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 . 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 . the thermal winds are also forecast better with the three-parameter model than with the two-parameter model . 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 . 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 . 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 . b ) . examples of forecasts . 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 1-8 . 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 . 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 ) ) . 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 . the smaller depression originally west of Ireland filled and its associated trough was orientated N-S over eastern Norway . the numerical forecast dealt quite well with the main depression although the movement and deepening were not quite sufficient . the trough associated with the warm front and the preceding ridge were over-intensified and were not moved sufficiently north-eastwards . the weak trough over Norway was quite adequately forecast . 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 . 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 . 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 . 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 . pressure was forecast to be too high between 10 &amp;deg; and 20 &amp;deg; W , a result of spurious anticyclogenesis . fig 3 indicates that the 200 mb forecast gave much too high pressure in mid-Atlantic . the movement of the western Atlantic trough was quite reasonably forecast in middle latitudes but was moved too rapidly in the south . this rapid movement in the south was almost certainly associated with the strong gradients produced by the spurious anticyclogenesis . the vertical motion charts are shown in fig 4 and are quite consistent with the forecast positions of the synoptic features . 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-1 are less in the 600-200 mb layer than in the bottom layer . if the vertical velocities had been computed in cm sec-1 the magnitudes in the two layers would have been more similar . the numerical forecast based on the 00 GMT data for 5 May 1959 was one of the better numerical forecasts . 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 . these features were quite well forecast ( see fig 5 ) , although the central pressure of the depression was not quite right . 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 &amp;deg; N 20 &amp;deg; W did not materialize . fig 6 indicates that the movement and development of the troughs and ridges at 500 mb were forecast very well . the 200 mb forecast ( fig 7 ) was also successful , especially near Portugal and in the vicinity of the British Isles . however , the forecast position of the 200 mb trough near Greenland was not correct . the vertical motion patterns in fig 8 are consistent with the synoptic features forecast in figs 5 to 7 . 7 . conclusions . 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 . 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 . 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 . 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 . 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 . 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 . acknowledgments . the authors wish to thank the Director-General of the meteorological office for permission to publish this paper . . a graphical method of objective forecasting derived by statistical techniques . by M H Freeman . meteorological office , Dunstable . manuscript received 18 January 1961 ) . summary . 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 . each section of the diagram combines a new predictor with an estimate of the predictand obtained from the previous sections . 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 . only terms which are significant at the 5 per cent level are retained in the regression formulae so produced . at each stage the predictor to be selected is that which contributes most to the combination so far chosen . the method was used to forecast visibility ( as one of 32 code figures ) at London Airport three and six hours ahead . when it was tested on two winters &apos; independent data , correlation coefficients of 0.89 and 0.83 were obtained for the 3-hr and 6-hr forecasts , respectively . during the same period the figures for the normal subjective forecasts made at London Airport were 0.87 and 0.74 . 1 . introduction . an objective method of forecasting may be described as one which calls for no judgment on the part of the forecaster . given the same initial data any person using the method will produce the same forecast . numerous objective techniques have been described by workers in the U.S.A , but objective forecasting has received much less attention in Great Britain . 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 . 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 . 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 . formulae may be deduced from physical principles , but more often they are devised by statistical processes to produce regression equations . these have almost always contained only linear terms whereas more complicated relations may be required . 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 . in many systems the choice of predictors to be used had to be made subjectively . rigorous statistical methods were used in developing the present method , the computations being made on a Ferranti Mercury computer at meteorological office , Dunstable . the problem chosen for investigation during the development of the objective forecasting technique was the important one of forecasting visibility at London Airport . the system which was devised consists of a composite diagram such as that illustrated at fig 1 . the pecked line on the diagram indicates its method of use . 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 . 2 . visibility prediction diagrams for London airport . 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 ) . 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 . 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 . the selection of the parameters to be tried as predictors was one of the most important parts of the investigation . anything which physical principles suggested might be relevant was included , and the advice of experienced forecasters at London Airport was sought . most of the parameters tested are listed in table 2 . many were extracted directly from the London Airport registers but some had to be specially computed . the geostrophic winds over London Airport were measured from surface charts at the central forecasting office , Dunstable . the wind shear was defined as the ratio of the surface wind speed to the geostrophic wind speed . computed pressure gradient was a complicated parameter obtained from pressures and pressure tendencies at four neighbouring stations . 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 ) . the hydrolapses were similarly defined using dewpoints instead of temperatures . 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 . data for the three following winters were used to obtain an independent check on the efficacy of the system . 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 &amp;formula; 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 ) . the correlation coefficient r was calculated from the formula &amp;formula; where SD was the standard deviation of the visibility to be forecast . 