weather-crop yield correlations as applied to crop yield estimates tor the european ussr
PROVISIONAL It^TELLIGEHCE REPORT
WEATHER-CROP YIELD CORRELATIONS AS APPLIED TO CROP YIELD ESTIMATES
FOR THE EUROPEAN USSR
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Note
The data and conclueiona contained in thiB report-do not necessarily represent the final position of GRR end should be regarded as provisional only and subject to revision. Additional data or comments which may be available to the user are solicited.
CENTRAL INTELLIGENCE AGENCY Office of Research and Reports
COXTENTS
Page
Summary
I. Purpose and General Introduction
II. Area
III. Sources of Infonaatlon and Its Tabulation
IV. Purpooe and Method of Eliminating the Yield9
V. Methodology and
Weather Factors
Simple
Multiple Correlations . .
Multiple Regression Equations for
5. 30
VT. Sources of Current Weather 33
VII. Additional Proposed Investigations 35
Appendix A. 39
Appendix B. 63
Illustrations
f?l age
USSR: Weather-Crop Yield Study for European
USSR 6
Observed Yields and Yields Computed from Monthly
Weather Data for Selected Areas of the USSR
o 28
cia/rr
(orr) LUili
WEATHER-CROP YIELD CORREIATI0K5 AS APPLIED TO CROP Til
Summary
In thistudy le Bade of tbo relationship betvoen the ylolda ofspring groins (wheat, barley, ana oato) and selected weather factors in.the major grein-surpluo-producing districts of the European USSR. Total monthly precipitation mid mean monthlytemperature values were selected as tbo weather factors to be employed. Precipitation valuos were used both In the form ofmonthly totals and in tha form of combinations of monthly data. Only Individual mean monthly maximum valucit ware used for temperature, Tbona weather data, as well as the grain yialtl information, cover the.
From an analysis involving these factors, multiple regression equations have been developed in this atudy which, on the basis of current weather information, will be enployed fcr the first time by CRR in estimating the yields of^ groin crop in the USSR. Tho weather compouenta employed in too development of theseequations woro selectod on the basis of cooperative significance as determined through tho uao of alaple and multiple correlation coefficients. Tho significance of certain of these correlation coefficients formed the basis for hypotbasiling certain months or combinations of months as moatith roepect toand maximum tenperoturo, in determining the ultimate crop
0KCT7."
yield. Tho crop yield date were utilized inay that part of them vao employed in obtaining preliminary information and In eettlng up llio hypothecie ao to "critical" months, nnd another part was used to test the validity of thla hypothesis. The correlation coefficients computed in thla study formed the baela for setting up the multiple regression equations to be used Id estimating future grain yields In the USSR. However, sinceimited number of weather factors can he includedredictionesult obtained in any particular ceao may have to bo readjusted in the light of any significant meteorological or oomctoorological factor not considered In the equation.
On the buuls of results obtained tlmaontinuation of thin veothor-crop yield otudy la plaiuicd. In particular, the relationship between crop yields urd vapor pressure deficit values vlll be investlghted. Vepor preasure deficit,unction of both temperature and humidity,ough measure of the rate of transpiration and evaporation from plcnto. Preliminaryindicate that significant results may be obtained, particularly la regions of marginal precipitation.
in addition, studies on the major winter grains and other cropo, such as potetooe, sugar beets, end cotton, are planned.
a hoi hit
I. Purpose end General Introdjetlon.
Thla report deeletudy of the problem of determining peat weather-crop yield correlations and ascertaining whether it Is practical to use these correlations in estimating future groin yields in the European USSB. Thla otudyrogress report, and conclusions ore baaed on analyses nede up to the preeent time.
The importance of weathor factors in relation to crop yields haa long been recognized, but it has been extremely difficult to express these weather-crop yield relationships In mathematical termo that could be applied to estimating grain yields. Many seperate weather factors affect the final crop yields, and the problem la further ccoplicated by the fact that there are numerous Interectlona nsong the weather factors themselves. For example, in order to determine the effect of precipitation on the yield of spring wheat in any given area, not only the amount of precipitation but also the period of Its occurrence must first be considered. In addition to precipitation. It Is necessary to coiinider the effects of other weather factors occurring during the sumo purled. The effectB of these other factors ore not Independent of the precipitation or of each other but ore interrelated. Thus the problem is exceedingly complex.
