United States Department of Agriculture

Agricultural Marketing Service

Federal Grain Inspection Service

Unified Grain Moisture Algorithm

Recipe Book 

Prepared by 

David Funk and Zoltan Gillay 

February 22, 2012 

Revised Version April 12, 2023
1 

UNIFIED GRAIN MOISTURE ALGORITHM 

Recipe Book

Contents

Unified Grain Moisture Algorithm........................................................................................................... 2

Introduction........................................................................................................................................ 2

UGMA Steps ..................................................................................................................................... 2

Parameters, Coefficients, and Grain Groups....................................................................................... 6

Performance Statistics .......................................................................................................................... 13

Details of Secondary Density Correction Method ............................................................................. 14

Sensitivity Analyses ............................................................................................................................... 19
2 

Unified Grain Moisture Algorithm

Introduction

The purpose of this document is to present a concise description of FGIS’s Unified Grain 

Moisture Algorithm (UGMA) and associated equations for use by entities who are involved in

developing and seeking FGIS certification for UGMA-compatible grain moisture meters. More

detailed explanations of the method (for those without considerable familiarity with the UGMA) 

are available as links on the Moisture Equipment page of the AMS website (www.ams.usda.gov). 

UGMA Steps

1. Measure the dielectric constant (εmeas) of the grain at a defined frequency within the

range of 148.5 to 150.5 MHz where the selected frequency is controlled within + 0.05

MHz using a parallel-plate transmission line test cell of dimensions similar to those of

the FGIS master cell and a loading method that provides for operator-independent

measurements. This measurement requires the determination of complex impedance

or complex reflection coefficient for the transmission line test cell and conversion to

dielectric constant through an appropriate mathematical model for the specific test cell

design. (Note: Grain-group-specific dielectric offset (EOs) and dielectric slope (ESs)

factors may need to be applied (as εmeas ́ = εmeas·ESs + EOs) to compensate for slight

differences in loading methods among instrument models. The s subscripts refer to

grain-group-specific parameters that may be different for different instrument models.)

2. Measure the Mass of the grain within the defined volume of the test cell

(TestCellVolume).

3. Apply the Landau-Lifshitz, Looyenga-based density normalization to transform the

measured dielectric constant to density-corrected dielectric constant (εden) with a

common density basis (ρtarget = 0.67405 g/ml) for all grain types.

(1)

(Note: Grain-group-specific volume ratio factors (VRs) may need to be inserted as 

multipliers in the target mass calculation (target density times test cell volume) to 

compensate for slight differences in loading methods among instrument models.)

4. Apply grain-group-specific unifying parameters: Slope parameter (SPs), Translation

parameter (TPs), and Offset parameter (OPs) (Table 2) to the density-corrected

dielectric constant as in Eq. 2.

εadj = (εden − OPs) ∙ SPs + 2.5 +

TPs

6

(2)
3 

5. Calculate the initial moisture estimate (Moisture 1) from the adjusted dielectric

constant using the 5th order polynomial calibration (Eq. 3), where KCC is the vector of

polynomial coefficients.

 (3) 

6. Using Eq. 4, apply the translation parameter (TPs, moisture axis shift) to get the

predicted moisture (prior to temperature correction) (Moisture2).

MMMMMMMMMMMMMMMMMM = MMMMMMMMMMMMMMMMMM − TTTT (4) 

7. Apply the temperature correction function (Eq. 5). (Notes: The temperature correction

function (Eq. 7), a function of temperature and moisture, may use from one to three

coefficients depending on the nature of the correction required. The form of Eq. (5),

used here and below, is meant to state that the TempCorr is a function involving

parameters Temperature and Moisture2.)

MMMMMMMMMMMMMMMMMM = MM − TT TTTTTT (TT TTTT TT , MMMMMMMMMMMMMMMMMM) (5) 

8. Apply the secondary density correction to obtain the final predicted moisture result.

This correction, which was primarily intended to overcome the effect of kernel density

in corn, has also proven useful for adjusting the calibration line shape by moisture

range. Currently, this correction is applied to corn (density), long grain rough rice (line

shape), medium grain rough rice (line shape), oats (density) and soybeans (line

shape).

MMMMMMMMMMMMMMMMMMMMMM MM = MMMMMMMMMMMMMMMMMM − SS SSSS (MMMMMMMMMMMMMMMMMM, MM MMMM) (6) 

Measured Values: (Note: These are critical measured parameters for demonstrating 

conformance with the UGMA.)

− εden: density-corrected dielectric constant at approximately 149 MHz

− Sample temperature 

− Sample mass 

Unifying Parameters

Three grain-group-dependent parameters are necessary to use the same polynomial calibration 

(basic calibration curve shape) for all grain groups. Unifying parameters are derived using an 

optimization algorithm that FGIS will provide upon request as an Excel file.

