Abstract

This report describes computer programs for estimating in situ phytoplankton photosynthesis. The programs are written in Turbo Pascal and run on IBM compatible personal computers controlled by the MS-DOS operating system (in Windows 95, they run in an MS-DOS window). The theory of the programs is presented in detail along with instructions for use. Example data sets and resulting output are shown for each of the programs.

Keywords: Limnology; oceanography; trophic dynamics; computer; primary production; model; simulation

Preface

This manual is a revision of the "primary production model" user's manual (Fee 1984), which is now out of print. This section is intended for readers familiar with the previous report; it describes how those programs have been changed. Users unfamiliar with the previous report should skip to the Introduction.

There have been several changes in terminology. The term "primary production" is no longer used to describe what these programs estimate. Primary production and primary productivity are terms that originate in trophic dynamic theory (Lindeman 1942): Primary production is the chemical energy in an ecosystem that is the direct product of photosynthesis, and primary productivity is the sum of all photosynthetic rates in an ecosystem. Because phytoplankton are the only important photosynthesizers in deep lakes and the offshore oceans, it is reasonable to argue that phytoplankton photosynthesis and primary production are the same thing in these systems (note: Flynn (1989) argues that primary production should not be used as a synonym for phytoplankton photosynthesis even in these systems). But this is clearly not the case in small or shallow lakes and in estuaries, where terrestrially derived organics and photosynthesis by macrophytes and periphyton dominate organic carbon budgets.

The term "model" is no longer used because to many people it implies ecosystem simulations based on linked sets of differential or difference equations. This is quite different from what the programs described here do, viz., interpolate and extrapolate actual field data to estimate in situ photosynthesis. The terms "light", "irradiance", and "radiation" have been replaced with the more precise term "PAR", which stands for the photon flux of Photosynthetically Available Radiation. All references to the term "transparency", which was previously used to describe the attenuation of PAR a function of depth, have been replaced by the term "PAR extinction".

The algorithms used in the old programs required few modifications to bring them up to date. Here is a summary of all changes:

• As before, if data are missing from a SOL data file (PAR measured in the air), simulated cloud-free PAR values are automatically generated for the missing dates. However, previous versions used 100% of the cloud-free PAR values; the new programs use 70% of the cloud-free values, which is the percent of PAR that occurs on an average day at the Experimental Lakes Area. This percentage can be changed to a value more appropriate for other locations with the "M" run-time command.
• Cloud-free solar PAR values generated by versions of the old programs prior to 3.45 (December 21, 1987) contained a systematic error: The variation of the distance of the sun from the earth during the year was divided into the solar constant, but it should have been multiplied by the solar constant. Estimates of annual photosynthesis and mean PAR in the water column calculated from input of empirical solar data were unaffected by this error, but estimates derived from simulated "cloudless" weather could contain errors of up to 15% (J. Shearer, unpublished ELA data) and should be recalculated with the new programs.
• If hypsographic (lake area as a function of depth) data are supplied, mean PAR in the water column is now calculated taking into account the diminution of the volume of the waterbody with depth. Versions of the old programs prior to 3.42 (February 11, 1987) did not incorporate this factor.
• Mean PAR in the water column is now calculated for the full 24 hr day. The old programs calculated means for the period when the sun was above the horizon. The old method of calculating means can be still be selected with the "P" run-time command.
• The program used to estimate photosynthesis parameters from incubator photosynthesis vs PAR data is now interactive and graphical; this makes it easier to identify bad data points and results in more accurate parameter estimates.
• Users of the old programs will be relieved to know that the formats of input and output files are virtually unchanged and most data files prepared for previous versions can be re-run "as is". The only potential problem is that previously information on the line after a data type identifier in a DAT file (e.g., /ext) was ignored; this space could thus be used for recording notes (comments) about the data. The new programs do not ignore information following the data type identifier. The new convention for embedding comments is to enclose them in quotation marks. This is much more flexible since comments can now be placed anywhere in the DAT file, not just on the line containing the data type identifier.
• New run-time commands have been added:
  • (E)uphotic zone: Specifies the fraction of solar PAR at the bottom of the euphotic zone.
  • (F)raction: Specifies the fraction of solar PAR that occurs at the top of the water column; it is used to specify how much solar PAR penetrates through an ice cover.
  • (M)issing: Specifies the fraction of simulated cloudless PAR to use when data are missing from a SOL data file.
  • (P)artial: Causes mean PAR in the water column to be calculated only for the part of the day when the sun is above the horizon.
  • o(X)ygen: Specifies that input data are in oxygen units; causes output to be labelled in oxygen units.
• In the old IBM-PC (MS-DOS) versions of the programs, the last record in a data file was not read unless the file size was an exact multiple of 128 bytes. This was caused by a "bug" in the MS-DOS version of the PL/I compiler used to create the programs. In the new versions, which were made with Turbo Pascal, all ASCII data files are properly read.
• The new programs are smaller and about twice as fast as the old ones. Error checking and messages have been improved. The manual has been rewritten.

Introduction

This report describes computer programs used to estimate in situ phytoplankton photosynthesis and mean PAR in the water columns of lakes and oceans. (In this report, PAR is defined as the photon flux of Photosynthetically Available Radiation, i.e., the number of photons between 400 and 700 nm arriving at a point. PAR is elsewhere defined as Photosynthetically Active Radiation, but we avoid this term because it implies that all photons between 400 and 700 nm result in an equal photosynthetic response, which is not the case). These programs have evolved over a period of 20 years (Fee 1969, 1973, 1973a, 1977, 1984). The versions described here incorporate the following features:

• Daily and annual photosynthesis rates are estimated; results are expressed both in areal (per square meter) and volumetric (per cubic meter) units.
• Cloudless solar PAR can be generated for any time of year and any location on the earth.
• Separate estimates are made of photosynthesis in the mixed layer and below the thermocline.
• Daily mean PAR in the mixed layer and below the thermocline are calculated. This is useful for determining whether PAR limits photosynthesis (Hecky and Guildford 1984).
• The total mass of carbon fixed in the waterbody is calculated. This can be corrected for the fact that the volume of the lake decreases as a function of depth; Fee (1980) discusses the importance of this correction.
• The programs are based on input of the parameters of the photosynthesis vs light curve rather than tables of raw photosynthesis vs PAR data. This reduces the probability of inputting bad data and makes it suitable for estimating photosynthesis from remotely sensed chlorophyll data.