If practically unlimited timenta were available. It would
be Ideally desirable to measure the relationships between wcother
i
factors and crop yields by evaluating both the qualitative and the
quantitative effects of every conceivable combination of veatber factors at regular intervale throughout the growing season. since both time ana data are insufficient for such anapproach, the analysis ofimited number of weather factors is included in this study.
Since relatively comprehensive weather and crop yieldin the European USSR is available only for the, it was necessary to make use of this Information even though it is old. For the purposesorrelation study, however, such data arc entirely satisfactory, since the general pattern of theinvolved does not change.
*
- U
moan
II. Aren Covered .
The area selected for this study Includes most of the grain-surplus -producing districts of the European USSRVIth Its apex based in the Tsaristf the Don the selected area spreads away fanwlGe:
orthveetward, Including the following guberniyas of the Ukraine: Tokaterlnoslav, Poltava, Chernigov, and Kiev as well as the Bouthvoet guberniya of Bessarabia;
P. Northward, including the following gubernlyoa of the 'Black Soiloronezh, Kursk, Orel, Tambov, and Penza as well ee the semi-Black Soil gubernlyaa of Tula end Ryazan;
3- Northeastward, including the Volga River valloy gubernlyaa of Saratov, Samara, Slmbirnk, and Kazan an well as the Ural guberniya of Pern.
In) boundaries, ell or at least portions of ell of the following administrative divisions are located in this area with its apex based In Rostov oblnat of the former Don guberniya (the northwestern port of Economic Region. To the northweat in tho Ukrainian group (EconomicIII) are located the following: Stallno, Voroshilovgrad,
* This area is outlined in the amp following p. 6.
Cubernlyas, the larger administrative divisions In theb, correspond roughly to present-day oblasts, although in many cases they were somewhat larger. The next smaller administrative divisions in this period, the uyezds, though larger, are roughly ewparable to the present-day rayons.
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"
fcaporozo'ye, Dnepropetrovsk, Kirovogred, Poltava, Sumy, Chernigov, Kiev, and Vinnitsa oblasts end the Moldavian SSR and Izaall oblaat;
To the north in the Black Soil and oeml-Black Soil Belts (the southern port of Economic Region VJI) are located the following: Kursk, Orel, Tula, Bryansk, Voronezh, Tambov, Ryazan, and Penza oblasts and Hordovskaya ASSR, Chuvaahskaya ASSR, and Marlyskaya ASSR;
To the northeast in the Volga group (Economic Region VI) are located the following: Stalingrad, Saratov, Kuybyshev, and Ul'yanovak oblasts and Teterakaye ASSR. In addition, two Ural (Economic Region VIII) oblaata nro included: Molotov weDt of the Urals and Sverdlovsk east of tho mountains.
iii. Sources of Information and Ha Tabulation.
The raw materials for this study were obtained from two sets of Buooian data. The crop ylold data were taken from Uroz-hay (AnnuRl : f the Control l/ These volumes contain acreage and yield data for the major crops in Russia for each year during the The yields and acreages are given on both an uyezduberniya basis.
The weather information was obtained from Lotopic! (Annals of tho Central Physical/ The weather data in those volumes Issued during there comparable with tho selected yield data. Father complete weather Informationonthly, and in some cases evenaily, bonis forstations is contained In each of these yearly volumes. Despite the largo number of stations tabulated in each yearly volume, it was difficult, In,some regions, to find stations whichong-term record. The reason far this la that the same stations were not alwayo included in every volume. Sometimes old stations would be omitted and new ones added.
Preen the set of weather volumes, total monthly precipitation end moan monthly maximum temperature values were tabulated for all stations in the gubemiyas listed obove. Only stations having at leastearo of record within theere selected. The location of each of these stations woe then determined both as
lo guberniya and as to uyezd In order that yield tabulations might be made for each guberniya end for thoBe individual uyezds In which weather stations were located.
Tabulations were then made of the yields for three spring grains (wheat, barley, and oats) for each individual uyezd which contained at least one weather station havingears or more record and for each guberniya in which such uyezd was located. i69u, yields were recorded in chetverta per deeeiatlne, while they were expressed in poods per doBsiatine. For purposes of conformity, the chetvert values were converted to the equivalent pooda.*
*
The following conversion factors oro applicable for wheat:
chetvert
por per
deBSlatlna dessiatine
pood per dessiatine chetvert
1 pood
1 centner
ooda perentners per hectare
fentner per6
pounds1
0 l poundsilograms)
7 ounds
IV. Purpoao and Method of Eliminating the Yield Trend.
* This formula, howevor, describes any one of an infinite number of linee, and the problem is to determine which line best describes the data. The principle of "least squares" is used in determining this best line. The line of best fit to each series of yieldsine about which the sum of squares of the deviations (the differencesthe line and the actual yields) willinimum. There can be only one auch line.
