Forecast and Estimates of Crop Yields from Plant Measurements

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Forecast and Estimates of Crop Yields from Plant Measurements Powered By Docstoc



EARL E. HOUSEMAN aM HAROLO F. HUDDLESTON S,at/."cal U•• ,'" S,at •• O.port •• ,.,



R.portl •• S.rvlce, g A,r/cu/'",., '1o.ItI •• •••, O. C• "

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by Earl E. Houseman and Har,old F. Huddleston Statistical Reporting Service, United States Department of Agriculture Washington, D. C. There are two well-known sources of information for forecasting or estimating crop yields: (1) Farmer's reports on crop conditions or in sample plots within

amounts harvested and (2) counts and measurements a sample of fields.

This paper presents a discussion of progress and

recent. experience in the development of procedures and models for forecasting or estimating crop yields from plant counts and measurements. 'l11e principal crops on which work lias been done by the, Statistical Reporting Service i~clude cotton, corn, soybeans, wheat, tobacco, oranges, lemons, peaches, pears, sour cherries, walnuts, pecans, filberts, and almonds. In making plant measurements, there are three different periods of

plant growth that need to be considered because each poses distinctly different problems. The first is the period of growth up to the time has been set or the time when, if any additional

when all of the fruitY

fruit is set, the probability of it contributing to the yield is zero for practical purposes. The next period extends from the date all fruit is The third is a short period


set to maturity or close to the harvest date.

just prior to harvest when the problem is principally one of estimating the yield of the crop. Corresponding to the three time periods, the


In this paper "fruit" is used in a botanical ~ense and includes buds,

blooms and other developing parts that have potential for contributing to the fruitage, that is, the product for harvest.








_.- ..•.----'--:---~~


tenns "early estimates"

season forecasts,"


season forecasts,"

and "preharvest

will be used.



Each June a general purpoae agricultural bility area sampling, ia conducted.

survey, based on proba-

This survey provides information on livestock numbers, and other items. are identified Hence, this A subsample to acreage, For a

acreages planted to various crops, As farms are visited, all fields


in the area sampling units

and the kind of crop and the acreage in each are aacertained. survey provides a sampling frame for the work on crop yields. of the fields is then selected with probability proportional


giving a sample of fields

in which piant measurements are taken.

some tree crops ,special tree sample of fields. sample trees periodically when mature.

censuses provide the frame for selecting two plot8 or two

However, within each sample field

are selected

at random, marked, and identified,

then revisited of the plots


during the growing season, including harvesting

For the 1965 crop season, the Statistical to have in operation field a program of preharvest 1.

Reporting Service expects sampling on four leading

cropa as summarized in table

This program has been developing

over a period of years.

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For tree erops, interest


sampling, is not being done as the major to harvest. little With reference advantage over The amount of may vary

is in forecasts estimates

several weeks prior

to timing,

from preharvest

sampling offer

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based on growers' reports unpicked as a result

on aDlOun~s arvested. h of selective

some crops left considerably



from year to year.


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Table 1.- Plans for preharvest

SaIIIpling in 1965

:Number Crop



: sample :f1elda

ApproxilDate Approximate size : Stand d of po~tion • ar error lIize of : Acres : ercent of;of estimated plot in lin millionIlIU.S. totallyield per acre acres-


Winter wheat Corn Soybeans Cotton

2,800 8,80P 1,900 2,600

.0001 .0028 .0004 .0015
in each field.

81.4 S4.5 27.2 18.9

91 9S 9S 97

.25 bu. .70 bu. .80 bu. 7.50 lb.

