ACADIA model:  numerical experiments
 
 

                 In our study we used the ACADIA model version 4, with  3D climatological bi-monthly velocity and temperature/salinity fields used as input. These fields are model generated circulation and temperature/salinity structure fields representing bi-monthly mean conditions. We  focus in detail on the two spring periods, March-April and May-June  and on the summer period July-August to simulate alongshore transport of offshore algal blooms in the Gulf of Main. A finite element formulation of the non-conservative form of the vertically averaged Advection-Diffusion-Reaction equation that tracks depth-averaged single transport variable - Alexandrium tamarense cells concentration was used for  simulation. 
Investigation of the climatological mean seasonal cycle of Alexandrium tamarense consists of  6 separate 6 month long runs. In each experiment, zero cells concentration was used as initial condition, then velocity and temperature/salinity fields  from a particular period were specified (runs 1-2, 5-7 ). In some experiments a  boundary condition 10 cells/l flowing in through the open boundary in the Bay of Fundy was used (runs 3-5). An additional experiment was conducted assuming initial cells concentration equal to 10 cells/l (run 4).  In all the above mentioned experiments it was assumed that the only light is a factor limiting growth rate of the cells. Finally, one more run with nutrient limitation has been performed (run 6).

Below these runs are described and discussed in terms of the Gulf of Main circulation scheme outlined in Lynch et al, 1997. All runs are performed on 'g2s.5b' finite element mesh which includes Bay of Fundy domain.

                                                                                   Table 1                                             Summary of Model Parameters


      attenuation coeff (water)		             attenk =  0.20            1/meter

      attenuation coeff  (sedim)		             attens = 3000            1/meter

  day light averaged irradiance		               rad =  280             watt/m^2

      maximum growth rate		              G_max = 0.60             1/day

   maintenance respiration rate 		                 Gr =  0.05             1/day

       growth efficiency		               G_eff = 0.017      m^2/day/watt

        grazing/mortality		                 Graze = 0.1             1/day

        DIN half-sat constant		                aksn = 1.5             mkg/l

        "light" irradiance flux		                L_light = 2.4         watt/m^2

         "dark" irradiance flux		                L_dark = 0.024          watt/m^2

 

                                              Table 2                                                                     Run table


      Time period		    Initial condition     Inflow boundary       Biological model       *.fli movie name   data/obs comp (1998)

  March 1 -August 20		             C = 0           C =   0     germ, growth, mort        cell98_a1.fli      cell98_a1.jpg

          same		             C = 0           C = 10     growth, mortality        cell98_a3.fli       cell98_a3.jpg

          same		             C = 10           C = 10      growth, mortality        cell99_a4.fli       cell98_a4.jpg

          same		             C = 0           C = 10   germ, growth, mort        cell98_a5.fli       cell98_a5.jpg

          same		             C =  0           C =  0          germ        cell98_a6.fli       cell98_a6.jpg

          same		             C = 0           C =   0    germ, growth, mort, 
    nutrient limitation		       cell98_a7.fli       cell98_a7.jpg

          same		             C = 10           C = 10   growth, mort, nutrient
           limitation		        cell98_a8.fli        cell98_a8.jpg

 
 sc98c1.fliis the original Rich Signell's animation.

 run a1.   cell98_a1.fli     Basic run. Initial cells concentration is set to zero,  germination, growth and mortality included.  Initial distribution of Alexandrium cysts in the upper 1 cm of bottom sediments, derived from a survey in October 1997, displayed in init_cyst.jpg. Two maxima in cysts distribution are clearly seen there: approximately between isobaths 75 and 150 m offshore of Kennebec  River and Penobscot Bay. Also, an additional maximum may be tracked in the Bay of Fundy.  Climatological velocity fields for two two bi-monthly periods are displayed here.  Run starts on March 1, 1997 when the endogenous clock is on. 

 run a3.   cell98_a3.fli    Initial cell concentration is set to zero, no germination, the only grows and mortality are included. There is a cell flux 10 cells/l flowing in through the open boundary in the Bay of Fundy. 

