Statistically the three-parameter 1,000 mb forecasts for these 20 cases are much better than the two-parameter forecasts and are about the same as the C.F.O. forecasts .sx The 1,000-500 mb thicknesses and the 500 mb heights are much better forecast by the three-parameter model than by either C.F.O. or the two-parameter model .sx The thermal winds are also forecast better with the three-parameter model than with the two-parameter model .sx There is little to choose between the C.F.O. and three-parameter model forecasts of the 500-200 mb thicknesses and thermal winds , but the C.F.O. 200 mb forecast is rather better than that produced by the three parameter-model .sx The forecasts of the 200 mb contours and 500-200 mb thickness produced by extrapolation from the two-parameter model were , not unexpectedly , worse than those produced by the other two methods .sx It should be noted that C.F.O. do not produce forecast charts of the 500-200 mb thickness , and that the values attributed to them have been obtained by subtracting their 500 mb forecasts from their 200 mb forecasts .sx b ) Examples of forecasts .sx The numerical forecasts using the three-parameter model based on data for 00 GMT 26 February 1959 and 5 May 1959 are shown in Figs .sx 1-8 .sx These two situations were chosen because the former forecast produced a large r.m.s. error at 500 and 200 mb and was not one of the better forecasts , whereas the latter was typical of one of the good forecasts .sx A depression centred ESE of Newfoundland at 00 GMT 26 February 1959 ( Fig. 1 ( a) ) moved rapidly NE and deepened 12 mb in the following 24 hr ( Fig. 1 ( b)) .sx The axis of the high-pressure ridge in mid-Atlantic also moved rapidly NE and was lying from Iceland to the northern North Sea at 00 GMT 26 February 1959 .sx The smaller depression originally west of Ireland filled and its associated trough was orientated N-S over Eastern Norway .sx The numerical forecast dealt quite well with the main depression although the movement and deepening were not quite sufficient .sx The trough associated with the warm front and the preceding ridge were over-intensified and were not moved sufficiently north-eastwards .sx The weak trough over Norway was quite adequately forecast .sx Pressure was forecast to be about 8 mb too high in and to the west of the Bay of Biscay , the result of spurious anticyclogenesis .sx An inspection of the 1,000-500 mb thickness charts indicates that the numerical forecast distorted the thermal pattern in the region of the depression much more than actually occurred , and this was one of the worse thickness forecasts of the series .sx This is a typical error of this model since the geostrophic wind used for advection of the thickness lines is much greater than the actual wind in regions of cyclonic curvature , and the advection is overdone .sx Fig. 2 shows that the rapid movement of the 500 mb trough from east of Newfoundland to mid-Atlantic with the formation of a closed circulation was quite well forecast , although the trough was moved too rapidly in the south .sx Pressure was forecast to be too high between 10@ and 20@W , a result of spurious anticyclogenesis .sx Fig. 3 indicates that the 200 mb forecast gave much too high pressure in mid-Atlantic .sx The movement of the western Atlantic trough was quite reasonably forecast in middle latitudes but was moved too rapidly in the south .sx This rapid movement in the south was almost certainly associated with the strong gradients produced by the spurious anticyclogenesis .sx The vertical motion charts are shown in Fig. 4 and are quite consistent with the forecast positions of the synoptic features .sx The pattern for the 600-200 mb layer is similar to that for the 1,000-600 mb layer , but the magnitudes of the vertical velocities measured in mb hr :sx -1: are less in the 600-200 mb layer than in the bottom layer .sx If the vertical velocities had been computed in cm sec :sx -1: the magnitudes in the two layers would have been more similar .sx The numerical forecast based on the 00 GMT data for 5 May 1959 was one of the better numerical forecasts .sx An anticyclone moved eastwards from mid-Atlantic to the British Isles , and two shallow depressions in the vicinity of Newfoundland amalgamated and moved into the entrance to the Denmark Straits .sx These features were quite well forecast ( see Fig. 5 ) , although the central pressure of the depression was not quite right .sx The eastward movement of the Atlantic thermal ridge was forecast to be a little less than actually occurred , and a cold trough forecast about 50@N 20@W did not materialize .sx Fig. 6 indicates that the movement and development of the troughs and ridges at 500 mb were forecast very well .sx The 200 mb forecast ( Fig. 7 ) was also successful , especially near Portugal and in the vicinity of the British Isles .sx However , the forecast position of the 200 mb trough near Greenland was not correct .sx The vertical motion patterns in Fig. 8 are consistent with the synoptic features forecast in Figs .sx 5 to 7 .sx .sx CONCLUSIONS .sx The forecasts based on the three-parameter model are significantly better than those based on the Sawyer-Bushby two-parameter model for the 20 situations investigated .sx The extra degree of freedom allowed in the new model does not give rise to such vigorous over-development as in the two-parameter model , and although spurious anticyclogenesis still occurs it is not usually so intense as previously .sx Knighting and Hinds ( 1960 ) showed that the incorporation of a stream function into the two-parameter model gave a significant improvement in the results , and it is quite likely that the introduction of a stream function into the present model would produce a further improvement .sx The three-parameter forecasts of the 500 mb contours and the 1,000-500 mb thicknesses are statistically better than those produced by C.F.O. , but there is little to choose between the corresponding forecasts for the 1,000 mb contours and the 500-200 mb thicknesses .sx At 200 mb the C.F.O. forecasts are slightly better than the three-parameter model , probably because no allowance is made in the numerical forecasts for the presence of a portion of the stratosphere below 200 mb .sx The accuracy of the 200 mb numerical forecasts seemed worse on days of a low