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Contract No. DE-AC36-08GO28308

Using Whole-House Field Tests 

to Empirically Derive Moisture 

Buffering Model Inputs

J. Woods, J. Winkler, and D. Christensen

National Renewable Energy Laboratory

E. Hancock

Mountain Energy Partnership

Technical Report

NREL/TP-5500-62456

August 2014
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

Using Whole-House Field 

Tests to Empirically Derive 

Moisture Buffering Model 

Inputs

J. Woods, J. Winkler, and D. Christensen

National Renewable Energy Laboratory

E. Hancock

Mountain Energy Partnership

Prepared under Task No. BE12.2046

Technical Report

NREL/TP-5500-62456

August 2014
NOTICE

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Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

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iii

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Acknowledgments

This work was supported by the U.S. Department of Energy under Contract No. DE-AC36-08-

GO28308 with the National Renewable Energy Laboratory. The authors would like to thank 

Greg Barker (Mountain Energy Partnership) for his help with data acquisition, Jeff Tomerlin (the 

National Renewable Energy Laboratory) for his help in building the laboratory-scale chamber, as 

well as David Hoak and Eric Martin (Florida Solar Energy Center) for their help with the test 

setup at the Florida test home.
iv

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Nomenclature

A surface area (m2)

C molar concentration (kmol kmol-1)

dEMPD effective moisture penetration depth (m)

hm mass transfer coefficient (kg m-2s

-1

)

k mass transfer coefficient (m s-1)

M molar mass (kg kmol-1)

Mv cumulative transfer of vapor/moisture (kg)

m mass flow rate (kg s-1

)

mv  mass flow rate of vapor/moisture (kg s-1

)

mr rate of increase of humidity at beginning of tests (%RH s-1

)

N number of moles (kmol)

n molar flow rate (kmol s-1

)

P pressure (Pa)

psat saturation vapor pressure (Pa) 

T temperature (°C)

t time (s)

V volume (m3

)

w material moisture content (kg m-3

)

δ vapor permeability (kg m-1 Pa-1

s

-1

)

μ vapor resistance factor; ratio of vapor permeability in a material to that in air

Π lumped parameter for empirical model

φ relative humidity

ω humidity ratio (kg kg-1)
v

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Subscripts

amb condition/property of the ambient air

deep deep layer of the EMPD model

gain moisture added from internal gains or with humidifier

gen generated/injected

HVAC moisture removed with either air conditioner or dehumidifier

inf infiltration

matl material

scale mass measured by scale

surf surface layer of the EMPD model

zone condition/property of the house zone air

Abbreviations

CO2 carbon dioxide

EC effective capacitance

EMPD effective moisture penetration depth

FSEC Florida Solar Energy Center

HVAC heating, ventilation, and air conditioning 

RH relative humidity
vi

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Executive Summary

Building energy simulations can be used to predict a building’s interior conditions, along with 

the energy use associated with keeping these conditions comfortable. These models simulate the 

loads on the building (e.g., internal gains, envelope heat transfer), determine the operation of the 

space conditioning equipment, and then calculate the building’s temperature and relative 

humidity (RH) throughout the year. The indoor temperature and RH are affected not only by the 

loads and the space conditioning equipment, but also by the capacitance of the building 

materials, which buffer changes in temperature and humidity.

The thermal capacitance is typically included in these models, because it can strongly affect energy 

use. The moisture capacitance has a smaller effect on energy use, and the modeling of moisture 

capacitance is either simple (and inaccurate) or nonexistent in most building energy simulation 

programs. But this moisture capacitance has become increasingly important for modeling 

residential buildings because higher efficiency building codes have led to reduced sensible loads 

without a corresponding decrease in the moisture (latent) load. Researchers and builders are 

actively studying humidity control in homes, either through energy recovery ventilators, standalone dehumidifiers, or packaged air-conditioning systems with enhanced dehumidification.

This research developed an empirical method to extract whole-house model inputs for use with a 

more accurate moisture capacitance model (the effective moisture penetration depth, or EMPD,

model). The experimental approach was to subject the materials in the house to a square-wave RH

profile, measure all the moisture transfer terms (e.g., infiltration, air conditioner condensate), and 

calculate the only unmeasured term: the moisture sorption into the materials. After validating the 

method with laboratory measurements, we performed the tests in a slab-on-grade house with 

concrete block walls at the Florida Solar Energy Center in Cocoa, Florida. We used a least-squares fit 

of an analytical solution to the measured moisture sorption curves to determine the three independent 

model parameters representing the moisture buffering potential of this house and its furnishings.

After deriving these parameters, we measured the RH of the same house during tests with 

realistic latent and sensible loads, and then compared that to the RH predicted by the EMPD 

model using these inputs. This showed good agreement (Figure ES-1(a)), especially compared to 

the commonly used effective capacitance approach (Figure ES-1(b)). Even if we adjust the single 

parameter used in the effective capacitance model to try and match the data, we can only 

improve the R2 from 0.40 (for a commonly used effective capacitance of 10) to 0.52 (effective 

capacitance ~5). Both are considerably worse than the EMPD model (R2 = 0.81).

These results show that the EMPD model, once the inputs are known, is an accurate moisture 

buffering model. A sensitivity analysis showed that the model is fairly insensitive to changes in 

the model inputs up to 20%.

