Method of and apparatus for determining or forecasting the future value of certain meteorological parameters

摘要

749,589. Electric analogue calculating systems. GIAO, A., and RAYMOND, F. H. Dec. 1, 1952, No. 30387/52. Class 37. In apparatus for determining or forecasting the prospective value at a given geographical point, after a given time interval from a datum, of a meterological parameter such as atmospheric pressure, temperature, wind velocity, and the like satisfying equation (1) below from a chart of mean isothermal lines and a chart of isolines indicating the initial condition of the function Fo of the said unknown parameter as defined by equation (6) below; there are provided (a) means for automatically scanning the chart of mean isothermal lines along meridians, commencing with a datum meridian containing or lying closely adjacent to the given point and proceeding along successive meridians lying along a direction (referred to the datum meridian) of the isothermal lines contrary to the direction of transfer movement of the function Fo until an area has been scanned proportionally to the given time interval after allowance for corrections necessitated by variations in the chart scale along the meridians; such area lying between a pair of isothermal lines of which one intersects or passes adjacently to the given point, the datum meridian and a further meridian displaced therefrom in a direction contrary to the transfer movement of function Fo; (b) means for scanning the isoline chart along meridians commencing with the datum meridian and proceeding similarly along successive meridians in a direction contrary to the transfer movement of the function Fo; (c) electrical means for algebraically counting the isolines traversed by each scanning line of the isolinear chart with reference to the increase or decrease of the said unknown parameter or its function Fo along the direction of count across each isoline, to determine at each time instant of the count the value of the function for the position attained by the scanning means, and thus to obtain a voltage representing the value of the function Fo at a point on the said further meridian and lying either on or between the said pair of isothermal lines ; (d) electrical means for multiplying such functional value by a weight function defined by equation (5) below to produce a representative product voltage; (e) means for initiating repetitive performance of the operations set forth above with respect to further pairs of isothermal lines displaced towards the geographical pole from the first pair of isothermal lines; and (f) means for electrically integrating the succession of representative product voltage values thus obtained. The unknown meteorological parameter p is defined by where t=time ; #=the two-dimensional gradient operator; H=a transfer velocity vector tangential to the earth's surface and defined by equation (2) below; #=a vector having the dimension of length, given by equation (3) below; and it is stated that where K=an absolute constant; #=the geographical latitude; Q=the angular velocity of terrestial rotation; R = the gas constant for air; Tm=the mean air temperature over the given time period; r=the mean terrestial radius ; #Kz=the unit vector normal to the earth's surface; Kn=the unit vector of the meridians. Equation (1) above is stated to be soluble by the expression (4) in which (5) and (6) where N= length measured along the meridians towards the geographical pole of the appropriate hemisphere; #0=the latitude of the given point; #po = the initial value of parameter p (+ a constant, if necessary, to give positive values) ; Fo=a function transferable during the operative time interval along the streamlines of the transfer velocity vector H; {Fo}= the value of Fo at the given point and at other places on the meridian of such point at the end of the operative time interval. The Specification contains references to the literature in which the basic mathematics fundamental to the above relations is stated to be set forth. Fig. 1 shows a group of incremental isolines of function Fo and an associated group of incremental isotherms (equivalent to the streamlines of the vector H disposed about a meridian M of longitude #=#α) and the first portion of the apparatus determines the successive values of the function Fo; {Fo} 1 , {Fo} 2 , {Fo} 3 , {Fo} 4 , &c. to {Fo} n , for the values of the several streamlines and the corresponding values of # along the meridian M (#=#α) and in operating the transfer of function Fo to successive points along meridian M during the said given time interval, with due allowance for variable displacement of the isolines of Fo at vector velocity H along the several streamlines thereof in accordance with equation (7) Figs. 2, 3 show as mirror images on transparent surfaces 1, 2 the respective Mercator projections of the isotherms and isolines of the function Fo obtaining over the portion of the earth's surface shown