Scope of the programs

• FITSOLAR: Calculates an empirical constant that describes the net effect of local atmospheric factors (e.g., haze, altitude) on incoming solar PAR. This constant makes the equations used to calculate cloud-free solar PAR appropriate for a specific location.
• PSPARMS: Calculates (P)hoto(S)ynthesis (PAR)a(M)eter(S) from photosynthesis vs PAR data.
• YPHOTO: Simulates (PHOTO)synthesis as a function of depth at a single place for a range of dates (usually an entire (Y)ear or ice-free season). This program is used when a lake is sampled multiple times during the year and an estimate of photosynthesis for the entire sampling period is required.
• YTOTAL: Reads in the photosynthesis vs depth profiles calculated by YPHOTO and calculates integral and mean photosynthesis and mean PAR above and below the thermocline. Optionally, it corrects these (TOTAL)s for the decrease of lake volume with depth. This program provides estimates for a single location for a range of dates (usually an entire (Y)ear or ice-free season).
• DPHOTO: Simulates (PHOTO)synthesis as a function of depth at a single place for a single (D)ay. This program is used to analyze data when a station is sampled only once and an estimate of photosynthesis for that day is required. Data from many different stations sampled on different days (i.e., from an entire research cruise) can be analyzed in a single run.
• DTOTAL: Reads in the photosynthesis vs depth profile calculated by DPHOTO and from these data it calculates integral and mean photosynthesis and mean PAR above and below the thermocline. Optionally, it corrects these (TOTAL)s for the decrease of lake volume with depth. This program provides estimates for a single location for single dates.

Table 1. The data used in the programs, required units, and which programs use them. Note: An Einstein (abbreviated: Ein) is 1 mole of photons.

At the Freshwater Institute these programs are used in the context of research programs that operate in the following way (complete details are given in Fee et al. 1989): In the field, samples of whole water are taken; the vertical attenuation (extinction) of PAR is measured; and PAR in the air above the waterbody (solar PAR) is measured. In the laboratory, subsamples are taken from the water sample for determining the concentrations of dissolved inorganic carbon and chlorophyll. NaH¹⁴CO₃ solution is added to the water, which is then siphoned into bottles. Two bottles are put in the dark, and the others are placed in a chamber having various PAR levels; they are incubated for 1--4 hr. During the incubation, PAR at each bottle position in the incubator is measured. At the end of the incubation period, ¹⁴C uptake rates are determined and photosynthesis rates are calculated.

The computer programs described in this report are used to analyze these field and laboratory data: PSPARMS estimates photosynthesis parameters from chlorophyll and incubator data (photosynthesis vs PAR). YPHOTO (or DPHOTO) simulates in situ photosynthesis vs depth profiles from solar PAR, PAR extinction, chlorophyll, and photosynthesis parameter data. Finally, YTOTAL (or DTOTAL) corrects the calculated photosynthesis profiles for the decrease of lake volume with depth and estimates photosynthesis and mean PAR in the water column above and below the thermocline.

System requirements

Time requirements

Availability and transportability

Theory of the programs

This section describes the theoretical principles on which the programs are based. Table 2 summarizes the mathematical symbols used in this section.

Table 2. Definitions of mathemathical symbols.

Simulation of photosynthesis vs depth curves

Figure 1. The procedure used to estimate in situ photosynthesis.

The relationships that must be known are: (1) solar PAR (measured in the air above the waterbody) as a function of time I_o(t); top curve in Fig. 1. (2) photosynthesis as a function of PAR (P vs I; middle curve), and (3) percent of solar PAR as a function of depth (I_z); bottom left curve, expressed as a percentage).

For a given instantaneous value of I_o, the depth profile of PAR (bottom left curve) is calculated by multiplying I_o by the percent of surface PAR that reaches each depth (I_z). Photosynthesis as a function of depth (P_z; bottom right curve) is then calculated from the P vs I curve in the manner illustrated. The instantaneous areal rate of photosynthesis is obtained by integrating the P_z curve from the surface down to the depth of the euphotic zone (z_eu). The entire procedure is repeated at successive time intervals (DELTA_T) (top curve) to obtain a set of instantaneous depth integrals. The daily rate is the integral of these instantaneous depth integrals over the entire day.

This procedure assumes that P vs I and I_z are invariant during the day, which is not strictly true (Fee 1975; Bukata et al. 1989). However, the variations of P vs I curves are inconsistent, and Fee (1975, 1980) showed that even extreme variations have only minor effects on estimates of daily integral photosynthesis estimates. Bukata et al. (1989) concluded that diurnal changes of I_z curves did not greatly affect daily areal photosynthesis estimates.

The heart of the calculation procedure just described is the P vs I curve illustrated in Figure 2.

Figure 2. The photosynthesis vs PAR curve, illustrating the equation used and graphically defining the photosynthesis parameters.

This figure illustrates how it is calculated from chlorophyll concentration (B) and two photosynthesis parameters P^B_m and alpha^B (the superscript B indicates that P^B_m and alpha^B are normalized on chlorophyll concentration). P^B_m is the maximum rate of photosynthesis divided by the chlorophyll concentration, and alpha^B is the slope of the P vs I curve as PAR approaches zero divided by the chlorophyll concentration. P^B_m and alpha^B are physiologically meaningful parameters (Bannister 1974; Jassby and Platt 1976); they are used here because the process of calculating them makes it easy to identify errors in experimental P vs I data. Further, programs based on these parameters can be driven by remotely sensed chlorophyll data.

The equation used to describe the P vs I curve (Fig. 2) is:
P = 0 if I is less than I_k / 20
P = B*P^B_m if I is greater than or equal to 2*I_k
P = B*alpha^B*I' [1 - (I')/(4*I_k] otherwise,
where P is the rate of photosynthesis, I is PAR, I_k = P^B_m / alpha^B, and I'= I - I_k / 20. This formulation is adapted from an equation given in Jassby and Platt (1976); it is used here because it can be evaluated in only 20% of the time required to evaluate their recommended hyperbolic tangent equation and both equations give identical integral photosynthesis estimates. As it is formulated, photosynthesis is zero at PAR=I'; this constant was determined empirically and corresponds to Jassby and Platt's constant R^B. Inhibition of photosynthesis by high PAR is not included in this formulation; Marra (1978), and Welschmeyer and Lorenzen (1981) have shown that such inhibition probably does not occur in situ and Fee (1980) showed that it is of little quantitative importance even if it does occur.

Constants

There are two groups of numeric constants--those that are permanently coded into the programs and those that can be changed at the time that the programs are run. The first group includes constants that can only be changed by editing the appropriate line in the disk file GENVARS.PAS and recompiling the programs; this is also how you can change the default value of a constant in the second group. The names given below are the actual variable names used in the file GENVARS.PAS.