tET
Since the yield data extendedelatively long period of yuara. It uaa necosoary to perform preliminary testaield trend existed for which an allowance should be made. These teats, performed In the manner described below, indicated the presence of an increasing trend In yields over tho. This indicated trend was found to betatement by Timoehenkohat "the average yield of all grains increased during the periodn the average byood per dessiatlne yearly, orercent of the average yield for the period." The method of "leaet squares" was used for the determination of the linear trend. Underinear trend the formula will be of thehe "b" value in the formula indicates the elope of the trend line. Foralueould indicate that tha yieldood per deaslatlne each year and thatield incronse woo not caueod by weather factors but rather by increaoingly improved technology, better varieties, or other similar factors. Sioco thistudy on the relationship between weather and crop
yields, it was necessary to eliminate this variation, which was not caused by weather factors. Hence all yield data used in this study have been adjusted for this trend.
The possibilityignificant yield trend5 to the present alsoerious problem in arriving at currentestimates. The question is continually rniscd an to whether such factors as lime and fertilizers, increased mechanization,faro practices, and improved varieties have significantly Increased yieldaeriod of years up to tbo prooont time. Concerning fertilizers, Jasny Uj stetee that "commercial fertilizers have been applied toew crops, mainly sugar beets, cotton, end,maller extent, flax. Such crops as grain benefited only in so far aa they were grown In rotation witb fertilizedikewise there la no evidence available thet mechanization oflias had'an appreciable effect in increasing grain yields. As to improved varieties, an external research project is being tentatively outlined in on effort to determine what affect, if eny, they may have had in increeeing yiclcn.
Tho intelligent use of any yield prediction equationsdevoloped In this studyonsideration of any nonmeleorologlcel factors that can be shown to haveignificant effect in Increasing yields.
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BsM
V. Methodology and Results. 1. Weather Factors Used.
Having tabulated the weathor and yield data and corrected the yields on the basis of the Indicated yield trend, the nexttepoint analysis, of the data In the three series oftotal monthly preclpitstlon, Been monthly maximum tempers-ture, and yields of the selected crops. Before proceedingiscussion of the methodology employed, hovever, It would perhaps be beneficial to give an explanation and Justification for the uae of precipitation and maximum temperature as tho weathor factors to be used in thia study. Precipitation has been one of the factors employed in most studies of weather-crop yield relationships. This Is not surprising In viow of the fact that moisture lo an essential factor In all crop-producing areas. In regions of marginal or sub-aorginal precipitationor example, the valleys of the lover Volga and the Don as woll as pnrtB of South Ukraineoisture is the all-important factor. In these regions an average or even above average rainfall Is necessary for even mediocre crop production. Furthermore, the distribution of tho rainfall throughout the year, end particularly through the growing season, is of the utmost Importance. It is generally recognized that, during certain phases of development, plants are sore sensitive to environmentaland ure more easily damaged by extremes. Some authorities have tormed these periods of stress as "critical" stages in the
-eflBaUBa
h. I
growth or plants. For example, numerous scientists in the US, Canada, and Russia have considered the period Just prior to the heading of wheatcritical" stage in determining the ultimate crop yield. Adequate moisture must be available during this "critical" periodgood" yield ia to be obtained.
The reason for the use of maximum temperatures Is perhaps lees obvious. As previously mentioned, in many regions it was difficult to find stationsong meteorological record. In tha studies employing uyezd yiejde, precipitation anddata were,ule, avollablo from only one station. Even when guberniya yields were involved, weather data fromimited number of stations were available, varying from three to eight or nine. An average of the precipitation at this number of stationsuberniya la not nccuBPurily representative of the guberniyahole. This la particularly true during the growing season, elncc much of the precipitation during the summer occurs in convectional thunderstorms, which arc characteristically local in nature although frequently quite intense. Temperatures, on the other hand, arc much less variablearticular area than is precipitation. Furthermore, average maximum temperatures are quite closely correlated with actual precipitation. General cloudiness, often occurring with local thunderatorao over aarea, will be reflected in lower maximum temperatures. For
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this reason, tho less variable average maximum temperature eightetter clue to actual precipitationarge area than vould tho overage precipitation vnlueB recordedimitod number of stations.*
Employing the yield data and monthly data for the tvo weather factors, precipitation and maximum temperature, methods of correlation and regression were employed to determine the mutual relationships among these data first on an uyezd basie and thenuberniya baele.
