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Stochastic Modeling of Temperature and Dissolved Oxygen in Stratified Fish Ponds

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Stochastic Modeling of Temperature and Dissolved Oxygen in Stratified Fish Ponds

Work Plan 7, DAST Study 2; Work Plan 8, DAST Study 1

Zhimin Lu and Raul H. Piedrahita
Department of Biological and Agricultural Engineering
University of California, Davis, USA

 

(Printed as Submitted)

 

Introduction

Research on water quality modeling in aquaculture ponds has involved, for the most part, the development of deterministic models. In a deterministic model, the outcome of the model is always the same for a given set of input parameters. There are very few examples of models used in aquaculture in which stochastic variables, equations, or parameters are considered. Sadeh et al. (1986) used random water quality parameters in their study of economic profitability of shrimp production in ponds. In their model, water temperature was used as a determinant factor of shrimp growth rate. In turn, water temperature was determined from air temperature using a linear equation. The probabi-lities of temperature occurrences were estimated from records spanning more than 40 years. The effects of light and phytoplankton concentration on shrimp growth were not considered in their model.

Recent work undertaken by the UC Davis DAST has resulted in a first version of a water quality and fish growth model using stochastically generated weather parameters (solar radiation, wind speed and wind direction), and that model is described in this report. The water quality component of the model is based on a deterministic model of stratified ponds developed by Losordo (1988) and modified by Culberson (1993). The temperature model is based on an energy balance for the water column (Losordo, 1988). Dissolved oxygen (DO) is the primary variable considered in the water quality model, and is determined from mass balance calculations considering oxygen production, consumption, and transfer terms. Weather parameters (solar irradiance, air temperature, wind speed and direction) are critical input variables in modeling both water temperature and DO. Therefore, weather parameters for a stochastic pond model need to be obtained from some statistical treatment of existing records for a site.

Numerous papers have been published on modeling weather parameters. Program simulations have been developed generally using the probability distributions generated from measured values (Amato, et al., 1986). To obtain an accurate distri-bution, a long-term, complete data set is required. Unfortunately, large, reliable data sets are rarely available for prospective aquaculture sites, especially in rural areas, and some of the work undertaken in this project has been targeted at finding ways to make optimum use of limited weather data sets.

 

Model Structure

The combined water quality/fish growth model consists of four parts : 1. weather parameter generation; 2. temperature simulation; 3. DO simulation; 4. fish growth simulation. Initial versions of the first two parts of the model have been described by Santos Neto and Piedrahita (1994).

 

Weather parameter generation

The simulation of hourly values for solar radiation is carried out in two steps. A total solar radiation value for a given date is generated in the first step. The distribution of the total daily solar radiation over a day is obtained in the second step, and hourly values are estimated (Santos Neto and Piedrahita, 1994).

 

Total daily solar radiation for a given date is obtained from (Amato et al., 1986):

 

 

for i=1, 2,...n; j=1, 2, ..., m (i = day, j = year)

where,

= generated total daily solar radiation for day i

 

Temperature model

Water temperature is calculated from an energy balance as described by Losordo (1988) and by Culberson (1993). The main heat sources in a pond are solar irradiance and atmospheric radiation. Incident solar irradiance is obtained from generated solar radiation values as described above. Atmospheric radiation is determined by air temperature. The attenuation of solar irradiance with depth in the water column is estimated by using a bulk light extinction coefficient determined as a function of Secchi disk depth. Since the daily Secchi disk depth was not available in the CRSP data base, a site-specific regression equation between Secchi disk and chlorophyll-a concentration is used in the model. Energy exchange between layers in the pond water column is due to diffusion and convection (Losordo, 1988). Diffusion is estimated primarily as a function of wind speed, wind direction, and fetch (Losordo, 1988; Culberson, 1993).