The first group of constants includes:

• DELTA_T: The time interval at which in situ photosynthesis is simulated during the day; thus, it is the time interval between successive values of surface (solar) PAR in the SOL file. The default value is 30 minutes. Experiments showed no differences in daily photosynthesis estimates for values between five and 40 minutes (there were significant differences with greater values).
• MAXDATA: The maximum number of data pairs that can appear in a single PAR extinction, chlorophyll, P^B_m, alpha^B, or hypsographic (area vs depth) depth profile. The default value is 50.
• NIZERO: The maximum number of data points that can be input in a single solar PAR curve. The program uses 150, which is sufficient for a DELTA_T of 10 minutes.
• MINCHL, MAXCHL: As chlorophyll (B) data are read they are checked for plausibility. If a value less than 0.5 or greater than 350 is input, a warning message is issued.
• MINPARM, MAXPARM: As alpha^B and P^B_m data are read they are checked for plausibility. If a value less than 0.5 or greater than 10 is input, a warning message is issued. The values for MINPARM and MAXPARM are in carbon units; if the "X" run-time command is specified at the time the program is started, these values are multiplied by 32/12 to convert them to units of O₂.

  Variable	Minimum	Maximum
  Chlorophyll (B)	0.5	350
  alphaB	0.5	10
  PBm	0.5	10

• MINYEAR, MAXYEAR: If a year specified in a DAT file is less than 1950 or greater than 2050, the run will halt.

The second group of constants includes:

• ATMOS_EFFECT: An empirical constant that specifies the fraction of solar PAR at the top of the atmosphere that reaches the surface of the earth at the location of the waterbody under cloudless conditions. It is used when YPHOTO or DPHOTO simulate cloudless solar PAR; if empirical solar PAR data are input to these programs, this constant is not used. The default value (0.325) was measured at the Experimental Lakes Area in Northwestern Ontario. Use the program FITSOLAR to determine values for other locations.
• NDEPTHS: The number of intervals that the euphotic zone is divided into, i.e., it is the number of depths on the simulated photosynthesis vs depth profile. The default value is 11.
• EUPI: The fraction of surface PAR at the bottom of the euphotic zone. The default value is 0.005 (=0.5%). A warning message will be issued if the depth where this occurs is greater than 30 m.
• LATITUDE: The degrees from the equator (north positive) of the waterbody. It is used when YPHOTO or DPHOTO simulate cloudless solar PAR; if empirical solar PAR data are input to these programs, this constant is not used. The default value is 50^oN.

Interpolation procedures

B, P^B_m, and alpha^B data are input as functions of depth. Values for the specific depths where photosynthesis is to be calculated are obtained by linear interpolation in the input data. If the data do not encompass the depths for which values are needed, then they are extrapolated: The value at the shallowest depth that was input is used from the surface down to that depth and the value at the greatest depth that was input is used for all greater depths.

PAR extinction, and hypsographic (lake area vs depth) data are also input as functions of depth. The run will fail if a value is not input for a depth of 0 m, or if only one value is input, or if values do not decrease with increasing depth. Values for the specific depths where photosynthesis is to be calculated are obtained by linear interpolation in the input data (PAR extinction data are linearized by taking logarithms). If it is necessary to extrapolate to greater depths than were input, a linear regression (straight line) is fit to the available data. For PAR extinction data, if five or more data points are input, the first three points are not used in fitting the straight line since the logarithm of PAR extinction vs depth is frequently nonlinear near the surface.

For all data, if only one profile is entered, it will be extrapolated forward and/or backward in time as needed. For example, if an alpha^B depth profile dated June 1 is input and photosynthesis is calculated for the period May 1 through October 1, the June 1 value will be used for the entire period. Whenever input data are extrapolated forward or backward in time a warning message is recorded in the output.

Integration method

Calculation of cloudless solar PAR

The following is derived from Brock (1981). The declination of the earth during the year (PHI, the angle between the sun and the equator at solar noon, north positive) is calculated with the formula

PHI = 23.45^osin(360^o (284 + d) / LAMBDA_Y),

where d is the number of the day of the year, and LAMBDA_Y is the number of days in the year. Letting k = -tan(LATITUDE)*tan(PHI), the angle from due south of the sun at sunset (VARPHI) is calculated with the formula

VARPHI =	0o	if k > 1
	180o	if k < -1
	arccos(k)	otherwise

Since the apparent movement of the sun is 0.25^o of arc per minute (360^o/ 1440 minutes), daylength in minutes (LAMBDA_D) is simply

LAMBDA_D = 2*VARPHI / .25 = 8 * VARPHI.

Using a value of 373.4 mEin.m^-2min^-1 for the solar constant (THETA, the solar PAR at the top of the atmosphere at the mean solar distance), cloudless PAR at time t is calculated from the formula

Io(t) =	KAPPA_A*THETA*DELTA_S2*[sin(PHI)*sin(LATITUDE) +
	cos(PHI)*cos(LATITUDE)*cos(.25o(t-LAMBDA_D/2))]

where 0 is less than or equal to t, which in turn is less than or equal to LAMBDA_D, and DELTA_S² is the square of the deviation of the earth from its mean distance from the sun. It is calculated from the following empirical formula (Davies, 1981)

DELTA_S2 =	1.00011 + 0.034221*cos(k) +
	0.00128 * sin(k) - 0.000719 * cos(2*k) +
	0.000077* sin(2*k)

where k = 360^o*d / LAMBDA_Y.

FITSOLAR

PSPARMS

YPHOTO and DPHOTO

YTOTAL and DTOTAL

Like YPHOTO and DPHOTO, these programs divide the euphotic zone into discrete layers of equal thickness and calculate values for the following variables at the surface, at the bottom of the euphotic zone and at each of the depths where the layers meet: (1) The fraction of solar PAR that reaches each depth, (2) the daily photosynthesis at each depth, (3) the area of the lake at each depth (if hypsographic data are input). In addition, the depth of the mixed layer must be known. Given all of the required variables, it is straightforward to calculate the various integrals with Simpson's Rule.

Using the Programs

Disk files

Table 3. The file EXTensions used in the programs and the kind of data contained in each.

Table 4. Summary of file EXTensions read as input and produced as output by each program. EXTension names enclosed in square brackets are files produced only under special circumstances: A SOL file is produced if one is not found, a ### file is produced if a run fails or is interrupted, and a BRK file is produced if a run is interrupted. Table 3 explains what kind of information each file EXT contains.

The programs all read their input data in "free-format"; this means that it does not matter where you type data on an input line--successive values can be separated by blanks, commas, tabs, or the ends of lines, and alphabetic data can be entered in either upper or lower case. However, data must appear in the file in the proper order. For example, dates are input as the month name followed by the day of the month (e.g., Aug 1; only the first three letters of the month name are necessary). If you enter this date with the month and day reversed (i.e., 1 Aug) the programs will fail.

The first non-blank line in any disk file is simply copied to the top of the output files; it serves to identify the output. You can put any information that you want on this "header" line, but be sure that the location and time period are included so that the output will be understandable.

Error Handling

If YPHOTO, YTOTAL, DPHOTO, or DTOTAL fail for a known reason, a message describing the problem will be displayed on the screen. This message will also be permanently stored in a disk file with the same NAME as the NAME of the input DAT file and an EXT of "###". This facilitates the use of the programs in DOS batch files: If you submit several runs to DOS for execution in a single batch file you can find out which (if any) of the runs failed simply by typing the DOS command "DIR *.###".