*Twoplots are selected Prebarvest Estimates

As already indicated,

the problem of prebarvest


is A minimum

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one of sampling and estilll8tion,

not forecasting.

of about three years should be allowed to develop and, implement an operating tions. program of yield estimates for a crop

preharvest prebarvest

observasurvey intensive of work

In fact,

if the goal ill to have a successful basis during the third year,

on an operational effort

a well-planned, in this line


by experienced matbematical stati~ticians


is needed. Typically, number of fields establishing the first year's effort would be limited to a very small for and to


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to obtain preliminary

measures of variability

size of plots

and other aspects of sample design, for a pilot


develop operating Alternative tried.


survey tbe next year. on


of measuring the yield


would be

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This would include consideration objectively, or equipment. and ascertaining Potential

of various means of locating the advantages of alternat!ve or bias would be for developing


sample plots instruments identified

sources of error


and means of control harvesting

considered. losses, -3-

In addition,

means of estimating

sample plots

should be gleaned






Thua the goal of the first for trial



is to develop,

a8 fully

as possible

the following year,

sound, detailed

operating s~1ficlltions

including training

plans and a well-dedgned

plan for measuring the quality 'l11esecond year's extensive pilot effort

of the work done. could be regarded as an intend ve and or one-


using a sample that might be one-fifth for a fully operational program.

fourth the size anticipated second year's

From the

experience muchbetter


should become available of the

on variance components and time requirements job so the sample design can be optimized.

for various parts

Quality checks on the field procedures which

work should provide a basis for improvement of field must be rigorous and tightly contro1.1.ed. that preharvest yield

Experience has indicated for harvesting estimates either? losses)



are likely

to be. on a different

level than if it is

• ;

derived from reports Since potential provision

from farmers.

Which is correct,


biases may be inherent be made for ascertaining techniques.

in the procedures, the validity The probability

important that preharvest

of the of selec-

sampling and estimating

tion of each plot is very small so an IU1USUal amount of attention be given to avoidance of non-randOlllerrors. completely objective

Field workers may not be sample plots. Or, if

in the process of locating characteristics

plots. are subsampled for certain for bias in the techniques

there may be opportunity have occurred

of subsampling.

Also, instances



where the definition

of the fruit definition

to be harvested has been replaced by or interpretation, which resulted in

a wor1ter'sown personal fruit being harvested

from plots having biased sfze or weight charac-

tElZ'istics. -4-

(1. -----------------,.......,...--~....------,


There are various ways of getting a valid independent check, depending upon the crop. Take corn as an example. Farmers generally do

not have weight measurements

of the amount harvested and often have only To obtain a good independent

approximate measures on a volume basis. ch~ck" special arrangements

might be made with selected farmers for such as weight

getting the total weight and other relevant measurements,

or size per fruit, for the entire crop harvested from particular fields. Sample plots in these fields should be selected and harvested using identical field procedures. The number of plots would need to be large biaf

enough to give estimates having low s8lllplingerror so any appreciable can be detected. Adjustments

for such factors as differences in moisture

percentage at the time of the preharvest sampling and the time of harvest may be necessary. Also, when comparing yield estimates and actual yield


from the entire harvested field one should be on the alert for incon'sistencies in concepts of acreage. One of the problems is making surl!

that the boundaries of the land from which sample plots are selected coincide with what a farmer regards as the acreage in a field. For purposes of sampling, it is often useful to treat yield as the product of factors such as yield per plant and number of plants per acre,


or in the case of cotton, for example, as the product of weight per boll, the number of bolls per plant, and the number of plants per acre. Some factors are simple and inexpensive to measure, while others may be time consuming or 4ifficult to measure accurately.

A good example is

the counting of cotton plants in contrast to picking cotton or counting the fruit on a cotton plant. An optimum sampling plan considering time

and variance components may call for counting of all plants in a two-row plot 20 feet long, whereas observations such as detailed fruit counts

might be limited to only a few plants in a plot. -5-


Matters of sampling design could be discussed at length; the importance of a balanced effort procedures regarding all giving rigorous, tightly however, controlled

important sources of error that inherent

is being stressed. or close


Experience has indicated controlled supervision, field effectively quality

biases can be eliminated of the field concise, staff,



by intensive


checks, and providing clear, observation affecting



but astute of factors

is essential

for the identifica-

tion and control

the quality

of results.

Someadvantages of preharvest preharvest fanners' appraisal preharvest until sampling are available

sampling. earlier

Estimates derived from from postharvest only his based on or delayed

than estimates


,Prior to harvest,

a farmer can report

of the crop prospects.