This experimental method can be used in houses of other constructions (e.g., wood frame), and 

with other levels of furnishings, to develop a more comprehensive dataset. This can provide 

guidance on moisture buffering model inputs for use in building simulations, such that the indoor 

RH can be predicted with greater accuracy. This can help answer questions about the effects of 

insulation levels, cooling equipment selection, and ventilation practices on the indoor RH, and 

help anticipate potential problems.
vii 

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(a) 

(b) 

Figure ES-1: Comparison of measured relative humidity to modeled relative humidity. (a) EMPD 

model with inputs derived using new method used in this paper, (b) effective capacitance model 

with commonly-used value effective capacitance value of 10. 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 48 96 144 192 240 288 336 384 432 480 528 576

Relative humidity

Time [hr]

Measured RH

Modeled RH R2 = 0.81

EMPD

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 48 96 144 192 240 288 336 384 432 480 528 576

Relative humidity

Time [hr]

Measured RH

Modeled RH R2 = 0.40

Effective capacitance
viii

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Table of Contents

1 Introduction........................................................................................................................................... 1

2 The EMPD Model................................................................................................................................... 2

3 Methods................................................................................................................................................. 4

3.1 Experimental Approach................................................................................................................. 4

3.1.1 Experimental Setup............................................................................................................. 7

3.1.2 Experimental Validation ................................................................................................... 10

3.1.3 Incremental Whole-House Buffering Experiments........................................................... 19

3.2 Determining Empirical Model Inputs.......................................................................................... 21

3.3 Realistic Load Test Case ............................................................................................................. 23

4 Results and Discussion..................................................................................................................... 24

4.1 Incremental Whole-House Buffering Tests................................................................................. 24

4.2 Uncertainty Analysis................................................................................................................... 26

4.3 Empirical Parameter Derivation.................................................................................................. 29

4.4 Using the Calibrated Model ........................................................................................................ 31

5 Conclusions ........................................................................................................................................ 34

References................................................................................................................................................. 36

Appendix.................................................................................................................................................... 38
ix

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List of Figures

Figure 1. EMPD model schematic ................................................................................................................ 3

Figure 2. Experimental approach.................................................................................................................. 5

Figure 3. Test profiles for (a) RH (input) and (b) illustrative cumulative moisture sorption (output).......... 6

Figure 4. Test house at Florida Solar Energy Center for whole-house tests................................................. 7

Figure 5. Equipment setup for measuring moisture removal and addition.. ............................................... 10

Figure 6. Process used to validate field test method ................................................................................... 10

Figure 7. Chamber for laboratory-scale testing: (a) exterior, (b) interior ................................................... 12

Figure 8. Cumulative moisture transfer during an empty-chamber test in the laboratory .......................... 14

Figure 9. Cumulative moisture transferred into gypsum board in laboratory chamber .............................. 15

Figure 10. Field test of empty house with slab covered.............................................................................. 16

Figure 11. Field test of 2300 ft2 of gypsum board with slab covered ......................................................... 16

Figure 12. Cumulative moisture transfer for four cycles of whole-house tests with gypsum board........... 17

Figure 13. Comparison of tests on gypsum board in (a) laboratory chamber, (b) whole house ................. 18

Figure 14. Field test with carpet and pad installed over the slab ................................................................ 19

Figure 15. Field test with furniture and carpet............................................................................................ 20

Figure 16. Field test with interior walls, furniture, and carpet.................................................................... 21

Figure 17. Cumulative moisture sorption for 24-hour cycle tests............................................................... 25

Figure 18. Cumulative moisture sorption for 2-week cycle tests................................................................ 26

Figure 19. Percent uncertainty in the calculated material moisture sorption.............................................. 27

Figure 20. Contribution of measurement uncertainty to the overall uncertainty in the material sorption. 

Case (1): slight difference between zone and ambient humidity ratio................................... 28

Figure 21. Contribution of measurement uncertainty to the overall uncertainty in the material sorption. 

Case (2): large difference between zone and ambient humidity ratio.................................... 28

Figure 22. Empirical fit for 24-hour data for all materials in whole-house test.......................................... 30

Figure 23. Empirical fit for 2-week data for all materials in whole-house test........................................... 30

Figure 24. Measured temperature and humidity ratio for the building zone and ambient air during the 

realistic-load test case ............................................................................................................ 31

Figure 25. Model-predicted RH for the EMPD model ............................................................................... 32

Figure 26. Model-predicted RH for the EC model ..................................................................................... 32

Figure 27. Model-predicted RH for the EMPD model without a deep layer.............................................. 33

Unless indicated otherwise, all photos and graphics were created by the authors.

List of Tables

Table 1. List of Measurement Method/Instrumentation for Whole-House Field Tests................................ 8

Table 2: List of Equipment for Whole-House Field Tests............................................................................ 8

Table 3. List of Measurement Method/Instrumentation for Laboratory Chamber Tests............................ 13

Table 4. List of Equipment for Laboratory Chamber Test.......................................................................... 13

Table 5. Empirically Derived Parameters (Π Groupings)........................................................................... 29

Table 6: Example of Empirically Derived Material Properties .................................................................. 29

Table 7. Coefficient of Determination (R2

) for the Model Based on the Realistic-Load Test Case ........... 33

Table 8. Sensitivity of Results to a 10-Standard-Deviation Change in Each Input Parameter................... 34
1

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1 Introduction

Building energy simulation models use the principles of heat and mass transfer to provide 

essential information to building researchers, designers, and engineers. These models can predict 

the temperature and humidity inside a building and the energy use associated with keeping these 

conditions comfortable, given an appropriate set of parameters and inputs. They can also be used 

to study the effects of design options on energy use and interior conditions.

To calculate a building’s interior conditions, the building energy models must estimate the latent 

and sensible loads on the building (e.g., infiltration, internal gains, envelope heat transfer) and 

the performance of any space conditioning equipment. The model also needs to consider the 

capacitance of the materials in the building, which buffer the response of the interior conditions 

to these loads. For example, a sensible load will change the air temperature in an empty house 

with lightweight walls more quickly than in a furnished house with heavy walls, such as 

masonry, because much of the thermal energy is stored in the furnishings and the heavy walls, 

rather than in the air. This can have a considerable effect on energy use, as the diurnal variation 

in temperature can be buffered by this thermal capacitance, and is included in many building 

energy models.