If an unforeseen error occurs, the program will stop, displaying the message "Runtime error nnn at xxxx:yyyy". This is an emergency message produced by Turbo Pascal; nnn is the runtime error number, and xxxx:yyyy is the address of the error. Detailed explanations of runtime error messages are given in the Turbo Pascal manual. However, the cause of a problem will usually be obvious: e.g., the disk is full. If you cannot figure out why the program failed, please send a disk containing a copy of the dataset that caused the error along with a copy of the error message to the author.

If a run terminates abnormally, e.g., if the electrical power fails or if you get a runtime error message from Turbo Pascal, files with an EXT of "%%%" will appear in your disk directory. These are temporary files that will be erased automatically if you restart the interrupted run; you may safely erase them by typing "DEL *.%%%".

Input data are carefully scrutinized for plausibility. If a questionable value is found, the run continues but a warning message is recorded in any output computed from this datum.

Data Used by More than one Program

Solar data

Solar data are input as tables (one for each day) that give the instantaneous flux of solar PAR at time intervals of 30 minutes. Data are required only for times when the sun is above the horizon, but including zeros for the dark periods does no harm. A solar file containing data for two days follows:

ELA cloudless solar PAR data.
May 1
 0.0  11.9  18.8  27.0  36.2  46.0  56.2 
66.5  76.4  85.9  94.4 101.7 107.7 112.2
114.9 115.8 114.9 112.2 107.7 101.7  94.4 
85.9  76.4  66.5  56.2  46.0  36.2  27.0 
18.8  11.9   0.0  -1
May 2
 0.0  11.8  18.4  26.3  35.1  44.6  54.5 
64.4  74.2  83.6  92.1  99.7 106.1 111.0
114.4 116.1 116.1 114.4 111.0 106.1  99.7 
92.1  83.6  74.2  64.4  54.5  44.6  35.1 
26.3  18.4  11.8   0.0  -1

PAR extinction, P^B_m, alpha^B, and chlorophyll data

July 17
0 100
1 50
2 25
3 12.5
4 6.25
-1

July 17 0 100,1 50,2 25,3 12.5,4 6.25 -1

Hypsographic (lake area vs depth) data

0 27.7E8 2 24.47E8 4 23.90E8 6 21.29E8
8 17.37E8 10 10.74E8 12 0.65E8 -1

Mixing depth data

Apr  1   5
May  1   3
May  5   6
May 30  10

Organization of data in DAT files

In the previous version of these programs, any information on the line after the data type identifier (e.g., /ext) was ignored; this space could thus be used for recording notes (comments) about the data. In the new version, information on this line is not ignored. The new way of commenting data is to enclose them in quotes (either single or double quotation marks can be used, but the quotation marks must be properly paired; a comment may not extend beyond the end of a line). Comments can appear anywhere inside PAR extinction, chlorophyll, alpha^B, P^B_m, mixing depth, or hypsographic data.

Starting the Programs

A>YPHOTO ela84 

Generating cloudless PAR data...
Press B to breakpoint run

FITSOLAR

A>fitsolar

FITSOLAR  Version 4.0  
FWI Software Tools

Enter year (e.g. 1980): 1984
Enter latitude in degrees: 50

Enter month (e.g. May): jun
Enter day (e.g. 1): 1
Enter surface PAR at noon: 125.5
ATMOS_EFFECT =  0.3917

Enter date (e.g. May 1): ^C

PSPARMS

Yellowknife Lake Study, 1983 Data
Station-01 5.7
13     -1     0.14   -9
39.2   -1     0.67   0.78   -9
126.7  -1     2.49   3.05   -9
366.7  -1     3.05   3.13   -9
-1
'Station 75  5-Jul-83' 2.6
10.1   12.4   -1     0.11   -9
27.3   -1     0.57   0.57   -9
57.5   -1     1.49   1.62   -9
125.6  -1     5.36   3.57   -9
289.2  -1     4.80   -9
-1

If the data shown above are in a file called TESTPRM.INC, then typing

A>psparms testprm 

(D)rop point, (G)raph, (A)bort, (C)ontinue

• (D)rop point The program will ask you which point to drop. Enter the sequence number of the point. If you select a point twice it will be "undropped", i.e., re-included in the dataset for fitting the curve.
• (G)raph The data will be redisplayed, with dropped data points circled.
• (A)bort The run will be terminated immediately. You may want to do this if you need to make corrections to data.
• (C)ontinue If you have dropped any data points, the P vs I curve will be refit and the data with the new curve will be redisplayed. If you did not drop any data points, then the program will proceed to the next dataset.

It is an unfortunate fact that human judgement is a necessary part of the process of estimating P^B_m and alpha^B. The previous version of this program fully automated this process, but it became apparent that a single bad data point in an otherwise good dataset could result in very inaccurate parameter estimates. Fortunately, it is easy to identify bad data points when the photosynthesis vs PAR data are shown graphically. Obviously, data should be dropped with caution, and you should make permanent copies of the final graphs so that you will have a permanent record of what data were used. You can do this by pressing the Shift-PrintScreen key combination at any time that a graph is displayed on the screen. DOS supplies a program (GRAPHICS.COM) for this purpose (see your DOS manual for a description of how to use this program), but it does not work with all graphics cards or printers. The program Pizzaz (Application Techniques, Inc.) is a better print-screen program that works with all popular cards and printers; it also offers much more flexibility than GRAPHICS.COM (smoothing, placement on the page, scaling the graph to a specific size, printing to a file, etc.).

If the above example is run and no data points are dropped, PSARMS will produce a disk file called TESTPRM.PRM which should look like this:

Yellowknife Lake Study, 1983 Data
Identifier                    #Iter B(Chl) PBm alphaB Sum.Sq
============================================================
Station-01                      28   5.7  0.55  1.49  0.010
Station 75  5-Jul-83            30   2.6  1.96  4.76  0.442

YPHOTO

Lake Winnipeg 1976, Cruise 3
May 1, May 10, 1976
/ext
May 5   0 100   10    1     -1
/chl
May 1   0   1   -1   
May 10  0  10   -1   
/alp
Jan 1   0   5   -1
/pbm
Dec 31  0 1.98  -1

If the data shown above are in a file called TESTYR.DAT and if neither 1976.SOL nor CLDLSS.SOL can be found on the disk, then typing