tropopause over a significant part of the area than on days when the tropopause was nearer 200 mb .sx ACKNOWLEDGMENTS .sx The authors wish to thank the Director-General of the Meteorological Office for permission to publish this paper .sx A graphical method of objective forecasting derived by statistical techniques .sx By M. H. FREEMAN .sx Meteorological Office , Dunstable .sx Manuscript received 18 January 1961 ) .sx SUMMARY .sx The objective forecasting technique described consists of a composite diagram from which the forecast value of the predictand can be read directly , given the values of the predictors .sx Each section of the diagram combines a new predictor with an estimate of the predictand obtained from the previous sections .sx The isopleths in the diagrams are obtained by fitting a curved surface ( involving powers and cross-product terms of up to the fifth order ) to the basic data by a 'least squares' procedure .sx Only terms which are significant at the 5 per cent level are retained in the regression formulae so produced .sx At each stage the predictor to be selected is that which contributes most to the combination so far chosen .sx The method was used to forecast visibility ( as one of 32 code figures ) at London Airport three and six hours ahead .sx When it was tested on two winters' independent data , correlation coefficients of 0.89 and 0.83 were obtained for the 3-hr and 6-hr forecasts , respectively .sx During the same period the figures for the normal subjective forecasts made at London Airport were 0.87 and 0.74. .sx INTRODUCTION .sx An objective method of forecasting may be described as one which calls for no judgment on the part of the forecaster .sx Given the same initial data any person using the method will produce the same forecast .sx Numerous objective techniques have been described by workers in the U.S.A. , but objective forecasting has received much less attention in Great Britain .sx Swinbank ( 1949 ) , Craddock and Pritchard ( 1951 ) , and Saunders ( 1952 ) all produced methods of forecasting fog which were partly objective , but some of the predictors used had to be forecast subjectively .sx Most objective techniques depend on the production of either formulae or diagrams , and both methods have been subject to various weaknesses which the system to be described attempts to overcome .sx Many of the earlier systems produced forecasts in terms of only a few categories , e.g. , fog , fog in patches , or no fog ; for aviation forecasting a forecast of visibility in yards or miles is required .sx Formulae may be deduced from physical principles , but more often they are devised by statistical processes to produce regression equations .sx These have almost always contained only linear terms whereas more complicated relations may be required .sx In the graphical methods the lines on the diagrams often had to be drawn subjectively and it was not easy to tell whether the best lines had been drawn or not .sx In many systems the choice of predictors to be used had to be made subjectively .sx Rigorous statistical methods were used in developing the present method , the computations being made on a Ferranti Mercury Computer at Meteorological Office , Dunstable .sx The problem chosen for investigation during the development of the objective forecasting technique was the important one of forecasting visibility at London Airport .sx The system which was devised consists of a composite diagram such as that illustrated at Fig. 1 .sx The pecked line on the diagram indicates its method of use .sx The top left-hand section is entered with the appropriate value of the first predictor and successive turns are made at the appropriate isopleths of each of the other predictors , the forecast being read from the scale on exit .sx .sx VISIBILITY PREDICTION DIAGRAMS FOR LONDON AIRPORT .sx The particular problem specified was to forecast visibility at London Airport for 0900 and 1200 GMT using 0600 GMT data and for 1800 and 2100 GMT using 1500 GMT data ( i.e. , a 3-hr and a 6-hr forecast morning and evening) .sx The winter period , November to January , was selected and forecasts were to be given to the nearest 100 yards up to 1,000 yd and at 200-yd intervals up to 2,000 yd .sx This requirement and the desirability of having an approximately logarithmic scale of visibility led to the use of the visibility code shown in Table 1 .sx The selection of the parameters to be tried as predictors was one of the most important parts of the investigation .sx Anything which physical principles suggested might be relevant was included , and the advice of experienced forecasters at London Airport was sought .sx Most of the parameters tested are listed in Table 2 .sx Many were extracted directly from the London Airport registers but some had to be specially computed .sx The geostrophic winds over London Airport were measured from surface charts at the Central Forecasting Office , Dunstable .sx The wind shear was defined as the ratio of the surface wind speed to the geostrophic wind speed .sx Computed pressure gradient was a complicated parameter obtained from pressures and pressure tendencies at four neighbouring stations .sx The lapse rates were obtained as the difference between the surface temperature at London and the temperature 50 mb ( or 25 mb ) above the surface at Crawley ( or Larkhill for the early years) .sx The hydrolapses were similarly defined using dewpoints instead of temperatures .sx Data for the eleven winters November 1946 to January 1957 ( 1,012 days in all ) , were recorded on specially printed Paramount edge-punched cards and were used in the development of the objective forecasting technique .sx Data for the three following winters were used to obtain an independent check on the efficacy of the system .sx To assist in selecting the more promising predictors each parameter x was correlated in turn with the visibility to be forecast z. A polynomial of the form z = a + bx + cx :sx 2: + .sx . was fitted to the data by the method of 'least squares,' successively higher order polynomials being tried until further terms gave no further reduction in the r.m.s. error ( SE) .sx The correlation coefficient r was calculated from the formula r :sx 2: = 1 - ( SE/ SD) :sx 2: where SD was the standard deviation of the visibility to be forecast .sx