Similar to the thermal capacitance’s effect on temperature, the moisture capacitance of a 

building’s materials is important for predicting the interior relative humidity (RH). The materials 

absorb1

or release moisture depending on the RH of the surrounding air. This buffers changes to 

the air humidity. These calculations of moisture storage and transport are often simplified or 

ignored in building energy models. Although the simplified models adequately predict energy 

use in many cases [1], they do not adequately predict the interior RH. Predicting RH has become 

important as improvements to the building envelope and lighting have reduced the sensible load,

while the latent load from internal gains and required ventilation has remained relatively constant

[2, 3]. This can result in increased RH, and may require dehumidification equipment. Accurately 

predicting the interior RH is essential to understanding these potential problems and to properly 

evaluating and selecting potential solutions.

The simplest method for including moisture capacitance in modeling is to increase the 

capacitance of the air in the building to account for the added capacitance of the materials. This 

effective capacitance (EC) model assumes that the volume of the air in the building is 10–15 

times larger than the actual volume. This model is unrealistic and cannot be calibrated to give an 

accurate RH response [1].

A complex method for studying moisture capacitance and moisture flows in building modeling is 

the finite difference method, which spatially discretizes the differential equations within the 

material [4, 5]. This approach is accurate, but requires long simulation times.

Another approach is the effective moisture penetration depth (EMPD) model [6-8]. The EMPD 

model assumes that the moisture transfer takes place between the zone air and a thin fictitious 

 1 Moisture adsorption onto a material’s surface (including its internal pore structure) and absorption into the bulk 

material are collectively known as sorption. Both adsorption and absorption occur in building materials (adsorption 

at lower humidity, absorption at higher humidity). In this report, we use the following terms to collectively refer to 

either adsorption or absorption: sorption, absorption, and absorb.
2

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layer of uniform moisture content. The basis for this model is that the zone RH is cyclical. If it is 

perfectly cyclical (e.g., a sine wave), the model gives nearly the exact solution. If it is not 

perfectly cyclical, it can still be a good approximation [9]. The EMPD model offers a more 

realistic approach than the EC model and a simpler approach than the finite-difference method.

The EMPD model still requires more complicated inputs than the EC model, which simply uses a 

multiplier on the zone air capacitance. The EMPD model requires the moisture properties 

(permeability, moisture sorption curve, etc.) and the surface areas for each material in the house.

It is possible, though, to measure a material’s bulk EMPD properties, as demonstrated by several 

researchers [10-12]. In 2011, Vereecken et al. [13] demonstrated an experimental method for 

measuring a single set of EMPD model inputs for multiple materials at once.

In this research, we modified that experimental method so it could be extended to measuring the 

moisture buffering model inputs for a whole house. We first verified the accuracy of the method 

with laboratory-scale experiments on materials with known moisture properties. We then 

measured the moisture buffering of a whole house, and derived the necessary model inputs for 

building energy simulations. We validated the model with additional experiments on the same

house with simulated occupants.

In this report, we describe the experimental setup and present results for these experiments. 

Before this, we give a brief primer on moisture modeling with the EMPD model.

2 The EMPD Model

The primary equation for modeling moisture in buildings comes from a moisture balance on the 

zone air:

inf gain HVAC matl v v v v

zone

air zone m m m m

dt

d V =  +  −  −  ω

ρ (1)

where ρair is the air density, Vzone the zone volume, and ωzone the zone humidity ratio. Each term 

on the right-hand side is a moisture exchange [kg/s] with the zone air: 

inf mv  moisture entering the zone due to infiltration

gain mv  moisture entering the zone due to internal moisture generation

v HVAC m moisture exiting the zone as condensate at an air conditioner or dehumidifier

matl mv  moisture exiting the zone due to moisture sorption by the materials in the zone

The focus of this research is on the last term: moisture exchange with the building’s materials.

The EMPD model is one way to calculate this term, if the moisture properties of the materials are 

known. The EMPD model can be visualized with Figure 1. The material-air coupling takes place 

through a resistance between the zone air and a surface layer, which is a fictitious layer with an 
3

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assumed uniform moisture content. This surface layer is also connected to a deep layer through a 

second resistance. The surface layer responds relatively quickly to changes in RH, and therefore 

dampens higher frequency changes in the zone RH (e.g., daily fluctuations from daytime air 

conditioner use). The deep layer typically has a higher capacitance for moisture storage, but 

responds more slowly. It dampens lower frequency changes in the zone RH (e.g., changes in the 

weather).

Figure 1. EMPD model schematic

The moisture exchange between the zone air and the surface layer is calculated with:

m h A( (t) (t)) v matl = m ωzone −ωsurf  (2)

where hm is the mass transfer coefficient, A the surface area of the material, and ωsurf the 

humidity ratio of the surface layer. Note that this humidity ratio is not a realistic quantity. 

Instead, this value can be thought of as the humidity ratio of air in equilibrium with the moisture 

content of the surface layer (wsurf [kg/m3]). These are related through the material’s moisture 

sorption curve. If we assume the curve is linear with RH, which is a reasonable assumption for 

the RH range typically seen in buildings (20%–80%), these two quantities are related with:

( ) sat surf

surf

surf p .

P

d

dw

w

ω

ω

φ + = 0 622 (3)

where dw/dφ is the slope of the moisture sorption curve, P the absolute pressure, and psat the 

saturated vapor pressure. In the EMPD model, the moisture content of the surface and deep 

layers needs to be calculated at each time step. This is done with a moisture balance on each 

layer:

( ) k A(w (t) w (t)) dt

dw t

Ad surf zone surf

surf

EMPD = − (4)

( ) k A(w (t) w (t)) dt

dw t

Ad deep surf deep

deep

EMPD−deep = − (5)

zone-air node

infiltration

internal gains

HVAC

1/ksurf 1/kdeep

deep

layer

surface

layer

moisture sorbent material
4

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where ksurf, wsurf, and dEMPD are the mass transfer coefficient, moisture content, and effective 

moisture penetration depth for the surface layer, and kdeep, wdeep, and dEMPD-deep the corresponding 

values for the deep layer. Note that these mass transfer coefficients, which are based on a 

material moisture content driving force, differ from that used in Eq. (2), which is based on a 

humidity ratio driving force. In this case, we’ve used Eq. (3) to link the zone humidity ratio 