 

Dissolved Oxygen model

Dissolved oxygen concentrations are determined from mass balance calculations in which photosynthesis constitutes the main source of oxygen. Oxygen sinks include respiration by phytoplankton, fish, benthic organisms, etc. Oxygen transfer with the atmosphere may constitute a source or a sink, depending on whether the oxygen concentration in the surface layer of the pond is below or above saturation. Calculation of oxygen production and consumption rates requires some estimate of phytoplankton concentration. In previous models Losordo (1988) and Culberson (1994) used measured chlorophyll-a values, but those are not available on a daily basis as needed for simulations covering many consecutive days. Therefore, Culberson's model was modified by adding a mass balance term for chlorophyll-a, and introducing a term relating phytoplankton carbon to chlorophyll-a concentration (carbon:chlorophyll-a ratio, or CCHL). CCHL is highly variable, and values are reported between 10 and 1000 (Steele, 1962). An estimate of CCHL can be obtained from (Lee et al., 1991 a, b):

 

 

where,

= ratio of phytoplankton carbon to chlorophyll a,

= slope of photosynthesis rate to light intensity (P-I) curve,

= maximum light intensity,

= maximum phytoplankton growth rate,

= temperature dependence, 1.08(t-20)

= constant, 2.718

In the model, a and µmax are inferred from a previous deterministic model (Culberson, 1993). CCHL is depended on the maximum light intensity Imax and water temperature. In the present model, Imax is determined as the weighted average of the light intensity for the previous three days (Lee et al. 1991b):

 

where Imax, Imax2, and Imax3 are the lightest intensities one, two, and three days prior to the current day

 

Fish growth rate

The fish growth model was adapted from the model developed by the OSU-DAST (Bolte et al., 1994). The adaptation was carried out as part of work carried out by the UC Davis DAST, on modeling of integrated aquaculture-agriculture systems, and is described by Jamu and Piedrahita (Aquaculture Pond Modeling for the Analysis of Integrated Aquaculture/Agriculture Systems, Work Plan 8, Study 2 in this volume).

 

Results and Discussion

A period of 83 days was simulated, from Julian day 40 to 123, with a time step of 0.0625 hours. The length of the simulation was limited by the internal structure of the modeling software (16 bit addresses, or a maximum of 32,768 steps), and was independent of hardware (same limitation on Macintosh and Windows machines). Simulation results (maximum, minimum, and average values) are obtained after running the model 50 times using stochastically generated weather parameters as described above, and are shown in Figures 1 through 15. The data used for model execution were collected at the CRSP site in Thailand, and correspond to the data set used in the development of previous models by the UC Davis DAST (Santos Neto and Piedrahita, 1994; Culberson , 1993). Simulated water temperatures of the three layers are shown in Figures 1 through 3. Measured values available for the 83 day time period lie within the range of temperatures defined in the simulations with two exceptions, one on day 82, and one on day 110 (0.5, and 0.3 °C higher than the maximum temperatures simulated for the corresponding times). Simulation results for the middle and bottom layers lie further from the mean values, and stray beyond the range of temperatures estimated from the simulations for the bottom temperature for days 40 and 110 (Figures 5 and 6).

Dissolved oxygen fluctuations were more pronounced for the surface layer than for the middle and bottom layers (Figures 7-9). The probability of the pond dissolved oxygen concentration dropping below 2 mg/L was most evident during the second half of the simulation period, where the minimum DO calculated often was under 2 mg/L during at least part of the day in all three layers (Figures 7-9). The minimum DO calculated over the 50 simulation runs reached 0 mg/L for all three layers on days 102 and 103 (Figures 7-9). Comparing the simulated and measured DO values for the three layers shows better agreement for the surface and middle layer than for the bottom layer (Figures 10-12). The large fluctuations of temperature and DO are caused primarily by the large changes of the stochastically generated solar radiation values (Figure 13). The maximum solar radiation intensity generated, Imax ranged from 500 to 2800 µmol/m2/s, with the measured values being lower than the mean of the predictions for most days (Figure 13).

Chlorophyll-a concentration rises throughout the simulation period (Figure 14), but no data are available in this particular data set to compare to the simulated values. However, chlorophyll-a concentrations are often observed to rise during a growing season. Fish biomass is being overestimated in the current version of the model (Figure 15), and revisions to the fish growth estimation as a function of feed quantity and quality, and of water quality parameters will be necessary to improve the accuracy of the predictions.

 

Anticipated Benefits

The results presented in this report are for the first version of a model of water quality and fish growth in fish ponds using stochastic weather inputs. The results show the power and usefulness of using a stochastic approach to simulate pond production. By being able to generate a range of possible water quality and fish yield outcomes for a site and for a particular pond management strategy, the modeler will be able to identify risks associated with a given operation and make more informed decisions on site selection and on pond management. Improvements are needed in the model, especially in the dissolved oxygen and fish growth simulations.

 

Figure 1 (60 K file). Temperature predictions for the surface of a startified pond after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean temperature obtained at each hour of the simulation are shown.

