160603.DAT, enter 160603). The spreadsheet will automatically load your data into the appropriate columns and calculate values of [pic], [pic], [pic] and H. It also shows mean and standard deviation statistics, which are displayed over the top of the data columns. Graphs of the w, T, [pic], [pic] time series are shown on chart sheets. H and other parameters of interest are printed at the top of each graph sheet.

Before doing any further analysis, note down the values of the various statistical parameters that were calculated by the spreadsheet. Then look at the data in the time series graphs and answer the following questions:

1. Do the two time series look strongly correlated or weakly correlated?

2. Can you relate any changes in w, T, [pic] or [pic] to the timing of changes in the observed weather during the IOP?

Record your observations in your notebook

Sampling Errors

An important source of uncertainty in the eddy covariance [pic] is due to sampling error, which arises because there are large fluctuations in [pic] about the mean value. A simple way of estimating this error is to calculate the standard error of the mean [pic] as [pic], where ( is the standard deviation of [pic]. Calculate [pic] using this formula and hence estimate the accuracy of the experimental value of H.

Unfortunately, the above method of estimating [pic] is not strictly correct when successive values in a series are correlated (as is the case in this experiment). Then such an estimate is generally smaller than the true sampling error of the mean. Also, we cannot use this approach to predict how the accuracy of the measurement depends on the frequency with which we sample w and T. However, we can get some idea of the effect of sampling frequency by sub-sampling our original series. Thus suppose we take every 2’nd data point, starting from data point 0. Then we can estimate a value of H given by

[pic] ,

where M is the number of data points in the sub-sample (approximately N/2).

To do this using the spreadsheet, go to sheet Process and click on the button marked Subsample. You will be asked to ‘Enter a sub-sample interval’. For this experiment enter 2. Then on request enter the first and last points of the series to be used, i.e. 0 and 2399 for this exercise. Note down the value of [pic] calculated by the program. Then repeat the exercise using sub-sample intervals of 4, 8, 16 and 32. Compare these values with the value of H calculated from the full data set and interpret results.

Instrument response time

Using an instrument with a finite response time means that rapid fluctuations in say temperature tend to be smoothed out by the instrument. Consequently, the effect of fluctuations with time scales less than the order of the lag constant of the instrument are not represented in the measurements. This can lead to an under-estimation of the observed heat flux if these rapid fluctuations actually contribute significantly to the total flux.

Here we simulate the effect of increasing the lag constant of the instruments by filtering the data numerically. The numerical filter simulates the effect of an instrument with a first order response, i.e. one for which the rate of change of the sensed parameter [pic] is given by

[pic] ,

where [pic] is the environmental value of the parameter and [pic]is the lag constant of the instrument (refer to module MT12C). The larger the value of [pic], the greater the smoothing of the fluctuations by the instrument.

To use this method, go to the spreadsheet Process, click on the lag filter button and enter the required value of the lag constant (. Investigate the effect of varying [pic] on the sensed time series and the measured heat flux. (You could try [pic]=0.5, 1, 2, 3, 4 and 5 seconds, for example.) In each case, a graph will be plotted and various data values including H are printed at the top of the graph. Inspect the graphs to see the effect of the filtering on the measured series.

Tabulate results in your notebook. Then draw and interpret a graph of H versus [pic]. (Don’t forget to include the value of H obtained without any filtering, i.e. for [pic].)

Instrument error

Calculating H using (1) involves the product of parameters measured using two instruments. It follows that the effect of instrument error can be estimated using

[pic], (3)

where [pic] is the uncertainty on the measured heat flux and the squared quantities are the fractional errors of the anemometer and thermometer sensitivities (see calibration sheet).

Use this to estimate the instrumental error on H and compare with your earlier estimate of sampling error. Combine these to arrive at an estimate of the overall accuracy of H calculated using the full data set.

Solving the SEB equation

Obtain a mean value of [pic] from the group carrying out experiment 1. Hence use (2) to estimate the surface latent heat flux and its associated experimental error. Also calculate the corresponding value of the Bowen Ratio.

DISCUSSION

An assumption of this experiment is that the vertical eddy sensible heat flux measured at the sampling height equals the surface upward heat flux H. Give reasons why this might not be true in practice.

With the instruments used in this experiment, is anything to be gained by sampling at 10 Hz rather than 2 Hz? Would you expect the answer to this question to be the same if a sonic anemometer (response time ~0.1 s) replaced the Gill anemometer (response time [pic] seconds where U is the wind speed)?

Would sampling at 0.1 Hz give useful results?

In the light of these questions, would you expect your value for H to be an under- or an overestimate of the true mean surface heat flux over the period of this experiment?

( Hz is the abbreviation for Hertz, which is the SI unit of frequency in seconds-1. Thus 1 Hz means “once every second”, while 2 Hz means “once every 0.5 seconds”.

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