− OPs: Offset parameter

− SPs: Slope parameter

− TPs: Translation parameter
4 

Calibration Coefficients

The calibration is the relationship between the adjusted dielectric constant and reference 

moisture content (back corrected for sample temperature and secondary density correction, and 

adjusted by the translation parameter). KCC is the vector containing the coefficients of the fifth 

order polynomial calibration equation. One “dummy point” was inserted in the calibration data 

(Figure 1) to control the shape of the extreme high moisture end of the polynomial curve. At 

some point in the future, the order of the polynomial curve may be increased to 7 to allow better 

fit for extremely dry samples; manufacturers should allow for this possibility in their software. 

Currently the secondary density correction is being employed in a special way to accomplish 

small line shape changes on certain grains, because changing the polynomial curve would 

require modification of all calibrations that are based on the existing curve.

Figure 1. Calibration curve

Temperature Correction

Temperature correction is applied to the predicted moisture to minimize the effect of sample

temperature—that is, to cause the final moisture estimate to closely match the estimate that 

would be given for that sample if measured at room temperature (22°C). FGIS has developed

temperature corrections over a wide temperature range (from -18°C to 45°C). The UGMA 

exhibits a significant advantage (relative to most other moisture meters) in its ability to accurately 

predict moisture content for grain (at normal market moisture levels) at temperatures well below 

0°C. The form of the correction can be moisture level dependent and may be linear or quadratic 

with temperature. Accurate temperature correction over wide temperature and moisture ranges 

usually requires the moisture-dependent/quadratic temperature correction, but less demanding 

applications may use the simpler corrections with fewer determined coefficients. (That is, the 

KCTQ and/or KTCS values may be zero.)

1 )(

)(2 )( 3

2

TKTCS TTC

Moisture TKTC TTC TKTCQ TTC Moisture

s

s s

−⋅+

−⋅−−⋅− = (7)

2 3 4 5 6 7 8 9 10 11

0

10

20

30

40

50

60

70

Normal Corn Samples

Dummy Point

Calibration Curve

Adjusted Density Corrected Dielectric Const.

Adjusted Moisture, %M
5 

The target temperature (TTC) was chosen as 22°C because that is the nominal laboratory

temperature for all the calibration sample tests at FGIS. Making the target temperature equal 

to the nominal laboratory temperature minimizes the interaction between the temperature 

coefficients and the unifying parameters and polynomial calibration coefficients. 

The listed temperature correction coefficient values (see Table 3) were estimated from FGIS 

tests done in 2007-2013 using a special insulated test cell (GP test cell) and precision impedance 

analyzers (HP-4291A and Agilent E4991A) and FGIS tests performed in 2013 with commercial 

UGMA moisture meters. FGIS conducted additional tests in 2017-2019 with commercial UGMA 

moisture meters.

Secondary (Bulk) Density Correction

The secondary (bulk) density correction is applied to the predicted moisture to reduce the error 

caused by extremes in corn density related to kernel density. This correction appears to be 

unnecessary for most grain types other than corn. The correction (Eq. 8) was developed by 

Zoltan Gillay in 2010 and was published at the ISEMA 2011 Conference in Kansas City in June 

2011. Additional details are shown below. Note that both the TargetDensity and the 

SlopeCorrection values are moisture-dependent and are found by linear interpolation from the 

TD Table (Table 5) and SC Table (Table 6), respectively. This method may also be applied as 

a line shape correction to the predicted moisture to improve moisture measurement accuracy at 

moisture extremes for some grain types. When used for line shape correction, the parameters 

in the secondary density correction equation are adjusted to modify the slope of the calibration 

curve in selected moisture ranges—without making a secondary density correction.

Note that the value of the Mass/TestCellVolume term in Equation 8 is approximately 0.5 and 

varies only a little around this value. The values of TargetDensity and SlopeCorrection at 

different predicted moisture levels are specified in lookup tables (TDTable and SCTable, 

respectively). By setting TargetDensity to a number much larger than 0.5 (such as 100) and the

SlopeCorrection value to a small number, the slope of the calibration curve can be adjusted as 

desired without interference from sample mass.

(8) 

Where: 

TTTT TT TT = LL LL (TT TTTTTT , MMMMMMMMMMMMMMMM ) (9)

SS SS = LL LL (SS , MMMMMMMMMMMMMMMMMM) (10)
6 

Parameters, Coefficients, and Grain Groups

The parameters may be refined annually as FGIS conducts tests on additional samples. 

The full numeric resolution shown in the tables is necessary to agree with FGIS results within 

0.01% M.

