NRC Publications Archive Archives des publications du CNRC A numerical model for calculating temperature profiles in ice covers Goodrich, L. E. This publication could be one of several versions: author’s original, accepted manuscript or the publisher’s version. / La version de cette publication peut être l’une des suivantes : la version prépublication de l’auteur, la version acceptée du manuscrit ou la version de l’éditeur. Publisher’s version / Version de l'éditeur: Technical Memorandum (National Research Council of Canada. Division of Building Research); no. DBR-TM-114, 1974 NRC Publications Archive Record / Notice des Archives des publications du CNRC : https://nrc-publications.canada.ca/eng/view/object/?id=d282a642-2338-445c-a9a2-a042f442bdbe https://publications-cnrc.canada.ca/fra/voir/objet/?id=d282a642-2338-445c-a9a2-a042f442bdbe Access and use of this website and the material on it are subject to the Terms and Conditions set forth at https://nrc-publications.canada.ca/eng/copyright READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE. L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site https://publications-cnrc.canada.ca/fra/droits LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB. Questions? Contact the NRC Publications Archive team at [email protected]. If you wish to email the authors directly, please see the first page of the publication for their contact information. Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez pas à les repérer, communiquez avec nous à [email protected]. (i) PREFACE The thermal regime of river ice has long been of importance for hydro-electric operation, flooding, navigation and water supply problems. In recent years it has become increasingly important for such diverse problems as determining the effect of warm water discharge from nuclear plants on downstream ice conditions, the effect of river ice on fish spawning grounds, and the effect of snow disposal in rivers on water quality and ice formation. In recognition of this increasing importance, the Snow and Ice Subcommittee of the Associate Committee on Geotechnical Research sponsored a research seminar on the subject, 24-25 October 1974, at Foret Montmorency Research Station of Laval University. This Technical Memorandum records the papers presented at this seminar. There was much informal discussion during the seminar but only written discussion has been included in the Proceedings. Several of the papers are presented in summary form; additional information can be obtained by writing to the authors. The seminar was divided into three sessions; the first dealt with surface heat exchange, the second with ice formation in rivers, and the third with operational problems. The seminar was designed to be informal, with attendance limited to those active in one or more of the session topics. The seminar was fortunate in having active participation from several guests from the united States. The Associate Committee wishes to express its appreciation to Dr. Bernard Michel for handling the local arrangements so effectively, to Dr. Andre LaFond, Dean of the Faculty of Forestry and Geodesy, for giving the welcoming address and for making the excellent facilities at the Research Station available for the seminar, and to Mr. G.P. Williams, Chairman of the Working Group, responsible for organizing the seminar. Carl B. Crawford, Chairman, Associate Committee on Geotechnical Research. (ii) PREFACE Le regime thermique de la glace de riviere tient depuis longtemps de l'importance dans les problemes de fonctionnement hydro-electrique, de debordement de cours d'eau, de navigation et d'approvisionnement d'eau. Ces dernieres annees, il prend de plus en plus d'importance au regard de divers problemes tels que celui de determiner l'effet d'un deversement d'eau chaude provenant d'une installation nucleaire sur les conditions de la glace en aval, l'effet de la glace de riviere sur les frayeres, et l'effet de l'action de disposer de la neige dans les rivieres sur la qualite de l'eau et la formation de la glace. Reconnaissant cette importance toujours grandissante, Ie Sous-comite de la glace et de la neige du Comite associe de recherches geotechniquesa commandite un debat sur Ie sujet, les 24 et 25 octobre 1974, a la Station de recherche de la Foret Montmorency de l'Dniversite Laval. Le present memoire technique rapporte les articles qui ont ete presentes lors de cette etude. Bien que la seance ait comporte beaucoup de discussion sans formalites, Ie proces-verbal ne comprend que la discussion ecrite. Plusieurs articles ont ete presentes sous forme de resumes; des renseignements supplementaires sont disponibles en ecrivant aux auteurs. Le debat comportait trois seances, dont la premlere traitait de transmission de la chaleur a la surface; la deuxieme, de la formation de la glace de riviere; et la troisieme, de problemes de fonctionnement. II avait ete prevu que Ie debat serait sans