The APM (Benemann and Tillett 1987, 1990; Tillett 1989) describes a shallow, paddle wheel — mixed pond system. It incorporated climatic, design, operational, physicochemical, and biological parameters and submodels to predict the pond, and algal culture, behavior. Simplying assumptions in the model include the following:

• the pond exhibited no nutrient, biomass or temperature inhomogeneities (e. g., gradients),

• mixing was essentially plug flow for large systems and mixed tank behavoir for smaller ones,

• CO2 and O2 outgassing can be estimated from measured gas transfer coefficients, and

• evaporation was 1.5 times pan A evaporation data, for example.

Climate input parameters were obtained from local U. S. climate stations in machine-readable form, including daily data on air temperatures (diurnal), relative humidity, rainfall, wind speed and total solar radiation. These data were then averaged over several years to provide daily and monthly average data sets. The use of such climate data is critical for predicting pond conditions at a particular site and location. Design variables included pond area, depth, mixing velocity, and length-to-width ratios. Physical inputs were the alkalinity of the media, the starting and ending pH for the carbonation station, and the outgassing coefficient. Finally, for a biological parameter a productivity assumption (from 20-40 g/m2/d, or a % maximum sunlight conversion efficiency) was used, along with C content, O2 yield, heat of combustion, and saturating light intensity for photosynthesis (assuming simple light saturation, and application of the Bush equation).

The model included an energy balance (input sunlight, radiation, evaporation, air temperatures, etc.), which continuously predicted the pond temperature, based on pond depth, and ambient conditions. From the productivity assumption (on a diurnal basis) and a CO2 outgassing coefficient for the ponds, the total inorganic C balance can be calculated based on alkalinity and pH as the major determinants of inorganic C in ponds. Like CO2 (and pH, etc.), O2 is also dependent on productivity, and outgassing. The model was written in Fortran (Tillett 1989).

The model was validated at the Roswell test site, with the 3-m2 ponds, which were instrumented (for pH, DO, wind, air temperature, etc.) and a data acquisition system developed to obtain short — (< 1h) and long — (>1 d) term data. The model was also validated with the larger ponds. Measured and predicted pond temperatures agreed well, as seen in Figure III. B. 10a for a diurnal data set for a heated and unheated small pond, and Figure III. B. 10b for a single unheated pond for 2 weeks.

Simulations were also run for a larger, 1,000-m2 earthen pond as built at Roswell (an arid and cool climate), which were then compared with a site in West Palm Beach, Florida (a humid,
warm climate), using monthly average climate data. The model was exercised for 4 representative months of the year for both locations, and assuming ponds of 10, 20, 30 and 100­cm depth. (This last point was to demonstrate the limited effect of managing pond temperature extremes by depth.) Minimum water temperatures do not rise above 10°C for shallow ponds for most of the year in Roswell; they never drop below this level in West Palm Beach. Maximum summer temperatures seem to be only modestly higher in Florida than in New Mexico. These results point to low temperatures as a major factor in Roswell operations.

Only a limited attempt was made to verify the model in relation to productivity, by using a fitted Ik (saturating light intensity) parameter, as well as an assumed heat of combustion (5.7 Kcal/g) and biochemical conversion efficiency (from prior work by Weissman and Goebel 1987). Although the agreement between calculated and measured productivities was excellent (both gave about 15.3 g/m2/d), this was probably fortuitous, as the Ik actually used in the model was well below what had been previously measured with the same organism (Monoraphidium sp.). This requires further investigation.

One interesting use of the model was to predict CO2 utilization and outgassing from various assumed pH, pCO2 and alkalinity regimes. This is a central issue in the operation of algal pond systems, as these parameters must be used to optimize for productivity and overall CO2 utilization efficiencies. The higher the pH and the lower the alkalinity, the greater the utilization efficiency. However, for CO2 supply, pH must be decreased transiently. With moderate alkalinity (2.5-5 mM), and CO2 requirements, the pH transients can be relatively small, allowing minimal outgassing even for seawater systems, resulting in predicted CO2 use efficiencies of over 85%.

A final important parameter is dissolved O2, which was predicted to accumulate within 1 hour to a level of 210% of air saturation with a 30-cm deep culture and a productivity of 30 g/m2/d. Much higher concentrations would build up during the day, and are actually observed in ponds. This could be a major factor in reduced productivities in ponds (see Section III. B.5.).

This model is of sufficient detail and predictive value to minimally direct the laboratory and small-scale outdoor research in making these more representative of the outdoor pond environments. Laboratory applications are discussed in the following section.

Figure III. B.10. Comparison of measures and predicted pond temperatures in Roswell, New Mexico.

a. ). Top: Comparison of measured and predicted diurnal temperature profiles for heated and unheated ponds. October 4, 1987.

b. ). Bottom: A comparison of predicted (line) versus measured (symbols) maximum-minimum temperatures in miniponds using simplified inputs for Roswell, N. M.