2. Simple Correlations.
* It la also conceivable that since maximum temperature is quite sensitive to cloudiness, there may be some relationship between maximum temperature and the rate of evaporation andby planto.
Since yiclda are directly dependent on weather factors, use of the term regression coefficient rather than correlation coel'fl' clent would be technically more nearly correct. The distinction between the two is that regression coefficient la the appropriate tern if thex late, in this case yields, may be considered as dependent upon the other, in thiB ease, precipitation ortemperature. Correlation, on the other hand, ia themeasure of the relation between two variates neither of which may be looked upononsequence of the other. has acquired many of the concepts of regression, and often the distinction between the two has been almost lost.
Staple correlationere computed between the uyezd yields of each of three spring grains (wheat, barley, and ouIb) and monthly precipitationombination of the recorded data for such combinations of months as might possibly have seme bearing on yield. Similar coefficients also were computed between yield data and temperature values.
upcrflclel examination of certain coefficients computed with the use of monthly dataombination of monthly data Indicated that in certain cases llltlo or no relationship erlated. In otherore or leas poaltlve pattern of re-lationohlpa was Indicated. Based on these Indicatedorking hypothesis was assumed as to the "critical" months with respect to both precipitation and temperature for each uyezd under consideration.
The next atop waa to test, on the booiouberniya oo whole, the workingumcd for the several uyozde within that guberniya. For these tests the method of simple correlations waa eoployed.
For example, the simple correlation coefficients between spring wheat yields in Samaraf Samara guberniya* andec if led weather factors attetion In Samara uyezd, are ub follows:
* Computations for Samara guberniya arc uaod un examples throughout thia study. The boundaries of the 'Pisoriot guberniya Include all or at least portions of the following prcaent;day oblastB: Sarutov, Kuybyahev, and Ul'yanovsk.
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Simple Correlation Coefficients for Spring Wheat in Saoara Uyezd of Sasara Guberniya
WeatherCorrelation
Precipitation
Sep-Oct plusW
Average Maximum TcBperature
Jul
correlation coefficient, generally designated as r, isto summarize In one number the degree ofbetween two scries of observations: for example,and average June precipitation. Or it might he defineddegree to which the wheat yields and precipitation valuesutep as they Increase or decreeoc in amount. Theis* designed to vary betweennd tl. The twoindicate perfect linear relationship. egativeindicates an inverse relationship: in other words, anin one variable Is associatedecrease in theero valuendicates that the two variablen
asterisks in tablesighly significant that is, significant atercent level. Inthe chances areutf obtaining alarge as Abie due to chance alone. The levels ofobtained by use of the tables In Statistical MethodsW. Sncdecor. *J
Twenty-seven observations were used Id computing each of the above coefficients. All the coefficients except that for May averago maximum temperature ore highly significant: that la, significant atercent level.
Other simple correlation coefficients for various uyezds are glvon In Appendix A, Tables, and 3- uperficialof the data in these tablos suggests that on an uyezd basis Kay-Juno appear to be more nearly "critical" months ae regards precipitation in moat guberniyae, while Juno appeara moro nearlyas regards maximum temperature. The validity of this apparent significance will be tested later in this study.
It is obvious that there should bo variations among these correlations on an uyezd level, and It Is difficult to attach any great significance to individual valuesiven uyezd. The primary purpose of computing these coefficients on an uyezd level was to gain preliminary information as to the nature of the variability among various localitica ae well as toough idee as to which weather factors appeared toredominant role within these various localltlee.
The correlation coefficients based on the individual uyezd yields formed tho basis for settingorking hypothealB to be tested on the basis of guberniya yields. Main emphasis was placedtudy of the three itpring grains previously mentioned.
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Ae previously elated, numerous correlation studies In the US, Canada, and Russia liavc indicated that the period Juat prior to the heading of grains lo "critical" in dote raining the ultimate crop yield. The heading stage for spring grains in moat of the area studied occura within the period of late May to early July. For this reaaon, the sum of the Kay and June precipitation was used ae one portion of the working hypothesis to be tested in Individual gubernlyas by the simple correlation method. It was felt that theforonths wouldore realistic value to use than the precipitation for any single month.
