the water layer* This figure indicates, that at a mean water temperature 

 of -1.5*0. and for an ice thickness increment of 70 cm., the water masa 

 adds only approximately 18$ of the total time, while at a mean water 

 temperature of 0.5*0. the heat of the water mass adds about 63$ of the 



total time* 



Figure 12 shows the increase in the f reeling time for 10 cm. of ice 

 for differing initial thicknesses ranging from 25 to 85 cm,, when the 

 water layer increases in depth from 10 to 100 meters* At an initial 

 thickness of 25 am and a layer depth of 10 m., no appreciable time is 

 added to the time needed to freeze 10 cm, of ice when the meteorological 

 conditions are as indicated on the diagram,, However, when the warm layer 

 depth is increased to 20 m, , the time increases by about 0.5 day. The 

 variation from this point to a layer depth of 100 m c is essentially linear. 

 At the 100 m. layer depth the time added for an initial thickness of 25 

 cm. is about 10.2 days. All of these values are computed for a mean layer 

 temperature of 0.5 S C. At the upper limit of initial ice thickness, 85 cm. 

 the increase of freezing time added by a layer depth of 40 meters is 

 practically zeros a * 100-meter depth it is about 5«2 days. 



F. PRACTICAL ICE THICKNESS FORECASTING 



The above analysis is mainly concerned with the development of theo- 

 retical formulas expressing ice thickness as a function of time. In order 

 to take up the problem of the practical prediction of 1c© thickness there 

 are two main avenues of approach, (1) the graphical method, and (2) the 

 computational method. 



The graphical method consists in the utilization of a diagram showing 

 the ice thickness as a function of time and the meteorological parameters. 

 For this purpose the diagrams coustituting Figure 13 are suitable. In 

 these diagrams the ice thickness is on the vertical scale, the air temper- 

 ature on the horizontal scale, and the wind velocity lines indicate the 

 growth curves for varying velocities,, . The figure is divided into three 

 parts for cloud coverages of 0, 50 and 100$ and shows ice growth over a 

 period of 14 hours. Now, for example , If It is required to know the thick- 

 ness of ice, which will result from a temperature of -15*0., wind velocity 

 of 5 ns/sec, cloud cover 0$, for a period of 14 hours, the required value 

 taken from Figure 13a is 6.0 cm. If the cloud cover had been 50% instead 

 of 0, Figure 13a would give the required thickness as 5»5» em„, and if the 

 cloud cover were 100$, the thickness taken from Figure 13a -would be 4.8 cm. 

 To determine the ice thickness for a longer period than 14 hours it is 

 only necessary to know the average value of the parameters over each 14- 

 hour period and make a cumulative sum of the thickness for integral multi- 

 plies of 14 hours plus the fractional part. This diagram, however, has a 

 definite weakness in that it does not take into account the snow cover or 

 the initial thickness of the ice ? both of which are important factors in 

 determining the rate at which ice is formed. This Is a weakness inherent 

 in all diagrams of this type, because of the fact that it is impossible to 

 include all of the important parameters on the diagram. For this reason, 