On the other hand, estimates losses

sampling must be based on average harvesting

such time as harvesting harvest.

loss can be determined from gleaning

sample plots after In addition of the estimates

to the time advantage~just mentioned and the objectivity owing to the techniques involved, preharvest sampling cannot

provides a means for getting otherwise be easily from fields, obtained.

much valuable information that Via laboratory analysis

of samples taken can be 10ss8s

information on various attributes Crop quality, to varieties,

of crop quality

made available. ~ can be related

components of yield, cultural practices,

and harvesting

weather, and other factors yield and quality. damage,

to get a good picture r,

of the variables


Also, if deemedworthwhile,

information on some types of insect

, ~

such as the number of ears of corn damagedby corn ear worms, can be readily obtained.




II -------------~---------- ...••.-----...••..--..,...-...•..-..---'




LIte Season Forecasts Forecasting the yield of a crop at periodic intervals during a yield at

growing season is obviously much more difficult time of harvest.

than estimating

It is necessary to discover plant characteristics


may be used to predict based upon observable of the fruiting characteristics contrast

components of yield •. Forecas;t fonJUlas must be plant characteristics and a comprehensive knowledge plant

behavior of the crop.

the formulas must translate forecasts. In

observed on any date into accurate

to the development of a program for preharvest forecasting

sampling, any procedures is of having of models.

time schedule for developing and perfecting muchmore tenuous. A major reason for this




is the necessity

"between years experience" In fact, crop after

for the formulation an~ testing


one may continue to use more than one model for a particular a forecasting program becomes operational a longer time test. "late season" begins when all the In fruit in order to give


the most promising alternatives For purposes of this has been set. number of fruit




Thus, the problem can be confined to estimating present and predicting

the droppage and the sizing. the survival of fruit

other words, the problem is that in terms of number of fruit (ears

of predicting

of corn, cotton~lls,

oranges, etc.)

per acre and the average weight or size of fruit Predictioo survival of number of fruit.

at time of harvest. of

It is known that the probability which suggests a simple

is related

to IIIllturity of the fruit,

model as follows:




-----------~--------------~------_ .._-------_._-'


where N



number of fruit category

per plot in the ith maturity



probability that a fruit in the ith maturity category will survive and contribute to the fruitage estimated number of fruit that will be on the plants per plot at the time of harvest Pi' is a function of time, that is, the probability of-



The probability, survival

for a small cotton boll on the 15th of August, for example, is for a small boll on the 15th of September. at least for some crops,

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not the same as the probability incidentally,



our general experience suggests,



that an index of the crop's time reference littie later.

stage of development may provide a better Hor~,will be said on that point a

than calendar date.

The problem of defining maturity c1~sses differs various crops. A trained Cotton, for example, has clearly

widely amongthe

demarcated stages. On the other hand,

observer can accurately

c1ap[lify the fruit.

the demarcation of maturity categories Consequently, a major, skilled training,

for ears of com is more tenuous. is required to establish standards,


and supervisory amongfield

procedures for achieving uniformity of classi-



observers and between years. of survival,

To,obtain adequate information on the probabilities observations need to be taken at frequent intervals

during the fruiting

period for several years. of fruit

This can be done by noting the disappearance provided the If rates

that has been "tagged" by maturity categori~. the probability substantially the rates varietal -8-

method of tagging does not affect of survival are found to differ

of survival.

frCIIIyear to year, a

search for means of adjusting of environmental observations,

frCIIIyear to year on the basis changes, or other relevant factors


·.-.- ......•

may be called for. Take corton as an example. good information by maturity survival, that is, After several years of experience, became available on rates of to to which


the fraction

of the fruit

that would contribute of survival in relation

the fruitage.

In. Fig. 1, the average rate

the stage of development of the crop is shown for squares (buds), is one of the fruit maturity categories used in the forecasting the lower the


The more advanced a crop is at time of observation



tha1: a "square" will contribute

to the yield.