(ωzone) with the material moisture content in equilibrium with the zone humidity ratio (wzone). The 

mass transfer coefficients are defined as [9]:

φ μ

δ

φ

δ

EMPD

air sat

EMPD

matl sat

surf dw d d

p

dw d d

p k 2 2 = = (6)

air sat

EMPD deep

matl sat surf

EMPD deep

surf

deep

p

dw d d

p k

dw d d

k

k

δ

φ μ

δ

φ

2

1

1

2

1

1

− − +

=

+

= (7)

where δmatl and δair are the vapor permeability of the material and the air, respectively, and μ is 

the ratio between these permeabilities, termed the vapor resistance factor:

matl

air

δ

δ

μ = (8)

These equations represent the EMPD model. By discretizing the time derivatives, the equations 

can be solved to determine the moisture exchange between the zone air and the materials. The 

moisture properties in these equations must also be known. This is the focus of the remainder of 

this report: determining the moisture property inputs for the EMPD model based on whole-house 

field tests.

3 Methods

The methods for this research can be split into three areas: (1) the experiments used to measure 

the moisture exchange between the air and materials of a house due to a prescribed RH profile;

(2) the analysis that takes these data and empirically derives the input parameters for the EMPD 

moisture buffering model; and (3) tests on the house with realistic sensible and latent load 

profiles, which is used to validate the empirically derived parameters and the EMPD model.

3.1 Experimental Approach

For our experimental approach, we calculate the moisture sorption into (and desorption from) the 

building’s materials by rearranging Eq. (1):

matl v inf v gain v HVAC

zone

v air zone m m m

dt

d

m = − V +  +  −  ωρ (9)

where mv,matl  is the moisture transfer rate into the materials. We can integrate this equation from 

time t = 0 to time t to get the cumulative moisture transfer into the materials:
5

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Mv,matl = −Mv,air + Mv,inf + Mv,gain − Mv,HVAC (10)

Where

( ) ∫ =

t

v,matl v M m t dt

0

matl  (11)

( ( ) (0)) v,air air zone zone zone M = ρ V ω t −ω (12)

( )( ( ) ( )) ∫ = −

t

v,inf air,inf amb zone M m t t t dt

0

 ω ω (13)

( ) ∫ =

t

v,gain v M m t dt

0

gain  (14)

( ) ∫ =

t

v,HVAC v M m t dt

0

HVAC  (15)

If we measure all the right-hand-side terms in Eq. (10), we can calculate how much moisture is 

being absorbed into the materials. Figure 2 illustrates the experimental setup, and indicates the 

positive direction of each term in Eqs. (9) and (10). The details of these measurements are 

discussed in Section 3.1.1.

Figure 2. Experimental approach, showing each term in Eq. (9). Arrows indicate the positive 

direction for each term. Measurement techniques are explained in Section 3.1.1.

The tests used a square-wave RH profile (Figure 3a), which gives a strong forcing function. This 

is not a perfect square wave because of the finite addition and removal of moisture by the 

humidifier and dehumidifier, with the transient period on the order of 1 hour. An example curve 

(humidifier) (dehumidifier & AC)

tank

scale

building 

materials

(Tzone , ωzone) (Tamb , ωamb)

inf mv 

matl mv 

v HVAC m gain mv 
6

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for the cumulative moisture sorption (Mv,matl) is shown in Figure 3b, with the materials 

absorbing moisture during high RH periods (ṁv|matl > 0), and desorbing moisture during low 

RH periods (ṁv|matl < 0). 

These tests were performed in both a tightly controlled laboratory setting (Section 3.1.2), and in 

a well-characterized test house (Section 3.1.3). The former was used to validate the experimental 

setup, and the latter was used to obtain data to derive the EMPD model inputs for a whole house. 

The square wave in Figure 3 has a cycle period of 24 hours, which was used to measure the 

response of the materials to high-frequency changes in RH. We also tested with a cycle period of 

2 weeks (tests were performed serially, not concurrently) to determine the response to lowfrequency changes. In the EMPD model, these two responses are handled with the surface layer 

and the deep layer, as discussed in Section 2.

(a)

(b)

Figure 3. Test profiles for (a) RH (input) and (b) illustrative cumulative moisture sorption (output)

This test method differs from the method of Vereecken et al. [13] in a few key ways:

They measured the moisture added with the humidifier (Mv,gain) and the moisture in the zone 

air (Mv,air). They did not remove moisture from the space (Mv,HVAC) and did not measure 

infiltration moisture (Mv,inf). Instead, the RH of the space decayed because of infiltration during 

times when the humidifier was off, and they inferred the infiltration rate based on this decay rate. 

This assumes the infiltration rate and ambient humidity are relatively constant. In the method 

used here, we removed moisture with a dehumidifier during the low RH periods, and used an air 

conditioner for cooling, to maintain a constant temperature. We also measured the infiltration 

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12 14 16 18 20 22 24

Zone relative humidity

Time (hr)

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20 22 24

Cumulative moisture 

absorbed, 

Mv,matl (kg)

Time (hr)
7

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rate directly. This enabled the use of this method in the field, even for a house in a hot-humid 

climate. It also gave a cleaner signal, because the infiltration moisture transfer, which can vary

with time, was measured continuously via tracer gas rather than derived from the data.

Because we actively dehumidified during the low RH periods, we obtained a RH profile close to 

square waves. This allows a simpler data reduction method, with its clean step function changes 

compared to the slowly decaying RH profile used in Vereecken et al. [13].

The final key difference is that we measured the response to both short (24-hour) and long (2-

week) cycles, and derived a surface layer thickness (from the 24-hour tests) and a deep layer 

thickness (from the 2-week long tests). As we show in Section 4.4, this deep layer significantly 

improves the accuracy of the model.