An attempt wbh made, using uyezd correlation coefficients for toetporature, to determine for each guberniya which months appeared to bo most "critical." For example, if tho correlation coefficients Tor several uyezdsertain guberniya eeemod to indicate that June temperaturo wee most closely correlated with yield, thon, in that guberniya, the June temperature factor was used as the second portion ofworking hypothesis to be tested.
In Samara guberniya, for example, the averago maximum June temperature and the sum of the Kay and June precipitation were selected ao the two portions of the hypothesis to be tooted.
Under this hypothoBls tha correlations between spring wheat yielde In Samara guberniya and tho hypothesized weather factors are as follows:
Simple Correlation Coefficients for Spring Wheat in Samara Guberniya
Woathor Factor
Correlation Coefficient, r
of Hay and June Precipitation Average Maximum June Temperature
bJ
Double asterisks in tablesighly significant that is, significant atercent level.
The above coefficients are based onbservations, end both are highly significant.
These correlations and others similarly computed for
various gubernlyas ere ehovn inA, Table h. Simple corre-I
lation coefficients for precipitation and temperature usingyleldo have been computed forf the l8 gubernlyas listed above. Correlation coefficients for temperature on an uyezd baala indicated thatf theubernlyas the average maximum temperature for June appeared to bo more "critical" than thefor May or July. Therefore, In the eaoe of each of these nine gubernlyas, the June temperature was selected as the temperature
portion of the hypothesis. In tho caseentral block of six gubemlyas (Tambov, Ryazan, Tula, Oral, Kursk, endimilar coefficient* Indicated tho average maximum temperature for Kay uo being more "critical" than for June or July, and in the case of each of these alx guberniyaB, therefore. Key temperature was selected aa the temperature portion of the hypothesis. In certain of theubemlyas, correlations could not bo made on an uyezd boals. In such ceooa the hypothesis was formulated using the results of uyezd correlations in neighboring gubemlyaa.
A superficial examination of the data inndicates that in the case of each of three spring grains (wheat, barley, and oats) there frequentlyloRer correlation between temperature nod yield than between precipitation and yield. Also, thecoefficients for precipitation ore significant In more esses for barley ancj oota than for wheat,
ough check on the accuracy of tho working hypothesis previously assumed, simple correlations between spring grain yields end temperatures wore ccoputed for tho months adjacent to the month or June, which had been set up In the hypothesis as beingor example, in Samara guberniya the correlations between spring wheat yields end average oexiaum Kny and July temperatures are as Toll owe:
*
Simple Correlation Coefficienta for Spring Wheat In Samara Guberniya
Factor
Correlation Coefficient, r
Maximum May Temperaturo Average Maximum July Temperature
-
correlations for particular months could not be considored For oats, the June temperature correlations in all six gubernlyas uore higher than those for May. In view of these reaulte, it might have been better to have hypothesized June temperature oe "critical" for all gubernlyas In this study rather than to have made an exception for tho six gubernlyas dlecussod above.
Considering the olmilar sets of correlations in thoubernlyas where June temperature waa hypothesized as critical, there wereoses out of then which either tho May or July temperature correlation coefficients wore significantly better than the hypothesized June coefficients. The correlationin two gubernlyas, Bessarabia and Yekaterlnoslav, were consistently small, in moat cases not oven significant atercent level. If the coefficients for these two gubernlyas ere omitted from Jhe tabulation, inf the recalningets of correlations was either tho May or the July coefficienthigher than that for the hypothesized month of June. 3- Multiple Correlations.
As pointed out earlier In this discussion, the fluctuationsiven yield scries ore never dependent upon one Blngle weather factor. The next step, therefore, was to ccobine the two selected weather factorsultiple correlation with yield. Multiple
correlation conaiBtB of tho measurement of tho relationship between
*
a dependent variable, in this case yield, and two or morevariables, In this case monthly precipitation and maximum temperature values.
Toultiple correlation coefficient for three variables I, Xj,t le flrat necessary to ccapute three Blople correlation coefficientsVg,. Tho next step le to compute two standard partial regression coefficients,nd b'yj from the following relationships involving the simple correlations
rYlrYg rY2 -
1I?
Then the square of the multiple correlation coefficient la obtained
by
3 r r b'
1
The square root of this value gives us the desired multiplecoefficient, B. The multiple correlation coefficient, B, is always less then unity but Is greater than any of the simple correlation coefficients that enter into its computation.