A>YPHOTO testyr 

Simulated PAR data for 1976; latitude=50.0; atmos_effect=0.3250; % of cloudless=100.00
MAY  1
  0.0   4.8  14.3  24.0  33.6  43.1  52.3  61.0  69.1  76.4  82.8  88.1  92.4
 95.5  97.4  98.1  97.4  95.5  92.4  88.1  82.8  76.4  69.1  61.0  52.3  43.1
 33.6  24.0  14.3   4.8   0.0 -1
MAY  2
  0.0   5.3  14.8  24.4  34.1  43.6  52.7  61.4  69.4  76.7  83.1  88.5  92.7
 95.9  97.7  98.4  97.7  95.9  92.7  88.5  83.1  76.7  69.4  61.4  52.7  43.6
 34.1  24.4  14.8   5.3   0.0 -1
MAY  3
  0.0   5.8  15.2  24.9  34.5  44.0  53.1  61.8  69.8  77.1  83.4  88.8  93.1
 96.2  98.0  98.7  98.0  96.2  93.1  88.8  83.4  77.1  69.8  61.8  53.1  44.0
 34.5  24.9  15.2   5.8   0.0 -1
MAY  4
  0.0   6.2  15.7  25.3  34.9  44.4  53.5  62.1  70.1  77.4  83.7  89.1  93.4
 96.5  98.3  99.0  98.3  96.5  93.4  89.1  83.7  77.4  70.1  62.1  53.5  44.4
 34.9  25.3  15.7   6.2   0.0 -1
MAY  5
  0.0   6.7  16.1  25.7  35.3  44.8  53.9  62.5  70.5  77.7  84.1  89.4  93.7
 96.7  98.6  99.2  98.6  96.7  93.7  89.4  84.1  77.7  70.5  62.5  53.9  44.8
 35.3  25.7  16.1   6.7   0.0 -1
MAY  6
  0.0   7.2  16.6  26.2  35.7  45.1  54.2  62.8  70.8  78.0  84.4  89.7  93.9
 97.0  98.9  99.5  98.9  97.0  93.9  89.7  84.4  78.0  70.8  62.8  54.2  45.1
 35.7  26.2  16.6   7.2   0.0 -1
MAY  7
  0.0   7.6  17.0  26.6  36.1  45.5  54.6  63.2  71.1  78.3  84.7  90.0  94.2
 97.3  99.2  99.8  99.2  97.3  94.2  90.0  84.7  78.3  71.1  63.2  54.6  45.5
 36.1  26.6  17.0   7.6   0.0 -1
MAY  8
  0.0   8.1  17.4  27.0  36.5  45.9  54.9  63.5  71.5  78.6  84.9  90.3  94.5
 97.6  99.4 100.0  99.4  97.6  94.5  90.3  84.9  78.6  71.5  63.5  54.9  45.9
 36.5  27.0  17.4   8.1   0.0 -1
MAY  9
  0.0   8.5  17.9  27.4  36.9  46.2  55.3  63.8  71.8  78.9  85.2  90.5  94.7
 97.8  99.7 100.3  99.7  97.8  94.7  90.5  85.2  78.9  71.8  63.8  55.3  46.2
 36.9  27.4  17.9   8.5   0.0 -1
MAY 10
  0.0   8.9  18.3  27.8  37.3  46.6  55.6  64.2  72.1  79.2  85.5  90.8  95.0
 98.1  99.9 100.5  99.9  98.1  95.0  90.8  85.5  79.2  72.1  64.2  55.6  46.6
 37.3  27.8  18.3   8.9   0.0 -1

Lake Winnipeg 1976, Cruise 3
                                            Depths
               0.00  1.20  2.40  3.60  4.80  6.00  7.20  8.40  9.60 10.80 12.00
      mg/m^2 ------------------------- mg C/(m^3.day) -------------------------
MAY  1   163 |    28    27    26    24    19    13     7     4     2     1     0
MAY  2   328 |    56    54    52    47    38    25    15     8     4     1     0
MAY  3   494 |    84    82    78    71    58    38    23    12     6     2     0
MAY  4   662 |   113   110   104    95    78    51    30    16     8     3     0
MAY  5   831 |   142   137   131   120    98    65    38    20     9     3     0
MAY  6  1001 |   171   166   158   144   118    78    46    25    11     4     0
MAY  7  1173 |   200   194   185   169   138    92    54    29    13     5     0
MAY  8  1346 |   229   222   212   194   158   105    62    33    15     5     1
MAY  9  1519 |   258   250   239   219   179   119    70    38    18     6     1
MAY 10  1694 |   287   279   266   244   200   133    78    42    20     7     1
================================================================================
total    9.2 |   1.6   1.5   1.5   1.3   1.1   0.7   0.4   0.2   0.1   0.0   0.0
(gm)
                                     I N P U T   D A T A

                                            Depths
               0.00  1.20  2.40  3.60  4.80  6.00  7.20  8.40  9.60 10.80 12.00
             ------------------------------------------------------------------
PAR extinction: % of Surface PAR

MAY  5        100.00 57.54 33.11 19.05 10.96  6.31  3.63  2.09  1.20  0.69  0.40

Chlorophyll: mg/(m^3)

MAY  1          1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00
MAY 10         10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

alphaB: mg C/(mg chl.E.m^-2)

JAN  1          5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00

PBm: mg C/(mg chl.hr)

DEC 31          1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98

Command line: TESTYR

Solar data: Cloudless PAR data for 1976 latitude = 50.0 atmos_effect = 0.3250

Warning: TESTYR, MAY  5: PAR extinction data extended to start date
Warning: TESTYR, JAN  1: alphaB data extended to finish date
Warning: TESTYR, DEC 31: PBm data extended to start date
Warning: TESTYR, MAY  5: PAR extinction data extended to finish date

This file contains the following information: For each day, the depth profile of photosynthesis and the integral of this curve over depth. The depth profile of photosynthesis for the entire time period for which calculations were made and the integral of this curve over depth follow. Finally, the values of the input data that were used at each depth where photosynthesis was calculated and warning messages (if any) are summarized. Here is the output produced from the example dataset.

Lake Winnipeg 1976, Cruise 3

           +----------+-----------------------------------------+-----------
           |  Uncorr. |          Morphometry Corrected          | mean PAR
           +----------+-----------+---------+-------------------+-----------
       Epi | mg C/m2  |  mg C/m2  | mg C/m3 | Mass Fixed, gm C  | mE/m2.min
      Depth|Total  Epi| Total  Epi|Total Epi| To zmax   In Epi  | Epi   Hypo
======|=====|==========|===========|=========|===================|===========
MAY  1  3.00  164    80   141    76   17   27 3.925E+08 2.098E+08 20.23  2.94
MAY  2  3.60  326   189   281   176   35   53 7.810E+08 4.901E+08 18.43  2.39
MAY  3  3.60  494   285   425   266   52   79 1.182E+09 7.391E+08 18.55  2.41
MAY  4  4.20  662   436   569   403   70  104 1.582E+09 1.120E+09 17.00  1.96
MAY  5  4.20  830   547   715   506   88  131 1.987E+09 1.406E+09 17.10  1.97
MAY  6  4.80 1003   735   863   673  106  154 2.398E+09 1.870E+09 15.77  1.60
MAY  7  4.80 1175   860  1011   788  124  180 2.808E+09 2.189E+09 15.86  1.61
MAY  8  4.80 1345   986  1158   903  142  206 3.216E+09 2.508E+09 15.94  1.62
MAY  9  5.40 1521  1210  1308  1098  161  226 3.633E+09 3.049E+09 14.79  1.32
MAY 10  5.40 1696  1349  1458  1224  179  252 4.050E+09 3.399E+09 14.87  1.33
======|=====|==========|===========|=========|===================|===========
totals (gm)   9.2   6.7   7.9   6.1  1.0  1.4 2.203E+10 1.698E+10

