The series of manuals on techniques describes procedures for planning and executing specialized work in water-resources investigations. The material is grouped under major subject headings called "books" and further subdivided into sections and chapters. Section A of Book 3 is on surface water. The unit of publication, the chapter, is limited to a narrow field of subject matter. This format permits flexibility in revision and publication as the need arises. Chapter Al8 deals with the application of dye and gas tracers for the measurement of stream reaeration coefficients. Provisional drafts of chapters are distributed to field offices of the U.S.

A mathematical model is presented for predicting the steady state two-dimensional distribution of solute concentration in a meandering nonuniform natural channel. Two features of the convectiondiffusion (mixing) equation degived herein are that it employs the transverse cumulative discharge as an independent variable replacing the transverse distance and that it is developed in an orthogonal curvilinear (natural) coordinate system which follows the general direction of the channel flow. With the help of the continuity equation of water the transverse convection term which cannot be neglected in a natural channel is eliminated from the mixing equation by a transformation wherein cumulative discharge replaces transverse distance. Introduction of scalar diffusivity coefficients into the mixing equation is found to be more justifiable in the natural coordinate system than in a rectangular Cartesian coordinate system. The transformed mixing equation unifies and generalizes essential concepts of several existing models which have been used successfully for simulating steady state transverse mixing in irregular natural channels. Solution methods, both analytical and numeri;:al, and parameter estimation methods are presented, after which some results of simulation are compared with observed data.

An analytical model is developed for the transverse diffusion of solutes from steady sources placed in a natural stream with steady discharge. In theoretical derivations, the steady-state convective diffusion equation for a natural stream is convertEd into an approximate equation suitable for analytical treatment by the introduction of cumulative partial discharge as an independent variable. Analytical solutions for the latter equation are obtained for point and line source injections of solutes. The validity of the model is tested using data from four natural streams, three of which are alined straight, while one has mild curves. The verification was satisfactory for the three straight channels, and the constant in Elder's formula for the transverse diffusion coefficient ranged from 0.2 to 0.3. In the curved channel, the model appears workable, but an increase of the diffusion coefficient in the downstream direction is observed. The applications to stream problems are discussed in the final section. The model may be employed for the description and prediction of thermal and other waste disposal problems, simulation studies by tracers, and the determination of transverse diffusion coefficient. Another use of the model, the estimation of mixing distances, is explained and demonstrated using the data of the Water Research Association, England.

The basic exchange equations for air-water interface are approximated by the Taylor series expansion around an undefined base temperature in order to calculate short-term heat exchanges. The expression 'short-term' is used here to indicate averaging over a period on the order of 1 hour. Numerical tests based on data from two shallow streams verify that the base temperature should be chosen so as to minimize deviations between the base temperature and the actual water temperature. The daily average natural temperature observed at a reference point is the most practicable base. The daily equilibrium temperature calculated from meteorologic data may be used as a base as long as it does not deviate excessively from actual water temperatures. Whereas the short-term natural temperature is the most accurate base, the short-term equilibrium temperature has no merit as a base temperature of linearization.Heat exchange at the air-water interface a deep body of water may be essentially conunder natural climatic conditions is a matter stant. When the assumption is so seriously of increasing concern to those who are engaged violated, can the equilibrium temperature in the abatement of thermal pollution as well method give reliable estimates of heat exas in the modeling of water temperature as change? N_o explicit reference to this problem an important element of water quality. Since has appeared in the papers devoted to the basic heat exchange equations are nonlinear equilibrium method. Recently Jobson [1972a] and complicated in form, approximations and raised this question in conjunction with his simplifications are often required. derivation of a linearization method based on A well-known method of approximation natural temperatures. among engineers is the equilibrium temperature The purpose of this report is to expand method [Edinger and Geyer, 1965], which is Jobson's derivation, which was limited to unhistorically derived for the calculation of daily natural excess temperatures, and to establish average heat exchange. As the modeling of general rules of approximation for the calculawater temperature has developed with the use tion of heat exchanges for time periods on the of digital computers, attempts have been made order of I hour. Simple Taylor series expansions to extend this method to the calculation of of the exchange equations are developed by the time intervals of less than I day [Federal use of an undefined base temperature. It is Water Pollution Control Administration, 1968]. argued that the natural temperature, definedSuch an extension should be undertaken with as the observed or predicted temperature at caution because it conflicts with a basic as-some reference point such as just upstream of sumption of the method, namely, that the dif-a waste heat discharge, is a better base temference between the equilibrium temperature perature than the equilibrium temperature as and the actual water temperature be small. far as the accuracy of approximation is con-Edinger et al. [1968] have shown that short-cerned. Nume...

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