3.1.1 Experimental Setup

The house used for the experiments is in Cocoa, Florida, at the Florida Solar Energy Center

(Figure 4). It is one of two houses that comprise the Flexible Residential Test Facility [14], built 

in 2010. These houses are single story, slab-on-grade construction with painted, uninsulated 

concrete block walls, and R-19 attic insulation. The inside of the exterior walls has furring strips 

and painted drywall. The 1536-ft2 floor area is one large room, with (initially) no interior walls 

or furnishings. Air infiltration can be adjusted using configurable leakage points and was less 

than 2.5 ACH50 for this study.

Figure 4. Test house at Florida Solar Energy Center for whole-house tests

For the moisture buffering tests, we made some modifications to ensure accurate moisture 

measurements. The windows were covered and sealed with rigid foam insulation to prevent 

condensation on the single-pane windows during the cool winter months, and to minimize any 

impacts from solar heating. The house air conditioner (located in the garage) was turned off, with 

the supply and return registers sealed. A separate air conditioner, along with the minimal 
8

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ductwork for distribution, was installed inside the conditioned space. This eliminated any 

possible leakage between the attic ducts and the unconditioned attic, which would have resulted 

in unmeasured moisture transfer.

As described in the previous section, the RH forcing function consisted of square waves of two 

different frequencies. A humidifier and dehumidifier increased and decreased the RH to meet 

these square wave profiles, while electric heaters and an air conditioner maintained a constant 

zone temperature. The key measurements (terms in Eq. (10)) and the measuring instruments used 

in the whole-house tests are listed in Table 1; the equipment used to control temperature and RH

is listed in Table 2. A brief description of the key measurements used in the whole-house test 

follows.

Table 1. List of Measurement Method/Instrumentation for Whole-House Field Tests

Measurement Measurement method/instrumentation

Zone humidity (Mv,air) Vaisala HMP-110 Temperature and RH sensor (±0.2 °C; ±1.7% RH)

Infiltration (Mv,inf) Continuous CO2 tracer gas (Dakota mass flow meter (±0.075 L/min) 

and GE Ventostat CO2 concentration transmitters (±3%)

Moisture addition (Mv,gain) Sartorius Signum 35-kg scale (±0.001 kg)

Moisture removal (Mv,HVAC) Sartorius Signum 35-kg scale (±0.001 kg)

Material sorption (Mv,matl) None (calculated from above measurements)

Table 2: List of Equipment for Whole-House Field Tests

Humidifier Humidifirst MP-15

Dehumidifier Ultra-Aire XT155H

Air conditioner

Nordyne 3-ton heat pump

(condenser: FT4BD; air handler: 

GB5BM)

Heater(s) (4) 1500-W electric ceramic heaters

Zone air (Mv,air): To measure the humidity of the zone air, we divided the zone into four 

quadrants and placed temperature and RH sensors in the center of each quadrant, 4 ft above the 

floor. The zone air was assumed to be well-mixed, with four ceiling fans and two small floor 

fans continuously operating. The zone air was calculated as the average of the four temperature 

and RH sensor measurements; however, the spatial distribution of humidity throughout the house 

was small. 

Infiltration (Mv,inf): Moisture infiltration was calculated as the difference between the indoor and 

outdoor humidity ratio, multiplied by the infiltration mass flow rate. The mass flow rate was 

measured with a continuous CO2 tracer gas, which was already in use by Florida Solar Energy 

Center researchers for previous, unrelated experiments. CO2 was continuously metered into the 

space at approximately 0.4 L/min. This flow rate was measured with a mass-flow meter, while

the zone and ambient CO2 concentration was measured with two CO2 concentration sensors. 

Because sensor drift is often a problem with CO2 sensors, they were checked and recalibrated 

every few months during the experiment.
9

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The concentration measurements and the known release rate were used to calculate the 

infiltration flow rate from a CO2 balance on the house:

( ) gen inf zone amb

zone

zone n n C C

dt

dC N = − − (16)

where Nzone is the total number of moles of air in the zone, ngen is the injection rate of CO2 into 

the zone, ninf is the air infiltration rate (kmolair/s), and Czone and Camb are the CO2 concentrations 

(kmolCO2/kmolair) for the zone and ambient air, respectively. 

Solving this equation for the infiltration rate gives:

zone amb

zone

gen zone

inf C C

dt

dC

n N

n −

−

= (17)

This infiltration was converted to a mass flow by multiplying by the molar mass of air (Mair =

28.97 kg/kmol):

air,inf inf m n = Mair  (18)

Gains and removals (Mv,gain and Mv,HVAC): Moisture was added to or removed from the space to 

match the prescribed RH profile (Figure 3a). We measured these additions and removals by 

weighing a tank of water, which supplied the humidifier with water and collected condensate 

from the air conditioner and dehumidifier (Figure 5). The humidifier was placed on the scale 

because of its non-negligible storage capacity. This leads to a simple equation for the moisture 

gains and removals:

M (t) M (t) M ( ) M (t) v,gain − v,HVAC = scale − scale 0 (19)

where time t = 0 is the time at the start of a RH cycle.
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Figure 5. Equipment setup for measuring moisture removal (condensate) and moisture addition 

through the humidifier. The humidifier is on the scale because it included a small tank that was 

filled periodically.

The key advantage of this method is that it measures the cumulative moisture removal and 

addition, instead of measuring the rate. This reduced the uncertainty for this measurement, which 

was negligible over all time periods of interest. If, instead, we had used flowmeters (one for 

humidifier supply, one for condensate), the cumulative term (in Eq. (10)) would be the addition 

of many rate measurements, each with its own uncertainty.

During humidification, the mains-water solenoid valve opened when the mass of the 

tank/humidifier system dropped below 20 kg, which filled the tank to 30 kg. During 

dehumidification, the drain solenoid valve would open when the mass of the tank/humidifier 

system reached 35 kg, and would drain the tank to 25 kg. The humidifier and dehumidifier were 

turned off during these fill and drain events.