Multiple correlation coefficients were flrat ccesputed by using only the weather factors for thoae months assumed under the working hypothesis to be "critical." For example, for Semura guborniya the components wero au follows: the yields of the three
spring grains (wheat, barley, andhe auai of May and June precipitation, and average maximum June temperature. Aa shewn in Appendix A, Tablehe multiple correlation coefficient for spring wheat In Samara guberniya baaed onbservationsighly significant value. Of thendividual multiplecoefficlente, computed under eimilar hypotheees and given in Table7 are highlyparcent level of Blgnlfl-conco)ther values arepercent level of significance).
hock on the multiple correlation coefflcienta computed under the working hypotheses, other coefflcienta were computed by using temperatures for months adjacent to the one considered "critical." For example, in the case of Samara guberniya, aa Indicated in Appendix A, Tablehe multiplecoefficient boood on cpring wheut yield, the sum of May-June precipitation, and overage maximum Hay temperature Isb. Similarly, the coefficient based on spring wheat ylold, the sum of May-June precipitation, and average maximum July temperature Both values are highly significant but slightly less than theomputed under the hypothesis baaed on June average maximum temperature, in Table 7 will be found othercorrelation coefficients for oprlng grains computed by using teapereturee for months adjacent to the one considered "critical."
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SiWlJfT
In the discussion of pimple correlations the question was raised as to the validity of hypothesizing Kay average maximumas "critical" in olx gubomlyoa* rather than Junewhich was hypothesized for tho remaining guhernlyas. lose examination of the multiple correlstion coefficients in Appendix A, Tableasts further doubt on the validity of hypothesizing either May or July average maximum temperature as "critical." Considering the id eetG of multiple correlations (each seteingas to May, June, or July temperature) involvingpring grains {wheat, barley, and oats) in each ofhe correlations baaed on June temperature were highestets, while May values wcro highcateta and July highest In U. Thoao resulta are identical with thouo obtained with simple correlations.
On this baslB, therefore, it seems deulrsble to reject that portion 4
of the temperature hypothosis wherein the Kay average maximumwas considered "critical" for six gubemlyas and, in Its place, to consider June temperature as "critical" for all gubernlyas.
Considering the similar sets of correlations in theubemlyas where June temperature actually was hypothesized ashere woreanes out of theIn which thobased on Kay or July temperatures were higher than those baood on June temperatures. Furthermore, In severel of theae aix cauea the differenceo in tho correlations were slight.
Tambov, Ryazan, Tula, Orel, Kursk, and Voronezh.
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One other attribute of tho given multiple correlation coefficient* might ehed some light on their interpretation. If the value of F, tho multiple correlation coefficient, lo squared, tho resulteasure of the proportion of the variability In yield that can be attributed to the precipitation and temperature values used in computing B. For example, assumeultiple correlations obtained by using the sum of May and Juno precipitation, the average maximum Juno temperature, and spring wheat yieldsiven guberniya. It can then be stated that the squarer G> percent of the year-to-year variability In the spring whoat yields, has been accounted for by the two given weathor factors and that onlyercent remaJnB unaccounted for.
- Multiple Regression Equations for Forecasting Yields.
The final step to be taken toormula suitable for UGe in forecasting yioldsiven urea in to employ multiple correlation coefficients, computediven hypotheals, to develop multiple linoar regression equations for two independent
variables of theVJ ? * In this
A
s the estimated or predicted yield, and X^ and
X^ are the independent variables, precipitation and temperature.
The expressions b and b are partial
coefficients. The fixst an be read as "the
II wit
regressionn independent" whilean be read
as "the rcgreselonndependent Ass using that
pring wheat yield in poods, thathe sua of May and June
precipitation in millimeters, and thathe average maximum
June teopcroture in degrees centigrade, then the
YX.f*
indicates the quantity of change (in terms of poods) In the yield of wheat for each millimeter change in the amount of May and June
* This formulaathematically simplified form of the following equation: 4
This longer form of the equatlco has an advantage In thatparts of the regression equation can be more s the estimated or predicteds theall thealues;tho two standard
partial regression coefficients described above; X and X are the
independent variables, while i and x are their respective means;
V 2 V
^ are the sums of squares of deviations frees
the moan of
fi
precipitation with the actual average maximum June temperature remaining conutont. Similarly, tlie expressionndicates tho quantity of change (In toma of poode) in tho yield of vheat for each degree centigrade change in the average maximum June teaperature with the actual Kay-June precipitation remaining constant. In other vords, the coefficients Indicate the netbetween the dependent variable, yield, and one of the independent varlablea (for example, tho sum of Hay and Junowhile allowing for the other independent variable (for example, average maximum Junehich also Is considered in computing the coefficient.