Mean PAR values are calculated for 24 hour period
Maximum depth = 12.00
Number of depth intervals = 41
Command line: TESTYR,I=41
Cloudless PAR data for 1976 latitude = 50.0 atmos_effect = 0.3250

Warning: TESTYR, MAY  5: PAR extinction data extended to start date
Warning: TESTYR, MAY  5: PAR extinction data extended to finish date

YTOTAL

This program requires the same input data files that YPHOTO required. In addition it reads the OUT file produced by YPHOTO. The DAT file must contain mixing depth data. If you wish to have the totals corrected for the diminution of lake volume with depth, the DAT file must also contain hypsographic data. An example DAT file for YTOTAL looks like:

Lake Winnipeg 1976, Cruise 3
May 1, May 10, 1976
/ext
May 5   0 100   10    1     -1
/chl 'this is a comment'
May 1   0   1  -1  "another comment"
May 10  0  10  -1   
/alp
Jan 1   0   5  -1
/pbm
Dec 31  0 1.98 -1
/hyp
0 27.78E8, 2 25.57E8, 4 23.90E8, 6 21.29E8,
8 17.37E8, 10 10.74E8, 12 0.65E8 -1
/zep
May   1  3
May  30 10

If the files TESTYR.OUT and CLDLSS.SOL produced by the example are on the disk, and if the data shown above are contained in the file TESTYR.DAT, then typing

A>YTOTAL testyr,i=41 

will produce a file called TESTYR.TOT:

Lake Winnipeg 1976, Cruise 3
                                            Depths
               0.00  1.20  2.40  3.60  4.80  6.00  7.20  8.40  9.60 10.80 12.00
      mg/m^2 ------------------------- mg C/(m^3.day) -------------------------
MAY  1   163 |    28    27    26    24    19    13     7     4     2     1     0
MAY  2   328 |    56    54    52    47    38    25    15     8     4     1     0
MAY  3   494 |    84    82    78    71    58    38    23    12     6     2     0
MAY  4   662 |   113   110   104    95    78    51    30    16     8     3     0
MAY  5   831 |   142   137   131   120    98    65    38    20     9     3     0
MAY  6  1001 |   171   166   158   144   118    78    46    25    11     4     0
MAY  7  1173 |   200   194   185   169   138    92    54    29    13     5     0
MAY  8  1346 |   229   222   212   194   158   105    62    33    15     5     1
MAY  9  1519 |   258   250   239   219   179   119    70    38    18     6     1
MAY 10  1694 |   287   279   266   244   200   133    78    42    20     7     1
================================================================================
total    9.2 |   1.6   1.5   1.5   1.3   1.1   0.7   0.4   0.2   0.1   0.0   0.0
(gm)
                                     I N P U T   D A T A

                                            Depths
               0.00  1.20  2.40  3.60  4.80  6.00  7.20  8.40  9.60 10.80 12.00
             ------------------------------------------------------------------
PAR extinction: % of Surface PAR

MAY  5        100.00 57.54 33.11 19.05 10.96  6.31  3.63  2.09  1.20  0.69  0.40

Chlorophyll: mg/(m^3)

MAY  1          1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00  1.00
MAY 10         10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00 10.00

alphaB: mg C/(mg chl.E.m^-2)

JAN  1          5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00  5.00

PBm: mg C/(mg chl.hr)

DEC 31          1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98  1.98

Command line: TESTYR

Solar data: Cloudless PAR data for 1976 latitude = 50.0 atmos_effect = 0.3250

Warning: TESTYR, MAY  5: PAR extinction data extended to start date
Warning: TESTYR, JAN  1: alphaB data extended to finish date
Warning: TESTYR, DEC 31: PBm data extended to start date
Warning: TESTYR, MAY  5: PAR extinction data extended to finish date

This file contains the following results: For each day, the mixed layer depth; uncorrected and (if hypsographic data were input) corrected integrals of photosynthesis over depth; average photosynthesis (per meter³) above and below the thermocline, and mean PAR above and below the thermocline. This is followed by integrals and averages for the entire time period for which calculations were made. Finally, warning messages (if any) are summarized.

Note in the example output that the uncorrected integrals (col. 4) do not exactly match the corresponding results in the file TESTYR.OUT; this is because the integrals reported by YTOTAL were calculated with 41 depth intervals while those calculated by YPHOTO were calculated with only 11 depth intervals. The reason for using more depth intervals in YTOTAL and DTOTAL than in YPHOTO and DPHOTO was previously discussed.

DPHOTO

Lake Winnipeg 1976, Cruise 3
318

L. Wpg, Sta 318, 1976 Cloudless weather
Jun 6, 1976
/ext 'this is a comment'
Jun 6  0 100   2 2.19  -1
/chl
Jun 6  0 1.7  -1 "another comment"
/alp
Jun 6  0 5.4  -1
/pbm
Jun 6  0 4.7  -1

If the data sets shown above are in the disk files TESTDAY.DAT and 318.STA, and if there are no solar data on the disk then typing A>DPHOTO testday will produce a file TESTDAY.OUT:

Lake Winnipeg 1976, Cruise 3

Command line: TESTDAY

L. Wpg, Sta 318, 1976 Cloudless weather
                                            Depths
               0.00  0.30  0.60  0.90  1.20  1.50  1.80  2.10  2.40  2.70  3.00
      mg/m^2 ------------------------- mg C/(m^3.day) -------------------------
JUN  6   105 |   114   104    83    53    31    16     7     2     0     0     0

                                    I N P U T   D A T A

PAR extinction: % of Surface PAR
JUN  6       100.00 56.37 31.78 17.91 10.10  5.69  3.21  1.81  1.02  0.57  0.32

Chlorophyll: mg/(m^3)
JUN  6         1.70  1.70  1.70  1.70  1.70  1.70  1.70  1.70  1.70  1.70  1.70

alphaB: mg C/(mg chl.E.m^-2)
JUN  6         5.40  5.40  5.40  5.40  5.40  5.40  5.40  5.40  5.40  5.40  5.40

PBm: mg C/(mg chl.hr)
JUN  6         4.70  4.70  4.70  4.70  4.70  4.70  4.70  4.70  4.70  4.70  4.70