The first eleven grain groups (soybeans, sorghum, sunflower, corn, oats, hard wheat, soft wheat, 

durum, barley, long grain rough rice, and medium grain rough rice) are the “major” grains and 

are evaluated annually. The other grain groups are revised as more samples of “minor” grain 

types are tested. 

Table 1. Grain types within grain groups

 Major Groups Grain Type Names

1. Soybeans Soybeans

2. Sorghum Sorghum

3. Sunflower Sunflower Seed, Oil-type

Sunflower Seed, Confectionary (minor grain)

4. Corn Corn

5. Oats Oats

6. Hard Wheat Wheat, Hard White

Wheat, Hard Red Winter

Wheat, Hard Red Spring

7. Soft Wheat Wheat, Soft Red Winter

Wheat, Soft White

8. Durum Durum

Khorasan (minor grain)

9. Barley Barley, Six-Rowed

Barley, Two-Rowed

Hulless Barley (minor grain)

10. Rice, Long Rough Rice, Long Grain Rough

11. Rice, Medium Rough Rice, Medium Grain Rough

Minor Groups

12. Rice, Short Rough Rice, Short Grain Rough

13. Rice, Long & Medium

Milled

Rice, Long Grain Milled

Rice, Medium Grain Milled

14. Rice, Brown Rice, Long Grain Brown

Rice, Medium Grain Brown

Rice, Short Grain Brown
7 

Table 1. Continued

Minor Groups Grain Type Names

15. Rice, Short Milled Rice, Short Grain Milled 

Rice, Second Head Milled 

Rice, Screenings Milled

Rice, Brewers Milled

16. Rice, Parboiled Rice, Long Grain Brown Parboiled 

Rice, Second Head Milled Parboiled

Rice, Long Grain Milled Parboiled

Rice, Medium Grain Milled Parboiled

Rice, Brewers Milled Parboiled 

17. Beans 1 Beans, Blackeye

Beans, Pinto

Beans, Cranberry

Beans, Pink

Peas, Split

18. Beans 2 Beans, Baby Lima

Beans, Garbanzo (Chickpeas)

Beans, Small Red

Beans, Yelloweye

19. Beans 3 Beans, Black

Beans, Great Northern

Beans, Large Lima

20. Beans 4 Beans, Small White

Beans, Pea

21. Beans 5 Beans, Kidney

Lentils

22. Peas Peas, Mottled

Peas, Smooth Dry

Peas, Wrinkled Dried

23. Safflower Safflower

24. Canola Canola

Rapeseed

25. Mustard Mustard Seed, Yellow

Mustard Seed, Brown

26. Mustard, Oriental Mustard Seed, Oriental

27. Triticale & Rye Triticale

Rye

28. Flaxseed Flaxseed

29. Popcorn Popcorn

30. Buckwheat Buckwheat

Buckwheat Groats

31. Hulless Oats Hulless Oats
8 

Table 2. Unifying parameters for each grain group with target temperature TTC = 22°C. 

FGIS-approved calibrations.

Grain Group Name OP SP TP

Soybeans* 2.21777 0.83990 0.25808

Sorghum* 2.49888 1.15784 0.52871

Sunflower* 2.89560 0.60030 3.31453

Corn* 2.58119 1.01116 0.04656

Oats* 2.50520 1.20700 1.71883

Wheat, Hard* 2.45262 1.17814 0.74465

Wheat, Soft* 2.4003 1.10205 0.47202

Durum* 2.47479 1.14080 0.97078

Barley* 2.40171 1.15489 0.86412

Rice, Long Rough* 2.56801 1.12434 -1.00000

Rice, Medium Rough* 2.60926 1.20464 -0.30137

Rice, Short Rough 2.53800 1.24900 0.00000

Rice, Long & Medium Milled 2.51059 1.04112 6.17909

Rice, Brown 2.61542 1.21730 2.24150

Rice, Short Milled 2.56639 1.12468 0.00000

Rice, Parboiled 2.72023 1.28083 3.53399

Beans 1 2.04415 0.82087 -2.14253

Beans 2 2.14871 0.90055 -1.22113

Beans 3 2.15008 0.95575 -1.12211

Beans 4 2.10321 0.95610 -1.20983

Beans 5 2.02755 0.77947 -2.34291

Peas 2.05219 0.99142 -2.30674

Safflower 2.79858 0.72184 2.44242

Canola 2.72737 0.88238 3.83532

Mustard 2.45021 0.82628 1.34283

Mustard, Oriental 1.08520 0.43347 -5.76496

Triticale & Rye 2.29327 1.04512 -1.00000

Flaxseed 2.49214 0.55567 0.00000

Popcorn 2.71612 1.22804 1.92617

Buckwheat 2.32026 1.06465 0.00000

Hulless Oats 2.47479 1.14080 0.97078

*Also NTEP-certified
9 

Table 3. Temperature correction factors for Eq. 7. Moisture limit is the upper limit for sample 

temperatures below 0°C. FGIS-approved calibrations.

