Full Spectral Model Research Articles

Heating Rate within the Upper Ocean in Relation to its Bio–optical State

Abstract Solar radiation absorption and local heating within the upper layers of the open ocean are strongly influenced by the abundance of phytoplankton as depicted by the chlorophyll concentration. According to whether this concentration is high or low, the heat deposition occurs within a layer that may vary in thickness from low than 10 m to more than 100 m. A simple parameterization, accounting for this dependence, is developed. It allows the vertical profiles of heating rate to be predicted from the phytoplanktonic pigment concentration, as it can (and will) be remotely detected from space, by using ocean color sensors. This computationally efficient parameterization has been validated in reference to the results of a full spectral model. In the simplified computation, the solar spectrum is partitioned into two domains, below and above the wavelength 0.75 µm. For the infrared waveband, not influenced by biological materials the irradiance profile is described by a single exponential function. For the...

A Chebyshev-Legendre Spectral Method for the Transient Solutions of Flow Past a Solid Sphere

A full spectral model for the stream-function-vorticity formulation is developed for the solution of unsteady flow past a rigid sphere. To convert the governing partial differential equations to discrete form, Chebyshev and Legendre polynomials are employed to expand the vorticity and stream function in the radial and angular directions, respectively, together with a first-order, fully implicit, iterative scheme for time advancement. The solution to the system of discrete nonlinear equations is accomplished by LU decomposition in conjunction with the influence matrix to resolve the lack of vorticity boundary conditions. Owing to the global nature of the orthogonal trial functions, the present technique provides a means to achieve highly accurate results with less number of unknowns than either traditional finite difference or finite element methods. Comparisons of numerical solutions with previous results show consistent trends as reported in studies dealing with Cartesian coordinates.

On the dependence of travelling wave stability on basic state wave phase speed

The dependence of stability on basic state wave phase speed is examined in a nondivergent barotropic model on a sphere for planetary scale waves with phase speeds typical of waves observed in the atmosphere. Triad interactions are examined analytically and compared to numerical results from a full spectral model. A number of triads may result in growth of the perturbation components for each basic state wave; for each triad there is a basic state wave phase speed where it is resonant, identified as the point where the critical amplitude for instability to that perturbation becomes zero. Critical amplitudes for instability obtained using the full spectral model generally agree well with triad results. Since the basic state wave phase speed determines which triad will grow, spatial structure and critical amplitudes for instability for the growing disturbances depend strongly on basic state wave phase speed. The results of this idealized study suggest that phase speed may be an important factor in determining the stability of planetary scale waves in the atmosphere.

Bio‐optical modeling of photosynthetic production in coastal waters

A physiological‐based bio‐optical model is used to estimate vertical profiles of instantaneous, diurnal, and integrated daily rates of in situ primary production throughout the water column at three stations across a coastal front. The model makes use of an empirical relationship between photosynthesis, quantum yield, and photosynthetically absorbed radiation and is a full spectral model with all relevant parameters determined as a function of wavelength. In the prior application of this bio‐optical model, parameters used to estimate quantum yield as a function of irradiance were wavelength‐independent and held constant. Here, the model is recast so that quantum yield is estimated with wavelength‐dependent photosynthesis‐irradiance parameters, Pmax the maximum rate of phytoplankton photosynthesis, and Ik the P‐I saturation parameter, which are allowed to vary with depth and time of day. Both Pmax‐dependent (assumed to be λ‐independent) and Ik‐dependent (known to be λ‐dependent) estimates of temporal/spatial changes in quantum yield were assessed. The model was tested in water masses where a net‐to‐nanoplankton transition was occurring in phytoplankton communities dominated by diatoms and prymnesiophytes. At each station there is close agreement between 14C productivity estimates derived from knowledge of diurnal patterns in P‐I parameters and productivity estimates derived from two variants of the bio‐optical model based on knowledge of spectral irradiance and phytoplankton pigmentation. The 14C and bio‐optical estimates of primary production also show similar vertical patterns for either instantaneous or daily integrated values. When compared with 14C estimates, Ik‐dependent bio‐optical estimates of photosynthetic rates give a closer match than bio‐optical estimates that are Pmax‐dependent. The model permits calculation of primary production from shipboard observations and may be useful for predicting production rates from bio‐optical data provided by untended buoys.