formalites, l'assistance etant limitee aux personnes qui s'occupent d'un theme ou plus des seances. Le debat recevait avec plaisir la participation active de plusieurs invites des Etats-Unis. Le Comite-associe desire exprimer son appreciation ! Monsieur Bernard Michel qui slest occupe si efficacement de faire les preparatifs necessaires, ! Monsieur Andre Lafond, Doyen de la Faculte de foresterie et de geodesie, qui a lu l'adresse et a rendu disponible les excellentes commodites de la Station de recherche, et a Monsieur G.P. Williams, President du Groupe de travail, qui est responsable de l'organisation du debat. Le President, Comite associe de recherches geotechniques Carl B. Crawford. (iii) TABLE OF CONTENTS - TABLE DES MATIERES FIRST SESSION - PREMIERE SEANCE Chairman B. Pratte, Le President National Research Council of Canada 1. Heat Transfer from Open­ N. Marcotte, Water Surfaces in Winter. Universite de 2 Moncton. 2. Radiation and Evaporation T. McFadden, Heat Loss during Ice Fog U.S. Army Conditions. CRREL, Alaska. 18 3. Energy Transfer in Snow. D.M. Gray and 28 D.H. Male, University of Saskatchewan. 4. A Numerical Model for L.E. Goodrich, 44 Calculating Temperature National Profiles in an Ice Cover. Research Council of Canada. 5. Convective Heat Transfer J.E. Cowley and 60 at an Ice-Water Inter­ S.T. Lavender, face. Acres Consulting Services Ltd. SECOND SESSION - DEUXIEME SEANCE Chairman G.P. Williams, Le President National Research Council of Canada Introductory Remarks - G.P. Williams 78 1. A Preliminary Investiga­ G. Tsang, 82 tion and Experimental Set­ Canada Centre up for the Study of Frazil for Inland Formation in Water with Waters. Surface Waves. 2. Mechanisms of Ice Growth B. Michel and 96 at the Ice-Water-Air T. OlD. Hanley, Interface in a Laboratory Universite Tank. Laval. (iv) 3. Supercooling and Frazil T. Osterkamp, 104 Ice Formation in a Small University of Sub-arctic Stream. Alaska. 4. Ice Regime Investigations K.W. Lathem, 109 on the Moira River at Crysler and Belleville, Ontario. Lathem Ltd. 5. Ecological Implications C.B. Stalnaker 121 of Frazil and Anchor and J.L. Arnette, Ice in High Mountain Utah State Streams. University. THIRD SESSION - TROISIEME SEANCE Chairman D. Foulds, Le President Environment Canada 1. Practical Application of J. Robinson and 128 Probability Forecasts of D. Witherspoon, Water Surface Temperatures Environment of St. Lawrence River ­ Canada. Kingston to Montreal. 2. Winter Temperature V.C. Kartha, 134 Measurements in Lakes Manitoba Hydro. along the Churchill River River Diversion Route. 3. Statistical Analysis of C.H. Atkinson, 145 Niagara Ice Boom Effects Acres Consulting on Water Temperature. Services Ltd. 4. Regime Thermique des R. Lariviere et 152 Grands Reservoirs Soumis F. Fonseca, aux Conditions de Glace. Hydro-Ouebec. 5. Ice Jams Related to H.R. Kivisild 170 Climatological and and J. Penel, Hydraulic Parameters ­ FENCO. Yukon River at Dawson City. 6. Alaska River Thermal R.F. Carlson, 177 Problems, Research and University of Design Criteria. Alaska. Summary - ｒ･ｳｵｭｾ B. Michel 181 Registration List - Liste 184 1 NATIONAL SCIENCE LIBRARY NATIONAL RESEARCH COUNCIL OF CANADA Ser TA701 N28t2 no.114 SLOG. RFS National FIRST SESSION - PREMIERE SEANCE 2 HEAT TRANSFER FROM OPEN-WATER SURFACES IN WINTER N. Marcotte INTRODUCTION Heat-transfer from open-water areas in rivers or reservoirs in winter is considered. Water temperature is assumed to be DoC. A brief review at the heat budget method will be given together with comments on various expressions for caluclating each term of the budget. A comparison will then be made between the overall K coefficient in mid-winter at Montreal and Nitchequon. A) HEAT BUDGET The sum of heat losses and gains by solar radiation, long wave radiation, evaporation and convection per unit area and per unit time is written: ( 1) units: cal/cm2-day. (a) Long wave radiation: 4 4 Q = (- c a T ) + (f' e ' aT ) (2 ) RI e a where s water emissivity = 0.97 a Stefan-Boltzmann constant 7 2 4 (1.171 x 10- cal/cm day °K ) T water temperature, oK e T air temperature, OK a f' = 0.95 (5% reflection) s' = atmospheric emissivity c ' = 0.74 + 0.025/ea + 0.0012 B [1 - 1:a] (3) 1 (After Anderson, Raphael, Ref. 4) e a vapor pressure in the air, mb B percent of sky cover 3 Range of values of £': low intermediate high in winter 0.74 0.84 0.89 in summer 0.79 0.90 0.98 Fog, falling snow and surrounding objects can increase £'. Figure 1 shows the variation of QRI and Ta and £'. (b) Solar radiation: (4 ) where QRSM solar radiation for average cloudless sky, cal/cm2-day fraction non-reflected correction for clouds F = 1 - 0.7 (B/lOO)2 (5) B Range of values of QRS in mid-winter: low intermediate high at Montreal +50 +110 +160 at Nitchequon +20 + 60 + 80 Tables of hourly and daily values of global radiation for average cloudless sky, with correction for reflection at the water surface, have been prepared for latitudes 42°N to 62°N (Ref.