Warning: 318, JUN  6: Solar data missing; 70% of simulated cloudless used

DTOTAL

This program requires the same input data files required for input to DPHOTO; in addition, it reads the output file produced by DPHOTO. The DAT file must contain mixing depth and hypsographic data the hypsographic data can be omitted if you do not wish to have the totals corrected for the diminution of volume with depth. The STA file for use with DTOTAL would look exactly like the DPHOTO. The file 318.DAT pointed to by this example contains the following information:

L. Wpg, Sta 318, 1976 Cloudless weather
Jun 6, 1976
/ext
Jun 6    0      100     2      2.19   -1
/chl
Jun 6    0      1.7    -1
/alp
Jun 6    0      5.4    -1
/pbm
Jun 6    0      4.7    -1
/hyp
0 27.78E8, 2 25.57E8, 4 23.90E8, 6 21.29E8,
8 17.37E8, 10 10.74E8, 12 0.65E8 -1
/zep
Jun 6  10.0

If the disk contains the TESTDAY.OUT file produced by DPHOTO and if the example data shown in above are contained in the file TESTDAY.DAT then typing

A>DTOTAL testday,i=41 

Command line: TESTDAY,I=41
Lake Winnipeg 1976, Cruise 3



L. Wpg, Sta 318, 1976 Cloudless weather

           +----------+-----------------------------------------+-----------
           |  Uncorr. |          Morphometry Corrected          | mean PAR
           +----------+-----------+---------+-------------------+-----------
       Epi | mg C/m2  |  mg C/m2  | mg C/m3 | Mass Fixed, gm C  | mE/m2.min
      Depth|Total  Epi| Total  Epi|Total Epi| To zmax   In Epi  | Epi   Hypo
======|=====|==========|===========|=========|===================|===========
JUN  6 10.00  106   106   103   103   13   13 2.873E+08 2.873E+08  2.81  0.00

Mean PAR values are calculated for 24 hour period
Maximum depth = 10.00
Number of depth intervals = 41

Breakpointing Runs

Run-time commands

• (A)tmos_Effect= <>: The number after the equal sign will be used as the value of ATMOS_EFFECT.
• (B)reakpoint: Causes YPHOTO to breakpoint after checking the input data for errors and computing photosynthesis for the first day. This allows you to check for bad input data, to see the depths at which calculations are going to be made, and to check the magnitude of the calculated results on the first day before committing the computer to a long calculation.
• (C)heck: Forces YPHOTO to check the solar data for errors before starting the calculations. YPHOTO does not normally check the solar data for errors (as it does all of the other input data) because a single solar PAR dataset is typically used for many different stations or for many different lakes. It takes about five times as long to read and check these data during the preliminary error checking phase of the program than it does to check all the other input data combined. Moreover, it is only necessary to check these data once (or indeed to not check them at all, e.g., when the program is using simulated cloudless weather).
• (E)uphotic zone=<>: Specifies the fraction of surface PAR at the bottom of the euphotic zone. The default value is 0.005(=0.5%). <> must be input as a fraction, i.e., a number less than 1.
• (F)raction=<>: Specifies the fraction of solar PAR (measured in air) remaining at the top of the water column. The default value is 1.0; this value will need to be changed only if the waterbody is covered by ice and snow, which absorb PAR. <> must be input as a fraction, i.e., a number less than 1.
• (I)ntervals=<>: The number after the equal sign will be used as the value of NDEPTHS. The default value is 11. Because of the integration algorithm used, <> must be an odd number. To assure reasonable accuracy, values less than five are not allowed. If more than 101 intervals are needed, then the program must be recompiled after changing the value of MAXINTR in the file GENVARS.PAS.
• (L)atitude=<>: The number after the equal sign will be used as the value of LATITUDE. This value is used when solar PAR values are simulated; it is irrelevant if you are using empirical solar PAR data which contain no missing data. Enter values for the southern hemisphere as negative numbers.
• (M)issing=<>: If data are missing from a SOL data file, solar PAR values will be simulated by the programs. This option is used to specify the fraction of the theoretical cloud-free PAR that reaches the surface of the lake on an day with average cloudiness. The default value is 0.7 (=70%); it was measured at the Experimental Lakes Area in Northwestern Ontario and will not be appropriate for waterbodies located in sunnier or cloudier climates. <> must be input as a fraction, i.e., a number less than 1.
• (O)utput=<>: This command specifies the letter of the disk drive (see the DOS manual for the disk drive nomenclature) where you want the output file(s) stored. If you do not specify otherwise, the output files will be written onto the drive that contains the input files.
• (P)artial: This causes YTOTAL and DTOTAL to calculate mean PAR in the water column only for the part of the day during which the sun is above the horizon. This was the way that previous versions of these programs worked (the default now is to calculate averages for the entire 24 hr day).
• (S)olar=<>: This command allows you to specify which disk drive contains the solar PAR data. By putting the solar data on a different drive, you can make more space available on the default drive for output files.
• (U)niform: This causes the input data values for B (chlorophyll), alpha^B and P^B_m to be applied uniformly over the input depths instead of being linearly interpolated. An example will make this clear: Suppose that the input data looked like:

  MAY 5 0.0 10, 5.0 100, 10.0 1000, -1
  

  If the (U)niform command is given, then all depths between 0 and 5 meters will be assigned the value 10, all depths between 5 and 10 meters will be assigned the value 100 and any depths greater than 10 meters will be assigned the value 1000. If you do not specify this command then values will be linearly interpolated: if calculation depths are at 0, 1, 2, etc. then the interpolated values for the above dataset would be 10, 28, 46, etc. For this reason, "U" should be specified whenever integrated samples are taken.
• o(X)ygen: Specifies that photosynthesis input data (P^B_m and alpha^B) are in oxygen units; causes output to be labelled properly.
• (Z)max[=<>]: By default, the programs that integrate over depth (DPHOTO, YPHOTO, DTOTAL, and YTOTAL) use the greatest euphotic zone depth (defined as that depth where 0.5% of surface light occurs; calculated from the PAR extinction data) as the depth down to which calculations are made. This will be inappropriate if the lake is so shallow that the calculated euphotic zone depth is greater than the actual maximum depth of the lake. You might also want YTOTAL or DTOTAL to integrate down to the maximum mixing depth of the lake rather than down to the maximum euphotic zone depth. The "Z" runtime command is the solution to these problems: It forces DPHOTO and YPHOTO to use the maximum depth that actually appears in the PAR extinction data as the integration depth; or it forces DTOTAL and YTOTAL to use the maximum depth that actually appears in the mixing depth data as the integration depth. You can also put an equal sign followed by a number after "Z" on the command line to force any of these programs to use a particular maximum depth.

A>YPHOTO ELA84,Z,B,I=15 

A>YPHOTO WPG76,Z=10.5,L=53,C,S=B,O=C,P 

Unusual problems

This section describes some unusual situations that may arise and presents solutions.