run a4.   cell98_a4.fli    Initial cell concentration is set to 10 cell/l;  no germination, the only growth and mortality are included. There is a cell flux 10 cells/l flowing in through the open boundary in the Bay of Fundy.

 run a5.   cell98_a5.fli  Initial cells concentration is set to zero,  germination, growth and mortality included.  There is a cell flux 10 cells/l flowing in through the open boundary in the Bay of Fundy. 

 run a6.   cell98_a6.fli  Initial cells concentration is set to zero,  the only germination included. There is no cell flux  flowing in through the open boundary in the Bay of Fundy. 

 run a7.   cell98_a7.fli     Initial cells concentration is set to zero,  germination, growth, mortality and nutrient limitation are included. NO3 distribution has been derived  from the climatic temperature and salinity fields using a regression formula.  Example of such distribution NO3 field received from the March-April climatology in case of two different regressions (2 and 5) is displayed here.

 run a8.   cell98_a8.fli    Initial cell concentration is set to 10 cell/l;  no germination, the only growth, mortality, and nutrient limitation are included. There is a cell flux 10 cells/l flowing in through the open boundary in the Bay of Fundy.

A composite of  cell distribution for 3 model runs: a6, a1, and a7 on  May 15,  June 15, July 15, and August 15 is presented in   cell_model_a617.jpg.A seperate plot displaying results of run a6 may be found here:  cell_model_a6.jpg.   A composite for runs 3, 4 is in    cell_model_a34.jpg.
 
 Cell densities (number of cells / l)  of Alexandrium sp. at 2m, 20m, and the average of these two centered on  June 11, July 11, and August 11 1998 are shown here: cell98_data_ave.jpg.  Cell densities for 2000 survey cruise centered on April 29 and June 9 are shown in   cell2000_data_ave.jpg.
The 100 and 600 cells/l contour lines are given.

 A growth rate diagnosis based on the climatical March-April, May-June, and July-August bi-monthly fields is presented here: cell98_diagn.jpg. 

 Notes on frames.

 Rows 1, 2: Temperature and salinity at the uppermost level.

 Row 3: NO3 field restored from  the climatological temperature and salinity fields using a regression relation.

 Row 4: The growth rate (1/day) depending only on light limitation.

 Row 5: The growth rate (1/day) dependent only on nutrient limitation.

 Note on equations used to compute NO3  field and growth rates.

                                                          NO3 = max(0,NO3'),  NO3' = -144.8 - 0.38 * T + 4.75 * S   (option 2)

                                        R-light = (G_max * G_fac + Gr) * tanh(G_eff * Rad/(G_max * G_fac + Gr))  - Gr ,  light limitation

                                                                       R-no3 = G_max * G_fac * NO3/(NO3 + aksn),  NO3 limitation,

                                                                          R = min(R-light, R-no3) - Graze,  light and NO3 limitation
 where,

                                                     G_fac = T_fac * S_fac, 
                                                     T_fac = -0.000347 * T^3 + 0.0097 * T^2 - 0.0133 * T + 0.131,
                                                     S_fac = -0.0022 * S^2 + 0.103 * S -0.195
 

                        updated on  02/26/2003
 

 A new set  of Alexandrium cysts distribution in the upper 1 cm of bottom sediments, derived from the 1981-83 cyst observations, has been added to that one from 1997 observations. Both sets have been merged and the final cyst distribution displayed in figure  cyst_comp.jpg.  Then, using this new distribution, runs a1,a5,a6, and a7 have been repeated and the results of new computation are presented in Table 3.
 A new run a9  ( similar to a4 ) has been added to the prvious ones. Initial cell concentration was set to C=100 cells / l  and  restricted by  the area where observations are available, and  C=0 elsewhere. No germination, the only growth and mortality processes are included in the model.

 It is interesting to analyze runs a6 and a9.

 Run a6. Due to the process of cyst germination cell concentration in the Eastrern Gulf of Main is higher then in WGM. Cell concentration gets its maximum there  at the end of June, then declines slowly during the July/August bi-monthly period. In a contrary, cell concentration in the Western Gulf of main gets its maximum at the end of July, then decreasing slowly during August. There is still enough cysts to maintain high level of cell concentration in the ephotic layer.