The stage of of large for model

crop development is measured by an index which is the ratio bolls to all bolls in the sample plots. categories, From similar


other kinds of fruit are obtained • •50

values for Pi in the forecasting


• > ..•






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.25.SO Maturity lndex Fig. 1 Survival of Corton Squares (Buds)


For SOlIecrops the c.o\U1tingof fruit by maturity categories may not , be neces8U)'. The orange crop is a good example. The forecast of the number of fruit at harvest is silllply the product of the present fruit


,----------y --~~--------_._--------~ ---




-...•...... _.-, .•..~,_.• ...

count and the probability

of survival

which ia • function

of time.


corn a8 another example, after no disappearance of ears.

com ears have ailked,

there is practically

Hence the forecasted

number of ears at harvest

is the same as the present count. into maturity categories

However, the ears My be classified ear size at harvest. the number of of a crop

for purposes of forecasting

Average weight or size of fruit. fruit at time of harvest, intensive

As in forecasting

study of growth patterns

is needed to develop reliable size of fruit

means of predicting

the average weight or for between

at time of harvest.

Study of the growth of citrus, increase in size of fruit


example, has revealed that the relative September 1 and harvest pattern


is nearly constant from year to year.

'nte growth


follows a logarithmic

curve which provides a good basis for not just calendar date, is taken at


provided stage of maturity, Projected estimates

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into account.

of fruit

size and number of fruit

time ~f harvest are converted to number of boxes, using information obtained from packinghouses to establish ,size and number of fruit as number of boxes. With'regard to com, two models are presently ear kernel weight at harvest. kernels per ear (adjusted One is a relationship being used to forecast of harvest weight of per box. the relationship forecasts between fruit are expressed

'ntus the yield




to IS percent moisture) to dry weight and total In this Case, the ratio of dry kernel continuous

f \. \

,,!eight at time of observation. weight to total

kernel weight observed provides a built-in,

type crop maturity index for forecasting observed dry matter in the kernels.

harvest weight per ear from separate

The other model entails

I t:



by ear maturity categories

from the length of the ears at

tille of observation. -10-



ErrOr of forecast.

For the forecasting

of crop yields

from plant the same

l118asurements,the Statistical

Reporting Service uses essentially sampling, table 1.

sample plots 'that are used for preharvest I118Dts taken may differ seasOD. However, tables success with forecasting. considerably

The meaSure-

from one date to another during the sUlllllllr)' f the degree of o used in this whereas

2 and 3 give a partial

Regarding terms of reference of cotton is a late

paper, the September forecast the August cotton forecast early season forecasts.

season forecast,

and the Mayand June forecasts

of wheat are

Table 2.- Forecast.and 'Sampling Errors for ~ttou!l

-------------FSY~--F-~-" Large bolls (Ho. per plot)


i963 1964

5.6 6.1

3.0 3.5

415 428 5.05 4.88 570 588

6.2 6.6 .037 .042 9.8 10.3

Boll weight (grams per boll) Gross yield (lbs. lint per acre)

1963· .025 .024 1964 .032 .029 1963 . 7.8 1964 9.2 4.8 5.9


1/ Data are frOll a sample of 1,200fields of 5 States. 2/ Forecast error, see text. Salllpling standard error of the mean.
Table 3.!tIS

representing -

a region comprised

Forecast and Sampling Errors ~Year~ May

for Wheat!! Preharvest Hean S-#/


Humberof heads per plot Weight per head Gross yield (bushels per acre)

5.2 2.2 .008 .007 .661 .442 9 States.

1962 1963 1962 1963 1962 1963

4.9 4.0 .008 .008 .655 .582

334 314 .466 .522 27.9 28.4

4.9 2.9 .004 .004 .42 .30

1/ Data from a sample of 900 fields



representing Forecast error, see text •. Salllpling standard error of the mean. -11-


'n1e errors of forecast shown in these tables are root mean square errors computed as follows:



Yi Yi n FE

the actual yield, or component of yield, for the two plots in the ith sample field at harvest, = the corresponding forecast of yield or a component,

= the nwnber of sample fields, and = error of forecast

The errors of rorecast do not include variability associated with selection of fields and of plots within fields. They reflect only between fields Data for

within years variability of the forecast component or error.

additional years are needed berore between years' error of forecast can be adequately measured.