In the^g the valuea
a, b nd b are all conetor.ta that can be qulto readily
. 1
computed from the given data on ylelda, precipitation, and
temperature, ^or example, in computing the multiple regression
equation for use In predicting spring wheat yields in Samara
guberniya, actual yields, May-June precipitation, and average
maximum June temperature foroars were taken into consideration
to obtain tho values a, b nd b which resulted in the
equation f9 + A9X2 as given In Appendix A, Table 8. lso contains other multiple regression equations, based on May-June precipitation and average maximum June temperature, for use as au sid in predicting spring grain yields In selected gubernlyna of the USSR. If the cum of Kay and June precipitation
In any particular year la substituted Tor X, and the average maximum June temperature is substituted for XP, it le possible to cceiputo
the estimated or predicted yield, Yf for that year. Gome of those prediction equations are mora reliable than others. eneral rule, those gubernlyea for which relatively high multiple correlation coefficienta woro obtained for tho various spring grains will tond to hove more reliable prediction equations.
Some of the results obtained by using the multiple ro-
greseion equations for computing yields of various groinsnd comparing them with the actual knownshown graphically ino 7- Failures Intho yields result In what are known as errors of The standard error of estimate, defined as
M easure of the variation emong errors of
* la thiss the multiple correlationy is the sum of squares of deviations about the mean of Y;s the number of observations In the scries, or the number of years of yield nnd weather rocorde usod in computing tho multiplo regression equation.
estimate. Tho greater the stondurd error, the poorer Is thebetween computed and actual yields. This standard error of eBtlmato le useful in establishing limits es to the accuracy of tho estimation. For example, If wotandard error of estimateooda, it lo possible to state that of all the estimates basadhe rogreseion equation, roughly two-thirds of them will be correct to within plus oroods. Stated
SECRET"
of all prediction estimates baaed on ihie regression equation will
be correct to within plus or8 poods.
ssumptions.
At thlB point it is desirable to state Beveral assumptions
made In this study snd to dlscusB their validity briefly. The flrat
assumption is that the relationship between yield and any weather
factor le linear. The validity of this assumption appears to depend
largely on tho area being considered. For example, where wheat is
grown under meteorologically optimum conditions, it would certainly
not be safe to assume that the yield would increase indefinitely as
tho June rainfall increased. Upertain point an increase in
precipitation would result in higher yields, but beyond thlo point
further precipitation might even lower the ultimate yield. The
uGCumption of linearity appce.ro Juetiflflble, however, so long ae
the weather factore conoldcrod do not fluctuate over too
range. For example, in most of the major wheat arooB in the USSR it la extremely unlikely that precipitation amounts will be ae groat as to cause reduced yields. In fact, lack of moleturo is far moro likely to cause low yields. In auch cases, any slight curvilinear relationship that does exiat uBually can be satisfactorilyby linear methods. Furthermore, when linear methods are applied to curvilinear data, the degree of relationship la really greater than that indicated by the correlation coefficient. It is possible to compute curvilinear regression aquations, but they are more
complicated and should ho used only with longthy aeries of.
A second assumption made In this study is that the effects of the independent varlablee (precipitation and marimum temperature) on the dependent variable (yield) are additivethativen change in eithor precipitation or marimum temperature hoe the ooae effect on yield regardless of tho alia of the other Independent variable. In the linear multiple regression equation discussedyl?ho effectiven change in X^ on the sizea constant regardleos of the Blze of xp. The effect of Xje independent of Xg. oint relationship, on the other hand, tho effect of on i1 le dopondent on Xg. The effect of Xjepends on the size of Xp. The computationinear Joint regreoslon equation is considerably more complicated. Several of these computations, however, were madeough check on the validity of essumlng additive rather than Joint relationships. The equation used was of theX^Xg. In thla equation tho product of the two Independent varlableo, XjXg, ezpreasee the Joint relationship. This method in the particular instances usod did not significantly improve the accuracy of the estimated yields. It would be unsafe to easume categorically that no Improvements could be made by using this or other combinations of Joint relationships, but it is questionable whether thewould he sufficiently great to warrant the necessary Increase
in the expenditure of man-hours -
It vould have been possible in this study to Include multiple regression equations based on more than three variables, but an Increase in the number of variables results Immediately- in increasingly complex computations. Furthermore,airly large number of observations ororediction equationarge nurabor of variables may notrue picture. The equation may accurately fit the data from which it was derived but when applied to other similar data may not give satisfactory results.