 Run a9. During the March/April bi-monthly period cell concentration in the entire Gulf of Main , initially homogeneous, gets slowly to decline. During next bi-monthly period -- May/June cell concentration starts to increase so that by the end of June the highest cell concentrations occur in the Bazzard bay and the Wynyard Sound areas. All this time cell concentration in the EGM went to zero. During July/August there was an active cells growth in the Western Gulf of Main but in the eastern part.
 

                                                   Table 3                                                                             Run table


           Time period		    Initial condition     Inflow boundary       Biological model       *.fli movie name   data/obs comparison

  March 1 -August 31		           C = 0           C = 0     germ, growth, mort        cell98_a1_new.fli      cell98_a1_new.jpg

          same		           C = 0           C =10     germ, growth, mort        cell98_a5_new.fli       cell98_a5_new.jpg

          same		           C =  0           C =  0          germ        cell98_a6_new.fli       cell98_a6_new.jpg

          same		           C = 0           C =  0      germ, growth, mort, 
    nutrient limitation		       cell98_a7_new.fli       cell98_a7_new.jpg

          same		           C = 100           C =  0     growth, mortality       cell98_a9_new.fli       cell98_a9_new.jpg

 
 
 A two additionall data sets derived from the April/May and May/June  2000 surveys were used to compare a model data to observations. The first survey was centered on 29 April, 2000, and the second one on 9 June, 2000. Both surveys were conducted at the early stages of the model run when cell concentration in the entire domain was at least an order  of magnitude lower then it is evidenced from observations. To make model and observations comparable, we used 2 methods: 1) simply multiply model data by the factor 10, or normalize data and observations. For normalizing, each data set was initially devided by its maximum value then multiplied by factor 1000 ( to keep cell concentration within known level between 0 and 1000 cells/l ).  Results of such comparison are presented in Tablle 4.

 
 
                                                                                      Table 4.                           Data/Observations comparison  ( 2000 )

            Run		             absolute value             normalized

           a1		        cell_2000_a1_new.jpg        cell_2000_a1_norm.jpg

           a3		        cell_2000_a3_new.jpg        cell_2000_a3_norm.jpg

           a5		         cell_2000_a5_new.jpg        cell_2000_a5_norm.jpg

           a6		        cell_2000_a6_new.jpg        cell_2000_a6_norm.jpg

           a7		        cell_2000_a7_new.jpg         cell_2000_a7_norm.jpg

 

                        updated on  04/18/2003
 

 A new set  of  Gulf of Main observations (1932-2001) is used to get a nutrient distribution in the GOM domain and use it in a model runs with nutrient limitation.  First of all, station positions  were plotted to see how uniformly stations occupy  GOM domain, see plot  stations .  It is clearly seen that NO3 and NO2 stations located mostly in the western GOM, and the only NO3+NO2 stations occupy the whole GOM domain. So, in further analysis, the only NO3+NO2 data was used. First of all, NO3+NO2 data was grouped in 3 consecutive bi-monthly periods: March-April, May-June, and July-August. Then, to get a horizontal distribution of the nutrient field at depths 0, 10, 20, and 30 m, all data in a depth range +/-1 m were extracted and then projected onto FE mesh "g2s.5b" using OAX procedure. Such distribution for each of the 3 bi-monthly periods displayed in figures MA  ,  MJ  , and   JA  .  Unfortunately, there is insufficient data at z=0 m to get robust NO3+NO2 distribution at this level. To get a statistics how observations distributed through the depth,  a corresponding histogram  displayed in this  figure: histogram.  Now we can see that the most of the stations on the uppermost layer are distributed through the depth range 0-5 m, and through the depth range +/- 2 m for the  rest of the depth levels. Using this statistics, NO3+NO2 distribution at z=0 m was reprocessed and is displayed in figure NO3+NO2_(0m).  To get a depth averaged nutrient distribution in Z-layer, all data in a depth range 0-21 m were combined and then OAX processed; corresponding distribution displayed in figure NO3+NO2_(0-21m). 