Early Season Forecasts Research work on early season forecasting from plant measurements has been less extensive than for late seasOD. For tree crops the dura-

tion of "late season" is quite long and "early season" forecasts have not been attempted. Cotton, wheat, com, and soybeans have received the 1IIOst


attention in the development of early season forecast models. Growth patterns a1llOngdifferent plant species are so varied that/ pot III1chcan be said about a general approach for finding a forecasting model. 1be nature of the problem obviously changes rap.1d.lywith the An important aid in developi1tgrealistic early

, ,





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stage of development.

season forecasting models is the availability or securtng of data weekly on fruiting and plant characteristics forecast date up to harvest. starting in advance of the firs~


However, the use of such detailed data fr~
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isolated are:


poses problems in statistical


amongwhich translation of

(1) The construction

of the models, (2) a logical

the model into observable characteristics intervals, (3) development' of constants

in surveys at less or tentative


parameters for model: date. and in

which will app~ to data observed for a specific (4) relationships unexpected ways. or have many fruit




or non-probability

samples may differ long period

For crops which fruit per plant, a "fruiting

over a relatively

model" may be developed based where some fields will have


on classifying fruit


or classifying show no fruit

fields present.

and other fields For a crop such as cotton, blooa. many fields and bolls, (or even plant~ within fields) ~hi1e other fields observable. has been set, one approach is to add a term not set to the model will have "squares,"

in a nearby area may have only squa.res or

even no fruit

Where part of the fruit for additional fruit

expected at harvest

from fruit

discussed on page 8 of the previous section. August I forecast of cotton. the relationship

For example, for the between "the number of index can be bolls at

cotton bolls at harvest used-the

from fruit

not set" and a maturity of large bolls relationship, at harvest

maturity index being the ratio To establish

to all fruit

the time of observation.


set at not

time of observation IIR1st e "tagged" so bolls b set can be counted. forecasts Incidentally.

from fruit

another type of model for early cotton model has been developed. 'n1is

called "the rate

of fruiting"

model is more complex and will not be diseussed here. Foz:whea~ the Kay forecast stalk counts using a relationship of number of heads i8' predicted' frOlll e~tablished from historical data.

Weight of grain per head is related

to plant density.

Hence head weight






is adjusted for plant density rather years. It appears that an historical satisfactory practices basis for a forecast

than using the average for several

average weight per fruit

may be a

when there is control of cultural so tb.e density

such as irrigation

and the thinning of tree fruits An historical

varies little

from year to year. if the forecast

average weight may also say several States;

be satisfactory

is for a large area,

so the average environment for the whole area fs abUut the same frOll year to year even though the environment for any given small local! ty may vary considerably from year to year •


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Progress and experience in the development of models and procedures for forecasting are discussed in this and estimating paper. crop yields frOli plant measurements

Three time periods are of importance:

(l) A short period prior and estimation rather

to harvest when the probleDI is one of sampling (2) the period after all fruit survival and

than forecasting,

has been set when the forecasting of fruit

problem is that

of predicting

already set and of predicting

weight per fruit fruit

at harvest, has been set.

(3) the growth period prior to the date when all

General experience frOll work on several crops is presented rather a detailed report for one or two crops.






Dans ce rapport Ie progr~s et l'experience dans Ie developpement des modes et procedes tes Bont discutes. me consiste pour prevoir et estimer les sont l noter:

rendements de la cueillette par action de mesurage des planTrois phases importantes et (1) Une courte periode avant la cueillette quend Ie probl~d'echantillonner d'estimer Ie fruit plutot que de Ie prevoir; (2) La periode apr~s que Ie fruit a ete

plante e.l.d. lorsque Ie probl~me eonsiste encore de predi-



re Ie survivance du fruit dej~ plante ainsi que son poids au tempts de la cueillette; genera Ie acquise lettes. (3) La periode de croissance est presentee avant la date que tout Ie fruit a ete plante. L'experienee de plusieurs cueillettes ic1 plutot qu'un rapport detaille d'une ou de deux cue1l-


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