Grain Group Name KTC KTCS KTCQ

Lower Temp. 

Limit (°C/°F)

Upper Moist. 

Limit (%M)

Soybeans* 0.00973 0.00694 -0.00022 -18/0 20

Sorghum* 0.10770 0.00000 -0.000656 -18/0 16

Sunflower* 0.00706 0.00508 -0.000624 -18/0 13

Corn* 0.15920 -0.00282 -0.0007688 -18/0 19

Oats* 0.09910 0.00000 -0.000348 -18/0 13

Wheat, Hard* 0.09590 0.00153 -0.000581 -18/0 19

Wheat, Soft* 0.09590 0.00153 -0.000581 -18/0 19

Durum* 0.09590 0.00153 -0.000581 -18/0 19

Barley* 0.12050 -0.00060 -0.0006995 -18/0 18

Rice, Long 

Rough*

0.22020 -0.00865 -0.001119 -18/0 18

Rice, Medium 

Rough*

0.22020 -0.00865 -0.001119 -18/0 18

Rice, Short Rough 0.22020 -0.00865 -0.001119 -18/0 18

Rice, Long & 

Medium Milled

0.06357 0.003096 -0.000372 -18/0 16

Rice, Brown 0.10380 0.00000 -0.000628 -18/0 16

Rice, Short Milled 0.10380 0.00000 -0.000628 -18/0 16

Rice, Parboiled 0.12898 0.00000 -0.000366 -18/0 13

Beans 1 0.04440 0.00648 -0.000146 -18/0 15

Beans 2 0.05876 0.00494 0.000000 -18/0 15

Beans 3 0.04440 0.00648 -0.000146 -18/0 15

Beans 4 0.04440 0.00648 -0.000146 -18/0 15

Beans 5 0.006029 0.010148 0.000000 -18/0 15

Peas 0.07163 0.003416 -0.00045 -18/0 15

Safflower 0.05840 0.00000 -0.000240 -18/0 12

Canola 0.026848 0.004508 -0.0001893 -18/0 8

Mustard -0.040953 0.015318 0.000000 -18/0 9
10 

Table 3. Continued

Grain 

Group 

Name KTC KTCS KTCQ

Lower 

Temp. 

Limit 

(°C/°F)

Upper 

Moist. 

Limit 

(%M)

Mustard, 

Oriental

-0.040953 0.015318 0.000000 -18/0 9

Triticale & 

Rye

0.072583 0.004229 -0.000691 -18/0 16

Flaxseed -0.01520 0.01090 0.000000 -18/0 10

Popcorn 0.15920 -0.00282 -0.0007688 -18/0 19

Buckwheat 0.109279 0.00000 -0.000528 -18/0 13

Hulless 

Oats

0.09590 0.00153 -0.000581 -18/0 19

* Also NTEP-certified

Table 4. FGIS-approved and NTEP-certified UGMA 5th order polynomial coefficients with 22°C 

target temperature. 

Exponent KCC

0 -112.71

1 111.3076

2 -40.37566

3 7.403341

4 -0.649454

5 0.02193348

Table 5a. TDTable for Corn. FGIS-approved and NTEP-certified secondary density correction 

target density lookup table (TDTable) to determine the Target Density value by linear 

interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Target Density

g/ml

0 0.7168

15 0.7168

17 0.7116

19 0.7018

27 0.6451

30 0.6297

33 0.6253

100 0.6253
11 

Table 5b. TDTable for Soybeans. FGIS-approved and NTEP-certified secondary line shape 

correction lookup table (TDTable) to determine the TargetDensity value by linear interpolation. 

Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Target Density

g/ml

0 100

5 100

7 100

10 100

100 100

Table 5c. TDTable for Long Grain Rough Rice. FGIS-approved and NTEP-certified secondary 

line shape correction lookup table (TDTable) to determine the TargetDensity value by linear 

interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Target Density

g/ml

0 100

8 100

15 0

21 0

30 100

100 100

Table 5d. TDTable for Medium Grain Rough Rice. FGIS-approved and NTEP-certified 

secondary line shape correction lookup table (TDTable) to determine the TargetDensity value 

by linear interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Target Density

g/ml

0 100

10 100

15 0

21 0

30 100

100 100
12 

Table 5e. TDTable for Oats. FGIS-approved and NTEP-certified secondary line shape 

correction lookup table (TDTable) to determine the TargetDensity value by linear interpolation. 

Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Target Density

g/ml

0 0.525

100 0.525

Table 6a. SCTable for Corn. FGIS-approved and NTEP-certified secondary density correction

Slope Correction lookup table (SC Table) to determine the Slope Correction value by linear 

interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Slope Correction

%M per g/ml

0 10.4

13 10.4

33 -17

100 -17

Table 6b. SCTable for Soybeans. FGIS-approved and NTEP-certified secondary line shape 

correction Slope Correction lookup table (SC Table) to determine the Slope Correction value 

by linear interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Slope Correction

%M per g/ml

0 -0.02

5 -0.02

7 -0.005

10 0

100 0
13 

Table 6c. SCTable for Long Grain Rough Rice. FGIS-approved and NTEP-certified secondary 

line shape correction Slope Correction lookup table (SC Table) to determine the Slope 

Correction value by linear interpolation. Moisture3 is the temperature-corrected predicted 

moisture from Eq. 7. 

Moisture3 Slope Correction

%M per g/ml

0 0.013

8 0.013

15 0

21 0

30 -0.035

100 -0.035

Table 6d. SCTable for Medium Grain Rough Rice. FGIS-approved and NTEP-certified 

secondary line shape correction Slope Correction lookup table (SC Table) to determine the 

Slope Correction value by linear interpolation. Moisture3 is the temperature-corrected 

predicted moisture from Eq. 7. 

Moisture3 Slope Correction

%M per g/ml

0 0.01

10 0.01

15 0

20 0

25 -0.016

100 -0.098

Table 6e. SCTable for Oats. FGIS-approved and NTEP-certified secondary line shape 

correction Slope Correction lookup table (SC Table) to determine the Slope Correction value 

by linear interpolation. Moisture3 is the temperature-corrected predicted moisture from Eq. 7. 

Moisture3 Slope Correction

%M per g/ml

0 -4.471

100 -4.471

Performance Statistics

FGIS collects calibration performance data on an annual basis for the 15 major crops. The minor 

grains have calibration performance data collected for three years on a rotating basis. However, 

the minor grains may be requested at additional times as needed to address any market 

concerns. Table 7 lists the minor grain groups in order of their data collection. The calibration 
14 

performance data is analyzed and reviewed every year to determine what, if any, changes are 

needed to maintain the alignment between the FGIS Master UGMA system to the USDA 

reference Air Oven moisture. FGIS posts the performance statistics for the spring/summer crops 

by May 1 each year and for all crops by August 1 each year on the Moisture Equipment page of 

the AMS website (www.ams.usda.gov). Refer to Table 8 for the list of grains for May 1 and 

August 1 implementation dates.

Table 7. Minor grain groups that FGIS requests samples for during a three-year period before 

moving to the next group. Three years after the start of Group Three, data collection will start 

over for Group One.

Group One Group Two Group Three

Beans 1 Beans 2 Beans 4

Beans 3 Hulless Barley Buckwheat

Beans 5 Hulless Oats Buckwheat Groats

Brown Rice Long Milled and Parboiled Rice Mustard Seeds

Canola and Rapeseed Medium Milled and Parboiled 

Rice

Processed Rice

Flaxseed Peas Rye

Short Grain Rough Rice Popcorn Safflower

Sunflower Seed 

(confectionary)

Short Grain Milled Rice

Triticale

Table 8. List of the spring/summer crops with performance statistics posted by May 1 and list of 

fall crops with performance statistics posted by August 1 every year. 

Spring/Summer Crops Fall Crops

Barley (all subclasses) Beans Peas

Hulless Barley Buckwheat and Buckwheat 

Groats

Rapeseed

Hulless Oats Canola Rice (rough, milled, and 

parboiled)

Oats Corn and Popcorn Rye

Rye Flaxseed Safflower 

Triticale Grain Sorghum Triticale

Wheat (all classes) Lentils Soybean

Mustard Seeds Sunflower (oil and 

confectionary)

Details of Secondary Density Correction Method

The secondary density correction dramatically reduces the error for corn caused by unusually

low (or high) density samples. Figure 2 illustrates key aspects of the correction. The plot shows 
15 

all the corn samples with the several low density samples (blue diamonds) segregated from the

“normal samples” (red +). A similar approach may be applied to other grains where the moisture 

error correlates to the density, such as with oats; it is anticipated that most grains will not need 

a density correction.

Figure 2. Target density curve (TDTable, Table 5) 

The separation or threshold function is by Eq. 11 and the dotted line in Figure 2. 

 (11)

ConversionParameter (0.01287 g/ml per lb/bu) transforms the values from lb/bu to g/ml.