3.1.2 Experimental Validation

A series of preliminary tests were performed to validate the experimental setup. The idea was to 

link the experiments with an established measurement method. We first linked the new method 

to an established method with tests in a laboratory chamber (Figure 6). We then linked results 

using the new method in the field with tests using the new method in the laboratory chamber.

Figure 6. Process used to validate field test method

Tank

Scale

to drain

Humidifier

from 

mains filter deionizer

solenoid

valve

solenoid valve

Dehumidifier

Air 

conditioner

from condensate 

drains

pressure 

regulator

pump

Established 

method 

deployed in the 

laboratory

New method 

deployed in 

the laboratory

New method 

deployed in the

field
11

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Linking new method to established method: The initial validation experiments were conducted 

under a well-controlled environment in an airtight, insulated chamber (Figure 7) in the Advanced 

HVAC Systems Laboratory at the National Renewable Energy Laboratory. The chamber was 

constructed with 4-ft × 8-ft sheets of aluminum-faced polyisocyanurate foam board on all six 

sides. A door was cut in the side for access to the experiment and to change materials, while two 

windows (cutouts replaced with polycarbonate sheets) allowed visual access during the tests. All 

edges and seams, including the door and windows, were sealed inside and out with aluminum 

tape.

The instruments and equipment used in the laboratory chamber test are shown in Tables 3 and 4. 

There was no dehumidification or cooling equipment in the laboratory chamber. Instead, the 

temperature of the chamber was kept slightly higher than the laboratory temperature so that no 

cooling was required. The tests were run as half cycles, without the dehumidification step, which 

would require cooling because the dehumidifier converts latent energy into sensible energy.
12

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(a)

(b)

Figure 7. Chamber for laboratory-scale testing: (a) exterior, (b) interior
13

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Table 3. List of Measurement Method/Instrumentation for Laboratory Chamber Tests

Measurement Measurement Method/Instrumentation

Zone humidity Type-T thermocouples (calibrated to ±0.2°C)

Edgetech dew point hygrometer (dew-point ±0.15°C)

Infiltration Calibrated out using tests with no materials

Moisture addition Sartorius Signum 35-kg scale (±0.001 kg)

Moisture removal No air conditioner or dehumidifier

Material sorption Adam Equipment CBK-16 Scale (±0.001 kg)

(and calculated from above measurements)

Table 4. List of Equipment for Laboratory Chamber Test

Humidifier Humidifirst MP-5

Heater(s) 1500-W electric ceramic heater

The airtightness of the chamber was inferred with several tests on an empty chamber with no 

moisture sorbent material. This would ideally give a horizontal line through the x-axis in Figure 

3(b); any deviation in the y-intercept from zero would likely be due to the moisture buffering 

capacity of the experimental equipment in the chamber, and any deviation in slope from the xaxis likely to air infiltration. These deviations were measured in 10 empty chamber tests; one test 

is shown as an example in Figure 8. In this figure, Mv,gain is the moisture added to the space from 

the humidifier and Mv,air is the change in moisture in the chamber air (measured as a change in 

humidity ratio). These nearly balance (i.e., most of the moisture added to the chamber goes to the 

air). The deviation (Mv,(?)) is caused by unknown sources, perhaps moisture sorption in material 

in the chamber, moisture transfer through the chamber walls, or measurement uncertainty. The 

deviations from the 10 tests were used to correct the results from subsequent chamber tests.

The validation tests in the laboratory chamber used 144 ft2 of gypsum board. The backside of 

each sheet of gypsum board was attached to the backside of another, with the edges taped, such 

that it was exposed on one side only. The established method for measuring moisture sorption 

into the materials is to weigh the materials directly as they absorb and desorb moisture. Any 

increase in weight as the RH increases is due to water sorption in the material. Therefore, the 

moisture absorbed by 16 ft2 of the total was also measured by weighing it with a second scale. 

This was extrapolated to the total 144 ft2, tying the new measurement technique to a wellestablished method for measuring material moisture sorption.
14

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Figure 8. Cumulative moisture transfer during an empty-chamber test in the laboratory

Figure 9 shows the cumulative moisture transferred during this validation test; each of the four 

lines represents a term in Eq. (10):

• Mv,inf is the line just below the x-axis. It is assumed to be infiltration through the chamber, 

but it accounts for any unknown moisture transfers, which were measured with the 10 

tests on an empty chamber (see Figure 8). It is negative because all these 10 tests showed 

some unknown moisture sink (which is consistent with infiltration from the dry 

laboratory air into the humid chamber).

• Mv,gain is the top line. This is the cumulative moisture added with the humidifier.

• Mv,HVAC is zero.

• Mv,air is the bottom line. This is the change in mass of the moisture in the chamber air.

• Mv,matl is plotted twice. The first is based on Eq. (10) (solid line). The second is based on 

the established method of directly measuring the change in material weight with time 

(open circles).

The uncertainty in the established method is due only to the uncertainty in the second scale 

(±0.001 kg). The uncertainty in the new method (caused by uncertainty in the zone volume, the 

zone humidity, and the calibrated infiltration) is shown with a single error bar near the 7 hour 

point. The magnitude of the uncertainty at earlier times was similar. 

This comparison shows that the new measurement method results in cumulative moisture 

transfer nearly equivalent to the established method.

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7

Cumulative moisture transfer (kg)

Time (hr)

Humidifier

Moisture unaccounted for

Room air

Mv,gain

Mv,(?)

Mv,air
15

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Figure 9. Cumulative moisture transferred into gypsum board in laboratory chamber that is used 

to validate the experimental method

Linking method in the laboratory with method in the field: The second step of validation was to 

link the field-test measurements to the laboratory measurements. To do this, we put 2300 ft2 of 

gypsum board (exposed on both sides) in the field test house and measured its moisture 

absorption. Before testing the gypsum board, we needed baseline results on an empty house 

(similar to the baseline tests on the empty chamber). For these tests, we left the exterior walls 

and ceiling exposed, but covered the bare concrete slab to avoid its expected large moisture 

capacitance. The house during this configuration is shown in Figure 10; the house with the 2300 

ft2 of gypsum board is shown in Figure 11.