 Using newly constructed nutrient fields, 6 new runs with nutrient limitation ( a7 is a  main run ) were calculated. Corresponding animations may be played using table 5. Runs with the   incident solar radiation rad=345 were used just to increase a cell concentration. 

 

                                                                Table 5.             New runs with nutrient limitation (NO3+NO2 observed)


       Run		          parameters           .fli movie            data/obs 
    comparison (1998)
              data/obs
     comparison (2000)

        a7a		  NO3 (20m);  rad=280    cell98_a7a_new.fli     cell_1998_a7a.jpg      cell_2000_a7a.jpg

        a7b		  NO3 (10m); rad=280   cell98_a7b_new.fli     cell_1998_a7b.jpg      cell_2000_a7b.jpg

        a7c		  NO3(0-20m); rad=280   cell98_a7c_new.fli     cell_1998_a7c.jpg      cell_2000_a7c.jpg

        a7d		  NO3(0-20m); rad=345    cell98_a7d_new.fli     cell_1998_a7d.jpg      cell_2000_a7d.jpg

        a7e		  NO3(10m); rad=345    cell98_a7e_new.fli     cell_1998_a7e.jpg      cell_2000_a7e.jpg

      a7f		  NO3(0-5m); rad=345    cell98_a7f_new.fli     cell_1998_a7f.jpg      cell_2000_a7f.jpg

          updated  05/16/2003
 
 

 NO3 distribution in the Gulf of Main basin was corrected using a special correcting procedure:

   - Garside's formulas #2 or #5 were used to get NO3 field from the climatic T & S;
   - the "nearest neighbor" algorithm was used to correct NO#3 field: if Sal < 31.3 then NO3 = NO3(nearest).

 Results of 2 new runs with nutrient limitation and NO3 fields received using  formulas #2 and #5, and corrected after that, presented in Table 6. Also, a diagnosis plots are presented here.

                                                                     Table 6.             New runs with nutrient limitation (NO3+NO2 corrected)


            Run		          parameters           .fli movie
     corrected
   not corrected
   a7_cor2
NO3 climatic,     corrected ; #2		    cell98_a7_new_cor2.fli    diag_cor2.jpg     diag_ncor2.jpg
     a7_cor5
 NO3 climatic, corrected; #5		    cell98_a7_new_cor5.fli    diag_cor5.jpg     diag_ncor5.jpg

          updated  06/18/2003
 
 

  Results of 2 new runs with nutrient limitation and corrected/not corrected NO3 field  presented in Table 7. NO3 field was first received using Garside's formula # 2, then corrected using Salinity limitation Sal=31.3. No germination. Initial cell concentration is zero everywhere in a basin; cell concentration at  the Bay of Fundy northern boundary is 10 cells/liter. Run 3 has been performed using same parameters as run 2 but  without nutrient limitation.

                                                                        Table 7.            New runs: without germination and  with nutrient limitation


            Run		          parameters           .fli movie
 a8_ncor2
NO3 climatic, not    corrected ; #2; no germination		    cell98_a8_new_ncor2.fli
  a8_cor2
 NO3 climatic, corrected; #2; no germination		    cell98_a8_new_cor2.fli
  a8_cor2_nolim
 NO3 climatic, corrected; #2; no germination; no NO3 limitation		    cell98_a8_new_cor2_nolim.fli

          updated  07/07/2003
 
 

  Results of 2 new runs using corrected cysts distribution  in case of  germination only and nutrient limitation (corrected NO3 field, #2)  presented in Table 8.  Corrected cysts map displayed  here.   Initial cell concentration for both runs is zero everywhere in a basin.

                                                                        Table 8.            New runs: germination only and  nutrient limitation


            Run		          parameters           .fli movie
 a6_fixed
    germination only		    cell98_a6_new_fixed.fli
  a7_cor2_fixed germination, growth, mortality, nutrient limitation; NO3 climatic, corrected; #2;     cell98_a7_new_cor2_fixed.fli