Including the low density samples in the calibration caused significant errors both for the normal

and low density samples. For optimizing the calibration for the normal samples, the low density

samples were not included in the calibration. The samples for which the density corrections are

zero lie on the solid line in Figure 2—the moisture-dependent target density (TD) curve. The 

predicted moisture error (correction to be applied) is proportional to the vertical distance between 

the sample density (Mass/TestCellVolume) and the target density (TD) curve. Therefore, the 

correction function (repeated here) is defined as: 

 (8)

The results of the SecDensCorr function are in units of %M. The calculated density correction 

is applied by subtracting it from the temperature-corrected predicted moisture as in Eq. 6. The 

slope correction factor SC (%M per g/ml density difference from target density at that moisture 
16 

level) is moisture-dependent. See Figure 3. The slope correction SC crosses zero at about 21% 

moisture.

Figure 3. Slope correction values. Visualization of the SC Table (Table 6).

Table 9 and Figure 4 show that by using the secondary density correction, the errors in predicted 

moisture for low density corn samples were significantly reduced. Furthermore, the standard 

deviation of the predicted moisture errors for “normal” samples was improved.

Table 9. Secondary density correction statistics; before (left) and after (right) correction. 

0 10 20 30 40 50 − 30

− 20

− 10

0

10

20

Measured Values

Slope Correction Values

SCTable Points

Reference Moisture, %M

Slope Correction

Samples.

Mean 

Diff. STD Slope

All -0.03 0.51 0.00

Low Dens. -0.60 0.46 0.05

Normal 0.05 0.46 -0.01

Samples

Mean 

Diff. STD Slope

Overall -0.01 0.41 0.00

Low Dens. -0.09 0.33 0.00

Normal 0.00 0.42 0.00
17 

Figure 4. Corn sample predicted moisture errors before and after secondary density correction

for 2008-2010 corn. 

Details of Secondary Line Shape Correction Method

The secondary line shape correction dramatically reduces the error for soybeans, long grain 

rough rice, and medium grain rough rice caused by unusually dry samples and/or wet samples 

for the grain group. This correction addresses subtle differences in a grain group’s line shape 

that may not be completely accounted for with the unifying parameters and without changing the 

UGMA from a fifth order polynomial to a seventh order polynomial. It should be noted that 

changing to a seventh order polynomial would require the unifying parameters for all grain 

groups be changed. Figure 5 illustrates key aspects of the correction. The long grain rough rice 

plot shows the samples below 15% moisture have a different slope compared to the samples 

above 15%. It also shows that the samples above approximately 20% moisture have a different 

slope compared to the samples below 20%.
18 

Figure 5. Long grain rough rice sample predicted moisture errors before secondary line 

shape correction for 2009 – 2013 crop.

Figure 6 illustrates the improvement in the moisture prediction error by applying the line shape 

corrections listed in Tables 5c and 6c. THR1 is the upper moisture limit for the slope correction 

applied to samples with a moisture below 15% (blue +) and THR2 is the lower moisture limit for 

the slope correction applied to samples with a moisture above 21% (green +).
19 

Figure 6. Long grain rough rice sample predicted moisture errors after applying the secondary

line shape correction for 2009 – 2013 crop.

Sensitivity Analyses

One of the major goals in developing the Unified Grain Moisture Algorithm was to define a 

measurement technology with sufficient detail that multiple manufacturers could design and 

produce instruments that could use the same calibrations and produce moisture measurements 

that are mutually consistent as well as accurate. Developers should not underestimate the 

extreme care required to design and manufacture instruments that can achieve UGMACompatible certification by FGIS. The purpose of this Sensitivity Analyses section is to share 

FGIS research results regarding the effects of several design parameters on moisture 

measurement results—and to thereby assist engineers in selecting innovative design strategies 

that can consistently achieve the necessary performance. 

1. Measurement frequency sensitivity. Our analysis evaluated two cases of frequency

sensitivity: 1) the deliberate choice of a known frequency other than 149.00 MHz, and 2)

imprecision or instability in the measurement frequency of specific moisture meters. The

exact choice of measurement frequency is not terribly critical; a manufacturer may have

reasons to choose a specific frequency to avoid interfering with or being influenced by

known problematic signal sources or sensors in the environment. The change in dielectric
20 

constant values versus frequency is relatively small, so the same unifying parameters and 

calibration curve may be used over a limited frequency range. An evaluation with data 

for over 6000 samples of multiple grain types showed an average -0.02% moisture error 

per MHz for measurement frequency changes around 149 MHz. This sensitivity value 

assumed that the test cell model parameters (but not unifying parameters or calibration 

coefficients) were optimized for each test frequency. The second case assumes that the 

measurement frequency varied from the intended value, and that the test cell model 

parameters were not re-optimized for the specific measurement frequency. In this case, 

the frequency sensitivity was about ten times larger (+0.2% moisture per MHz of 

uncompensated measurement frequency error). For further information see: Analysis of 

Frequency Sensitivity of the Unified Grain Moisture Algorithm, ASAE Meeting Paper 

#053047, Zoltan Gillay and David Funk, 2005.