We then shipped 48 ft2 of this gypsum board to the laboratory in Colorado and measured it 

(exposed on both sides) in the chamber. Note that Figure 9 is a moisture transfer plot for one 

type of gypsum board, which was tested before we received the gypsum board from Florida. A

second type (from Florida) was tested in both the field test and the laboratory chamber test.

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7

Cumulative moisture transfer (kg)

Time (hr)

Mv,gain

Mv,matl

established method

Mv,inf

Mv,air

new method
16

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Figure 10. Field test of empty house with slab covered

Figure 11. Field test of 2300 ft2 of gypsum board with slab covered

(Photo credit: David Hoak, FSEC. Used with permission.)

Similar to Figure 9, the same four cumulative moisture terms are shown in Figure 12 for the field 

tests with drywall. Four cycles are shown, each with a humidification and a dehumidification step. 

Compared with the laboratory chamber tests, a few differences are worth noting. The Mv,gain

line from Figure 9 becomes Mv,gain – Mv,HVAC in Figure 12, with Mv,HVAC representing the 
17

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moisture removed both with the dehumidifier and the air conditioner. The dehumidifier is on 

during the second half of each cycle (12 < t < 24 hours, 36 < t < 48 hours, etc.). The house is not 

as airtight as the laboratory chamber, so more moisture is transferred through infiltration. The 

abrupt changes in the slope of the infiltration line every 12 hours is from the changing indoor 

humidity: during humidification (RH = 65%) the humidity ratio was similar to outdoors; during 

dehumidification (RH = 35%) the humidity ratio was much lower than outdoors. This infiltration 

causes the average of the “Mv,gain - Mv,HVAC” line to deviate from the x-axis; there was more 

dehumidification than humidification to maintain the 35%/65% cycles because of the moisture 

gained from infiltration. The moisture absorbed by the materials also deviates slightly from the 

x-axis, but the deviation is much smaller. This deviation was likely due to one (or more) of the 

following three factors: (1) uncertainty in the infiltration measurement; (2) slow moisture 

absorption by some of the building materials (likely the concrete block walls); and (3) moisture 

diffusion through the building envelope, which is not captured in the infiltration measurement.

Figure 12. Cumulative moisture transfer for four cycles of whole-house tests with gypsum board

To validate the whole-house test setup, the Mv,matl line in Figure 12 was compared with the 

Mv,matl line from the laboratory chamber tests. Two corrections to the whole-house test were 

made before this comparison: (1) The results from the empty-house test were subtracted from the 

data. This isolates the moisture absorption into the gypsum board (results for the empty house are 

shown in Figure 17 in Section 4.1); and (2) The material moisture absorption during the 

humidification steps was averaged with the material moisture desorption during the 

dehumidification steps. 

The moisture sorption curve with these corrections is shown in Figure 13b; the data from the 

same material measured in the laboratory are shown in Figure 13a. We show the normalized 

sorption into the materials (kg/m2), because there was more gypsum board in the whole-house 

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 24 48 72 96

Cumulative moisture transfer (kg)

Time (hr)

Mv,gain – Mv,HVAC

Mv,matl

Mv,inf

Mv,air
18 

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test than in the laboratory chamber test. Two uncertainty bars are shown: one during the ramping 

RH period, and one during the steady RH period. These are representative of the uncertainties of 

all the points in each period, but for clarity only one is shown. 

(a) 

(b) 

Figure 13. Comparison of tests on gypsum board in (a) laboratory chamber, (b) whole house 

 

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

012345678

Cumulative specific moisture absorption 

(kg/m2)

Time (hr)

gypsum data (lab 

chamber test)

Empirical curve fit

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

012345678

Cumulative specific moisture absorption 

(kg/m2)

Time (hr)

Gypsum data (whole-house test)

Empirical curve fit

Empirical curve fit based on labderived parameters
19

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From these curves, we see that the RH increases more slowly in the whole-house test than in the 

laboratory chamber test. This is because the ratio of the humidifier capacity to the moisture 

capacitance of the air and materials in the space is smaller in the whole-house test. This 

difference means the results of the two tests cannot be compared directly. Instead, we use our 

parameter derivation method (see Section 3.2 for an explanation) to compare the results from 

each test. The red dashed line in Figure 13a is a best-fit line based on Eq. (10); the model 

parameters are calculated to minimize the sum of the squares of the error between the line and 

the data. Using the same parameters in Eq. (10), but with the temperature, barometric pressure, 

and RH data from the whole-house tests, gives the red dashed line in Figure 13b. We also 

calculated a best-fit line based on the whole-house data, which is the black solid line in Figure 

13b. These lines nearly match, with the derived model inputs within 3.5%. This links the 

measurements in the field to the measurements in the well-controlled laboratory chamber.

3.1.3 Incremental Whole-House Buffering Experiments

With the experimental approach validated, we turn to the incremental moisture buffering tests on 

the whole house with varying levels of furnishings. From the baseline test with the covered slab, 

we then measured the incremental moisture buffering effects of: (1) uncovered slab, (2) carpet 

and pad, (3) furniture, and (4) interior walls.

The vapor barrier was removed from the slab to determine its moisture buffering effect. During 

the construction of the house, a 6-mil polyethylene vapor barrier was installed below the slab, 

which minimizes moisture exchange with the soil.

For the carpet tests (Figure 14), we covered the slab with a polyester carpet over a 0.42-in. thick 

bonded urethane foam pad.

