If property 'C is substituted 

 into Eqs . (4), (5) and (6), Eqs . 

 (5) and (6) define the time rate 

 of change of the amount of ' C in 



each box d M 



ui 



V ./dt 

 ui 



and d M 



li 



'V with appropriate sub- 



v u /dt, 



scripts denotes volume. Dividing 

 through by volume (independent of 

 time to the order of the estimate) 

 and using Eq. (4) to transform 

 equations in 'M' to equations in 

 'C defines a matrix equation 



d C/dt = A C + p (t) (7) 



C = vector of box boundary 

 property concentrations 

 (upper and lower) 



A = matrix of coefficients 



derived from Eqs. (4), (5) 



and (6) 



This paper discusses the rela- 

 tions between freshwater flow, cur- 

 rents and salinity in the lower 

 Hudson Estuary relevant to the con- 

 struction of a box model, and applies 

 the model to the distribution of 

 chlorophyll a , an index of phyto- 

 plankton biomass. The Chlorophyll a 

 field derived from the model can be 

 compared to observed Chlorophyll a 

 field to determine whether additional 

 source (growth, resuspension) or sink 

 (grazing, sinking) terms are needed 

 to balance Eq. (7). These terms can 

 be calculated by direct substitution 

 of observed C's into Eq. (7). Thus 

 the model provides a method for 

 separating the component of the 

 phytoplankton dynamics due to circu- 

 lation from other effects and the 

 estimation of flushing times of phyto- 

 plankton from the estuary. The 

 characteristics of the data set used 

 are discussed in Malone et al. (1980) 

 and the present work extends and re- 

 fines the flux calculations given 

 therein. 



p(t) = vector of boundary condi- 

 tion functions 



MATERIALS AND METHODS 



If dC/dt = (property in steady- 

 state) and inputs occur in upper 

 layer upstream boundary and lower 

 layer downstream boundary, 

 algebraic substitution shows that 

 Eq. (7) is solved by C . = a S. + 



b, a and b determined by the 

 boundary condition C, S pairs. 



This model improves on 

 Pritchard (1969) by letting concen- 

 tration variables define box 

 boundary concentrations with mean 

 box values calculated by Eq. (4), 

 whereas the opposite approach is 

 used in the previous model. This 

 optimizes the use of observed 

 salinity data by using it directly 

 in Eq. (2) which is sensitive to 

 small changes in salinity. 



Samples were collected at ap- 

 proximately weekly intervals from 

 February to June and July to Septem- 

 ber during 1977 and 1978. Surface 

 chlorophyll (in vivo fluorescence) 

 and salinity (conductivity and temp- 

 erature) were monitored continuously 

 with and against the tide along a 

 transect between MP -7 and MP -25 

 (Figure 1). Vertical profiles of 

 current speed and direction, tem- 

 perature, salinity and chlorophyll a 

 were obtained at 6 stations (Figure 

 1) with a Savonius rotor current me- 

 ter , conductivity-temperature-depth 

 sensor, submersible pump and bottle 

 casts. Vertical profiles were ob- 

 tained every 1 to 3 h over two tidal 

 cycles on 8 occasions at MP -7 and 2 

 occasions at MP 18. Bottles were 

 used to collect samples for extracted 

 chlorophyll a and primary productivity 



170 