 

Figure 2 (57 K file). Temperature predictions for the middle layer of a stratified pond after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean temperature obtained at each hour of the simulation are shown.

 

Figure 3 (42 K file). Temperature predictions for the bottom layer of a stratified pond after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean temperature obtained at each hour of the simulation are shown.

 

Figure 4 (39 K file). Comparison of measured and predicted temperatures for the surface layer. The days shown are those for which measured values were available.

 

Figure 5 (34 k file). Comparison of measured and predicted temperatures for the middle layer. The days shown are those for which measured values were available.

 

Figure 6 ( 34 K file). Comparison of measured and predicted temperatures for the bottom layer. The days shown are those for which measured values were available.

 

FIgure 7 (63 K file). Dissolved oxygen predicitons for the surface of a startified pond ater 50 runs, and over an 83 day simulation. The maximum, minimum, and mean DO obtained at each hour of the simulation are shown.

 

Figure 8 (61 K file). Dissolved oxygen predictions for the middle layer of a stratified pond after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean DO obtained at each hour of the simulation are shown.

 

Figure 9 (45 k file). Dissolved oxygen predictions for the bottom layer of a stratified pond after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean DO obtained at each hour of the simulation are shown.

 

Figure 10 (44 K file). Comparison of measured and predicted DO for the surface layer.The days shown are for those for which measured values were available.

 

Figure 11 (38 K file). Comparison of measured and predicted DO for the middle layer. The days are shown those for which measured values were available.

 

Figure 12 (34 K file). Comparison of measured and predicted DO for the bottom layer. The days shown are those for which measured values were available.

Figure 13 (39 K file). Maximum solar radiation intensity I max obtained after 50 simulations compared to measure values available.

Figure 14 (32 K file). Chlorophyll-a predictions after 50 runs, and over an 83 day simulation. The maximum, minimum, and mean values obtained at each hour of the simulation are shown.

Figure 15 (26 K file). Individual fish mass predicted after 50 runs compared to measured values available.

 

Literature Cited

Amato, U. , A. Andretta, B. Bartoli, B. Coluzzi and V. Cuomo. 1986 Markov processes and fourier analysis as a tool to describe and simulate daily solar irradiance. Solar Energy 37(3): 179-194.

Bolte, J.P., S.S. Nath, and D.E. Ernst. 1994. POND: a decision support system for pond aquaculture. pp 48-67 In H. Egna, J. Bowman, B Goetze, and N. Weidner (Editors), Twelfth Annual Report. Pond Dynamics/Aquaculture CRSP Management Office, Oregon State University, Corvallis, Oregon.

Cuenco, M. L., Robert R. S. and William E. G., 1985. Fish Bioenergetics and Growth in Aquaculture Ponds: I. Individual Fish Model Development Ecological Modeling, 27:169-190.

Culberson, S.D. 1993. Simplified model for prediction of temperature and dissolved oxygen in aquaculture ponds: using reduced data inputs. M.S. Thesis. University of California, Davis. 212 pp.

Lee, J. H. W., Y. K. Cheung, and P.P.S. Wong, 1991a. Dissolved oxygen variation in marine fish culture zone. Jour. of Environmental Engineering. Vol. 117, No. 6:799-815.

Lee, J. H. W., Y. K. Cheung, and P.P. S. Wong, 1991b. Forecasting of dissolved oxygen in marine fish culture zone. Jour. of Environmental Engineering. Vol. 117, No. 6:816-833.

Losordo, T.M. 1988. The characterization and modeling of thermal and oxygen stratification in aquaculture ponds. Ph.D. dissertation. University of California, Davis. 416 pp.

Piedrahita, R. H. 1984. Development of a computer model of the aquaculture pond ecosystem. Ph.D dissertation. University of California, Davis, California. 162 pp.

Reynolds, C. S., 1984. The ecology of freshwater phytoplankton. Cambridge University Press. 384 pp.

Santos Neto, C.D. and R.H. Piedrahita. 1994. Stochastic modeling of temperature in stratified aquaculture ponds. CRSP report, work plan 7, study 2.

Sedeh, A., C. Pardy and W. Griffin, 1986. Uncertainty consideration resulting from temperature variation on growth of Penaeus stylirostris in ponds., The Texas Journal of Science., Vol. 38. No. 2.

Swartzman, G.L., and S.P. Kaluzny. 1987. Ecological simulation primer.