in Fig. 1, on which any selected point is determinable by orthogonal co-oidinates #, # of longitude and latitude; and the thick lines in Fig. 2 represent a group of streamlines of the transfer velocity vector H, i.e. the isotherms of the mean temperature field Tm of the geographical area shown in Fig. 1, according to equation (2) above; while the thick lines in Fig. 3 represent the isolines of function F 0 for the same area, traced in double lines when # F 0 /# # 0 and in single lines when # F 0 /# # 0 for optical sign discrimination. For a given longitude #α the intersections thereof with the streamlines of H (Fig. 2) define a series of ordinates # 1 , # 2 , #3, # 4 , &c. to # n (not shown) at points A, and for a transfer time t the path of each streamline at velocity - H determines a series of points B corresponding to respective points A and defined by a given longitude and latitude value. For each point B (Fig. 2) there exists a corresponding point C at the same longitude and latitude (Fig. 3) defining a particular value F 1 , F 2 , F 3 , F 4 , &c. to F n of the function Fo, which is transferable to ordinates #1, # 2 , # 3 , # 4 , &c. to # n (not shown) of points A at longitude #α and representing the desired transfer of function Fo along the streamlines of the velocity field H for a time t hours. It is shown from equation (2) above that time t hours is given by where A and B are two points of a streamline ofH; #Tm= the constant difference in air temperature between two successive isotherms in ‹ C. ; #NSP1/SP= the distance in millimetres between such isothermal streamlines of H measured along the meridians; #= longitude in degrees; E = the Mercator scale of the representation of H in Fig. 2; and neglecting sin # cosSP2/SP # the transfer time t is proportional to the area between successive streamlines and the meridians of points A, B. For a vertical scanning along the meridians in time 6 at linear velocity where α is a constant velocity, equation (8) reduces to (9) where ## is the scanning time interval A between successive streamlines of H. Fig. 5 shows a scanning device wherein the beams of cathode-ray tubes 18, 19 are deflected at constant velocity in the horizontal direction by a sawtooth waveform from a conventional frame time-base generator 27 and in the vertical direction by a conventional timebase generator 29 and line pulse generator 30; the former being adapted to produce a waveform such that the vertical beam deflection velocity varies in accordance with its deflected position to compensate for the non-linear distribution of degrees of latitude in Mercator projection. The moving spot traces out a raster on fluorescent screens 20, 21 to illuminate the tiansparent charts 1, 2 which are optically focused on the cathodes of photocells 23, 25, and the amplified output of cell 23 comprising a train of pulses coresponding to the intersections between the spot movement and the streamlines of the chart showing the field of vector H operates a step-bystep or binary pulse counter 33 which is reset after each line sweep during the line blanking flyback period by a signal derived at output 34 of the pulse generator 30. A decoder 35 associated with the counter delivers counting position index voltages one at a time for each position of the count to its multiple outputs (36 to 39 &c.) which are separately connected to the inputs of corresponding gating transfer stages (40 to 43 &c.) also receiving counter operating pulses from the amplified output of photocell 23 through a time delay network 45 and contacts 90 of relay 59. The transfer stages (which may comprise pentodes receiving the index voltages on their control grids and the pulses on their suppressor grids) thus operate one at a time to transmit counting index voltages at a fixed time interval from completion of the appropriate count to channels 46 to 49 &c. connected to transfer stages 54 to 57 &c. also receiving sawtooth waveforms from line timebase generator 29 over contacts 60 of relay 59 to successively convert the counting index voltages to analogue voltages representing the successive values of # 1 , # 2 , # 3 , # 4 , &c. to # n , (not shown) of the variable # for the meridian #=#α which are supplied to the corresponding input terminals 11SP1/SP# 11SP2/SP#, &c. to 11SPn/SP# of the recording servo-systems 8SP1/SP to 8SPn/SP (Fig. 4) set forth below. The line sweep sawtooth waveforms are summed by counter 61 which steps once at the beginning of each line to vary a bank of decoding resistances (not shown) delivering a voltage proportional to the count to one winding of differential relay 59 whose other winding is energized from potentiometer 63 by a voltage adjustable to the desired scanning longitude #α. Relay 59 operates after the scanning of any predetermined number of lines L in the range O to N (where N is the maximum count capacity equal to the number of vertical sweep lines per image), and closes contacts 60 so that the line sweep voltag