2. Temperature measurement sensitivity. Moisture measurement errors associated with

temperature are due to temperature measurement errors and temperature correction

function inadequacies. Typical temperature coefficients are about 0.1% moisture per

degree Celsius difference from the reference temperature (22 °C). If the sample

temperature sensor has significant thermal mass or other characteristics that cause

measurement error to degrade at temperature extremes, significant moisture errors may

result. Temperature measurement accuracy at room temperature must be especially

good to avoid contributing significantly to moisture measurement errors during routine infield performance verification (check testing). The temperature correction function must

be sufficiently robust to provide good corrections over the full intended temperature (and

moisture) range. Systematic temperature measurement errors for an instrument model

(which could be corrected through the selected temperature correction function) cannot

be tolerated in official moisture meters, which must use the same set of official moisture

calibrations.

3. Ranges of interest for dielectric constant, density-corrected dielectric constant,

and related factors. The following plots illustrate the ranges of parameters and

sensitivities that are relevant for Official grain moisture measurements.
21 

Figure 7. Complex reflection coefficients measured with UGMA Master System for grain 

samples in 2008, 2009, and 2010 Calibration Studies.

Figure 8. Complex impedance values measured with UGMA Master System for grain 

samples in 2008, 2009, and 2010 Calibration Studies.
22 

Figure 9. Loss tangent versus dielectric constant values for grains tested in 2008, 2009, 

and 2010 Calibration Studies.

Figure 10. Density-corrected dielectric constant (εden) versus moisture values for grains 

tested in 2008, 2009, and 2010 Calibration Studies.

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

0.25

Other Grains

Sunflower

Corn

Dielectric Constant

Loss Tangent

0 10 20 30 40 50

1

2

3

4

5

6

7

8

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Density Corrected Dielectric Constant
23 

Figure 11. Measured (εmeas) dielectric constant values (prior to density correction) for 

grains tested in 2008, 2009, and 2010 Calibration Studies.

Figure 12. Measured (εmeas) dielectric constant values (without density correction) versus 

sample mass for grains tested in 2008, 2009, and 2010 Calibration Studies.

0 10 20 30 40 50

1

2

3

4

5

6

7

8

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Measured Dielectric Constant

100 200 300 400

2

4

6

8

Other Grains

Sunflower

Corn

No Density Correction

Mass, g

Dielectric Const. no dens Corr

Target Weight
24 

Figure 13. Moisture prediction errors resulting from 1% (of value) errors in densitycorrected dielectric constant for grains tested in 2008, 2009, and 2010 Calibration 

Studies. Simulation equation: εden = εden ·1.01

Figure 14. Moisture prediction errors resulting from 1% (of value) errors in measured 

dielectric constant (prior to density correction) for grains tested in 2008, 2009, and 2010 

Calibration Studies. Simulation equation: εmeas = εmeas ·1.01

0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

0.6

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

0.5

0.6

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
25 

Figure 15. Moisture prediction errors resulting from a change 0f +0.1 in measured 

dielectric constant (prior to density correction) for grains tested in 2008, 2009, and 2010 

Calibration Studies. Simulation equation: εmeas = εmeas + 0.10

Figure 16. Moisture prediction error resulting from a simulated -0.3 gram mass 

measurement error for grains tested in 2008, 2009, and 2010 Calibration Studies. (A 

negative mass measurement error results in a positive moisture prediction error and vice 

versa.)

0 10 20 30 40 50

0

1

2

3

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50

0

0.02

0.04

0.06

0.08

0.1

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
26 

Figure 17. Moisture prediction error caused by a simulated +0.001 error (not relative) in 

the magnitude of the measured reflection coefficient (at the test cell connector) for grains 

tested in 2008, 2009, and 2010 Calibration Studies with the FGIS Master UGMA system. 

(Note: This sensitivity is dependent on instrument design.) Simulation equation: 

Г = (|Г| + 0.001) ∙ eeii∙aaaaaa (Г)

Figure 18. Moisture prediction error caused by a simulated +0.1% relative change in the 

magnitude of the measured reflection coefficient (at the test cell connector) for grains 

tested in 2008, 2009, and 2010 Calibration Studies with the FGIS Master UGMA system. 