VI. Sources of Current weather Data.
Current weather information on the USSR ia being received from several goutccb. The Department of Military Climatology, Air Weather Service, USAF, Andrews Field, ia cooporuting clooely in supplying detailed Information, and, under proposed new arrangements, precipitation totalsday intervals will be available during the crop season as well as mean maximum temperatures for theintervale. During the remainder of the year,omounto will he supplied as monthly totals. During tho winter months, any available Bnow cover conditions will be reported, as well aa minimum temperatures In areas with little snowhat ia, areas In which danger from winter killhe greatest.
Translated excerpts from the Soviet newspapermlcdcllyo) are obtained from the American Embassy in Moscow. These excerpts contain, among other Items, daily weather information (temperatureeneralof areas and intensities ofrop stage reports (stages of growth for various grains byccasional crop condition reports (for example, "Condition of spring grains in Upper Volga is good, with an above-average yieldnd oblaet procurement roporte ststing whether the oblaot has fulfilled its grain delivery plan. The weather data and crop stage reports are tabulatedaily basis by regions for most efficient use. Frequontly, sufficient information concerning the stage of development
articular grainfor example, the heading otagc of oprlng wheatla obtained, so that It is possible to chart the northern movement of the stage. Such information is extremely valuable when used in conjunction with current weather Information.
FDD also furnishes current weather and crop Informationfrom the Soviet newspaper SovKhoznoya Gaaeta and other provincial newspapers. This Information is included in thedescribed above. Finally, the weekly FBIS Abstracts contain weather survey sections giving general temperature enddata tabulatedaily basis by regionsuseful asand supplementary information.
-'SECREF
VII. Additional Proposed Investigations.
further investigations of the relationships between weather factor* end ylelda in the area covered by this study and In other areas of the USSR are cootemplated. In particular, the effect of vapor pressure deficit on crop yields will be examined. Vapor pressure deficitunction of the amount of moleture In the air and the temperature of the air and ia technicallyas the difference between the actual vapor pressure of the atmosphere and the vapor pressureaturated stnosphere at tho onmo temperature. As functions of temperature the vapor pressure deficit values are likely to show less variabilityegion than dees the average of the precipitation figuresalted number of stations. Also, as functions of humidity, the vapor pressure deficitneasure of the rate of tran-apiration and evaporation from plaoto. Significant correlation coefflcienta may be obtained, particularly Inregion of marginal precipitation.
Further and more intensive etudles on the major grain* are planned, particularly tho winter grains. In addition, other crops, euch uo potatoes, augur beets, end cotton, will be Investigated.
At the presentist of meteorological stations in the USSRecord of monthly precipitation valueseriod of ot leastears is being compiled. All known sources. Including many original Ruosian language publications, aro being used In un
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effort to obtain the maximum length of record for each station. The use of such long-term records makes possible considerably core accurate statements as toarticular crop aresiven year has monthly precipitation omounto which ore greater or less then the normal.
int of stationsatisfactory length of rocord has been compiled, the monthly precipitation values will be tabulated. The otations will be broadly grouped according to primaryregions, such as Lower Volga, Urals, Central Black Soil Zone, end then within each region they will be grouped according to oblasts.
omplete set of comparatively reliable mean values will be extremely helpful during the growing senoon us an indication of whether current precipitotiou amounts, as compared with the mean values, pointotentially above- or below-average crop yield.
All the items discussed in thie study have one ultimate goaltho attainment of Improved accuracy in tho estimation of Soviet crop yielde. One of tha first steps toward this goal ia the derivation of soma of the underlying relationships between crop yields end the numorous Interrelated weother factors. If oome apparently significant relationships are found and prediction equations are based thereon, several precautions Dust bo taken. First of all, no amount of mathematical manipulation can take Into account all the weather
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factors affecting the final yield. Hence any results obtained from the prediction equations must be carefully considered andif scene weather factors not included in the equation definitely appear to be important, in any particular Instance. Furthermore, adjustments must be made in the light of any known significant changes in nonmeteorologicel factors.
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SOURCES
Prozhay (Annual Publications of tho Central StatletlcalMlnictry of the Interior, St..
2. Letoplcl (Annual Publications of the Central Physical, St..
3- Vladimir P. Tiooobenko, Agricultural Russia and the Wheat Problem, Stanford University Food Research-
h. Kaum JaBny, The Socialised Agriculture of the USSR, Stanford University Food Research
5- Sncdecor, Statistical Methods, Iova State Collegep. 1U9.
Original document.
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