• If a run of YPHOTO in a batch file fails, the error messages are stored in a file with an extension of `###'. If the batch file then runs YTOTAL on the same dataset, the `###' file created by YTOTAL will overwrite the `###' file created by YPHOTO (the same applies to sequential runs of DPHOTO and DTOTAL). This happens because both programs use the same EXT (###) for storing fatal error messages. You can prevent this by putting "IF NOT EXIST <>.###" at the beginning of the line in the batch file that runs YTOTAL, where <> is the NAME of the DAT (or STA) file; this will cause DOS to ignore the command if the previous run failed.
• Chlorophyll data might be unavailable for a station where the photosynthesis vs PAR data were measured. Without chlorophyll data, P^B_m and alpha^B cannot be estimated, and without these parameters, in situ rates cannot be calculated. This means that the photosynthesis vs PAR data will be wasted. However, the chlorophyll values that are used to estimate P^B_m and alpha^B are later "factored out" when in situ rates are calculated. Therefore, so long as the chlorophyll, P^B_m or alpha^B values are not used for any purpose other than estimating in situ photosynthesis, a dummy value of chlorophyll (1.0) can be used for estimating P^B_m and alpha^B.
• It would be helpful in some lakes if the "U" option could be invoked in the mixed layer and then "turned off" for samples in the metalimnion and hypolimnion. This can be achieved by inputting the mixed layer data twice, assigning a depth of zero to the first dataset and the depth of the mixed layer to the second dataset.

Acknowledgments

Many colleagues helped me design these programs, tested preliminary versions, and notified me of inconsistencies (bugs). I thank in particular John Shearer, Ed DeBruyn, Martin Bergmann, Scott Millard, Harvey Bootsma, and Rose Mugidde.

References

Bannister, T.T. 1974. Production equations in terms of chlorophyll concentration, quantum yield, and upper limit to production. Limnol. Oceanogr. 19: 1--12.

Brock, T.D. 1981. Calculating solar radiation for ecological studies. Ecol. Modell. 14: 1--19.

Bukata, R.P., J.H. Jerome, and J.E. Bruton. 1989. Determination of irradiation and primary production using a time-dependent attenuation coefficient. J. Great Lakes Res. 15: 327--338.

Caceci, M.S., and W.P. Cacheris. 1984. Fitting curves to data. Byte 9: 340--362.

Davies, J.A. 1981. Models for estimating incoming solar irradiance. Can. Climate Centre Rep. 81-2.

Fee, E.J. 1969. A numerical model for the estimation of photosynthetic production, integrated over time and depth, in natural waters. Limnol. Oceanogr. 14: 906--911.

Fee, E.J. 1973. A digital computer program for calculating integral phytoplankton primary production in vertically stratified water bodies. Fish. Res. Board Can. Tech. Rep. 376: i+14 p.

Fee, E.J. 1973a. Modelling primary production in water bodies: a numerical approach that allows vertical inhomogeneities. J. Fish. Res. Board Can. 30: 1469--1473.

Fee, E.J. 1975. The importance of diurnal variation of photosynthesis vs. light curves to estimates of integral primary production. Int. Assoc. Theor. Appl. Limnol. Verh. 19: 39--46.

Fee, E.J. 1977. A computer program for estimating annual primary production in vertically stratified waterbodies with an incubator technique. Can. Fish. Mar. Serv. Tech. Rep. 741: v+38 p.

Fee, E.J. 1980. Important factors for estimating annual phytoplankton production in the Experimental Lakes Area. Can. J. Fish. Aquat. Sci. 37: 513--522.

Fee, E.J. 1984. Freshwater Institute primary production model user's guide. Can. Tech. Rep. Fish. Aquat. Sci. 1328: v+36 p.

Fee, E.J., R.E. Hecky, M.P. Stainton, P. Sandberg, L.L. Hendzel, S.J. Guildford, H.J. Kling, G.K. McCullough, C. Anema, and A. Salki. 1989. Lake variability and climate research in Northwest Ontario: Study design and 1985--1986 data from the Red Lake District. Can. Tech. Rep. Fish. Aquat. Sci. 1662: v+39 p.

Flynn, K.J. 1988. The concept of "primary production" in aquatic ecology. Limnol. Oceanogr. 33: 1215--1216.

Hecky, R.E., and S.J. Guildford. 1984. Primary productivity of Southern Indian Lake before, during and after impoundment and Churchill River diversion. Can. J. Fish. Aquat. Sci. 41: 591--604.

Jassby, A.D., and T. Platt. 1976. Mathematical formulation of the relationship between photosynthesis and light for phytoplankton. Limnol. Oceanogr. 21: 540--547.

Lindeman, R.L. 1942. The trophic-dynamic aspect of ecology. Ecology 23: 399--418.

Marra, L. 1978. Effect of short term variations in light intensity on photosynthesis of a marine phytoplankter--laboratory simulation study. Mar. Biol. (N.Y.) 46: 191--202.

Welschmeyer, J.A., and C.J. Lorenzen. 1981. Chlorophyll-specific photosynthesis and quantum-efficiency at subsaturating light intensities. J. Phycol. 17: 283--293.

Program changes since technical report 1740 was printed

Bug fixes

25 October 1990

21 January 1990

2 April 1992

21 April 1993

Here's how things work now: If DPHOTO or YPHOTO cannot find a solar data file (<>.SOL), they use a mathematical model to simulate solar PAR values. The 'M' parameter was originally designed to permit the user to specify the fraction of cloudless irradiance to use for those instances when a <>.SOL file IS found but contains a missing day (i.e., it is used to simulate a day of 'average' cloudiness and is thus more comparable to empirical solar data). However, it is entirely logical for a user to want to use the 'M' parameter to make simulated PAR values reflect average cloud conditions rather than perfectly cloud-free conditions; the programs have been changed to permit this: If the user does not specify a value for 'M' on the command line, things work pretty much as before---simulated cloud-free PAR solar values are used everywhere (as before for YPHOTO, YTOTAL, and DTOTAL, and now also for DPHOTO), and 70% of simulated cloud-free PAR (or the value of 'M' specified by the user on the command-line) is used to fill gaps in empirical solar data. However, if a value for 'M' is specified on the command line and empirical solar data (<>.SOL) cannot be found, simulated PAR values are everywhere multiplied by specified 'M' value. In the case of YPHOTO, these are stored in the file CLDLSS.SOL---which thus contains simulated solar PAR values for average cloudiness rather than cloud-free weather---and the percent of cloudless PAR values that are contained in this file are permanently stored in the header line at the start of this file. [Thanks to Harvey Bootsma for finding the bug and suggesting these changes.]

PASCAL SOURCE FILES

  LHA e source

Click here to download a self-unzipping file containing executable programs for calculating rates of photosynthesis by phytoplankton.

The International Canopy Network