(Note: This sensitivity is dependent on instrument design.) Simulation Equation:

Г = |Г| ∙ 1.001 ∙ eeii∙aaaaaa (Г)

0 10 20 30 40 50

0

0.05

0.1

0.15

0.2

0.25

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50

0

0.02

0.04

0.06

0.08

0.1

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
27 

Figure 19. Moisture prediction error caused by a simulated -1 degree error in the phase 

of the measured reflection coefficient (at the test cell connector) for grains tested in 2008, 

2009, and 2010 Calibration Studies with the FGIS Master UGMA system. (Note: This 

sensitivity is dependent on instrument design.) Simulation Equation:

Г = |Г| ∙ eeii∙(arg(Г)−1°)

Figure 20. Moisture prediction error caused by a simulated -1% (relative) error in the 

magnitude of the measured test cell complex impedance (at the test cell connector) for 

grains tested in 2008, 2009, and 2010 Calibration Studies with the FGIS Master UGMA 

system. (Note: This sensitivity is dependent on instrument design.) Simulation equation: 

ZZ = |ZZ| ∙ 0.99 ∙ eeii∙aaaaaa (ZZ)

0 10 20 30 40 50 − 0.1

0

0.1

0.2

0.3

0.4

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50

0

0.2

0.4

0.6

0.8

1

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
28 

Figure 21. Moisture prediction error caused by a simulated -0.1 ohm error in the 

magnitude of the measured test cell complex impedance (at the test cell connector) for 

grains tested in 2008, 2009, and 2010 Calibration Studies with the FGIS Master UGMA 

system. (Note: This sensitivity is dependent on instrument design.) Simulation equation: 

ZZ = (|ZZ| − 0.1) ∙ eeii∙aaaaaa (ZZ)

Figure 22. Moisture prediction error caused by a simulated -1 degree error in the 

measured phase of the test cell impedance (at the test cell connector) for grains tested in 

2008, 2009, and 2010 Calibration Studies with the FGIS Master UGMA system. (Note: 

This sensitivity is dependent on instrument design.) Simulation equation: 

ZZ = |ZZ| ∙ eeii∙(aaaaaa(ZZ)−1°)

0 10 20 30 40 50

0

0.1

0.2

0.3

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50 − 1

− 0.5

0

0.5

1

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
29

Figure 23. Moisture prediction error caused by a simulated 0.1 ohm resistance inserted

in the connection between the source-end connector and the center test cell center 

electrode for grains tested in 2008, 2009, and 2010 Calibration Studies with the FGIS 

Master UGMA system. (Note: This sensitivity is dependent on instrument design.)

Figure 24. Moisture prediction error caused by a simulated 0.1ohm resistance inserted

in the connection between the connector to the 50-ohm load and the center test cell center 

electrode for grains tested in 2008, 2009, and 2010 Calibration Studies with the FGIS 

Master UGMA system. The polarity of the change is opposite to that shown in Fig. 23. 

(Note: This sensitivity is dependent on instrument design.)

0 10 20 30 40 50

0

0.1

0.2

0.3

0.4

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)

0 10 20 30 40 50 − 0.4

− 0.3

− 0.2

− 0.1

0

Other Grains

Wheat

Sunflower

Air Oven Moisture (%M)

Moisture Prediction Error (%M)
30

Figure 25. Relationships between test cell plate spacing, characteristic impedance, and 

filling factor. The relationships are highly linear. These results are from finite element 

analysis using the dimensions of the FGIS “New Master” (NM) test cell. Note that the 

“Spacing Predicting Zc—air section” analysis is based on a finite element model that 

includes the presence of the metallic base plate in the NM test cell, whereas the “Spacing 

Predicting Zc” analysis excludes the effects of the base plate. For the latter case, the 

effects of the base plate and the test cell gate are separately included in the test cell 

model as a constant offset term in the dielectric measurement. In actual instruments, the 

effects of conductors near the test cell may be significantly more complex and problematic 

because of the potential for resonances at or near the measurement frequency.
31

Figure 26. Estimated effects on density-corrected dielectric constant of overfilling and 

under-filling of the test cell (as a function of filling height in mm). These results are based 

on finite element analysis of the “New Master” test cell.

Figure 27. The slope of the density-corrected dielectric constant change with filling height 

(dielectric constant units per mm) based on finite element analysis of the New Master test 

cell. These are the slopes about the center point of Figure 25 (at the top of the plates). 
32 

Over-filling causes the measured dielectric constant to be lower; thus, the sign of the 

slope is negative.

Figure 28. Plot of the slopes of density-corrected dielectric constant per gram of cell 

over-filling (or under-filling) for different nominal full-sample masses. These results, like 

those of Figs. 24-26, are based on finite element analysis of the New Master test cell and 

assume “rectangular” sample cross-sections. These are the slopes about the “full” point 

corresponding to the center point of Figure 25. Over-filling causes the measured 

dielectric constant to be lower; thus, the sign of the slope is negative.

For further information, please refer to the USDA-AMS website (www.ams.usda.gov/) or 

by mail or phone to the address below.

United States Department of Agriculture

Agricultural Marketing Service

National Grain Center

10383 N. Ambassador Drive

Kansas City, Missouri 64153

(816) 891-0401

www.ams.usda.gov