Figure 14. Field test with carpet and pad installed over the slab

(Photo Credit: David Hoak, FSEC. Used with permission.)
20

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For the furniture tests (Figure 15), an assortment of furniture typical for a three-bedroom home 

was added to the house (without removing the carpet). The furniture included:

• Living and dining room furniture (sofa, chair, throw pillows, end tables, dining table and 

chairs, rugs)

• Master bedroom (headboard, queen mattress set with linens and pillows, dresser, 

nightstand)

• Bedroom 2 (headboard, twin mattress set with linens and pillows, dresser, nightstand)

• Bedroom 3 (headboard, twin mattress set with linens and pillows, dresser, nightstand).

For the interior wall tests (Figure 16), the walls were not installed as a floor plan, but instead 

were built 4-ft tall and 8-ft wide and arranged in two groups of 12 and one group of 11 (total of 

2240 ft2 of interior wall surface area). This provided better mixing and therefore more uniform 

distribution of temperature and RH. The walls were built uninsulated with 16-in. on-center 

vertical studs, with the top, bottom and side plates sealed to moisture. The wide sides (gypsum 

faces) included wooden baseboards. Both baseboards and gypsum board were primed and 

painted with an eggshell finish, water-based latex paint.

Figure 15. Field test with furniture and carpet

(Photo credit: David Hoak, FSEC. Used with permission.)
21

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Figure 16. Field test with interior walls, furniture, and carpet

(Photo credit: David Hoak, FSEC. Used with permission.)

3.2 Determining Empirical Model Inputs

The Mv,matl data obtained from the experiments can be used to derive the EMPD model 

parameters for this house. We start with the model’s moisture balance equations for the surface 

layer (Eq. (4)). As discussed in Section 2, this equation contains the material moisture content in 

equilibrium with the zone air (wzone). We use the definition of the material moisture sorption 

curve to replace this with the sorption curve slope times the zone RH. 

( ) ( ) ( )





 





 = t − w t

d

dw k A

dt

dw t

Ad surf zone surf

surf

EMPD φ

φ (20)

The zone RH is measured, while the sorption curve slope is a new unknown parameter. This is 

an ordinary differential equation, which is relatively straightforward to solve. To do this, we split 

the problem into two parts. For the first part, we assume a linearly increasing zone RH (with 

slope mr), which is a good approximation for the transient time between the test start and the 

time when the RH reaches its steady state value. The second part is this steady-state value, where

we assume a constant zone RH.

Solving these ordinary differential equations for wSURF(t) results in the following two equations 

for the transient and steady-state parts (see Appendix for derivation):
22

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( ) ( ) 















+ − 













 = − + t

d

k

exp k

d

m

d

dw

m t

k

d

m

d

dw

w t

EMPD

surf

surf

EMPD

r r

surf

EMPD

SURF ZONE r φ φ φ

0 1 0 < t ≤ t (21)

( ) ( ) ( )















− − 



 





 = + 1 − 1 t t

d

k

exp d

dw

w t

d

dw

w t

EMPD

surf

SURF ZONE ,f SURF φ ZONE ,f φ φ

φ 1 t > t (22)

where t1 is the time when the period with linearly increasing RH changes to the steady-state 

period (65% RH). These equations give the moisture content of a uniform layer of fictitious 

material representing all of the materials in the zone. Combining these with Eqs. (2), (3),and 

(10), we can calculate the total accumulation of moisture in the materials:

( ) 



















 



















 − = − − t

d

k

exp k

d

m t

d

dw M t Ad

EMPD

surf

surf

EMPD

v,SURF EMPD r 1

φ 1 0 < t ≤ t (23)

( ) ( ) ( ) ( ) 



 



















 − − − 





 





 = 1 + − 1 1 1 t t

d

k

w t exp d

dw M t M t Ad

EMPD

surf

v,SURF v,SURF EMPD φ ZONE ,f SURF φ 1 t > t (24)

The data from the 2-week tests were used in a similar manner to calculate the deep-layer 

properties. But the initial ramp was less than 1% of the 2-week test, and can be ignored for 

deriving the deep-layer properties. The total accumulated moisture during these 2-week tests is 

accounted for in both the surface and deep layers. 

( ) ( ) ( ) 





























 − = + − −

−

− t

d

k

exp d

dw M t M t Ad

EMPD deep

deep

v,TOTAL v,SURF EMPD deep φ ZONE,f φ ZONE,i 1

φ t > 0 (25)

The measured data can be compared to Eqs. (23) and (24) for the 24-hour tests, and Eq. (25) for 

the 2-week tests. We calculate the moisture buffering parameters that minimize the sum of the 

square of the errors between the data and the model. To do this, we need to know what 

parameters to solve for. There are several unknowns: 

A material total surface area (m2

)

dEMPD surface layer EMPD thickness (m)

dEMPD-deep deep layer EMPD thickness (m)

dw/dφ moisture sorption curve slope (kg m-3 RH-1

)

ksurf moisture transfer coefficient between air and surface layer (m s-1)

kdeep moisture transfer coefficient between surface layer and deep layer (m s-1)

However, these variables do not need to be determined independently because many are coupled. 

There are two groups for the surface layer equations (Eqs. (23) and (24)): 
23

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dφ

dw Π1 = AdEMPD (26)

EMPD

surf

d

k

Π2 = (27)

And another two groups in Eq. (25):

dφ

dw Π3 = AdEMPD−deep (28)

EMPD deep

deep

d

k

−

Π4 = (29)

These four parameters can be reduced to three. We first use the definition of the deep-layer mass 

transfer coefficient (Eq. (7)):

( ) ( )

air sat

EMPD deep

EMPD

surf

EMPD

EMPD deep

air sat

EMPD deep

surf

EMPD deep

p

d

d

dw

d

k

d

d

p

d

d

dw

k

d

δ

μ φ

δ

μ φ

2

1 1

1

2

1

2

2 2

2

4

−

−

−

−

Π

+

Π

=

+

Π =

(30)

We then use the definition of the surface-layer mass transfer coefficient (Eq. (6)), along with the 

fact that Π3/Π1 = dEMPD-deep/dEMPD:

2

1

3

1 2

3

2

1

3

1 2

3

2

4

1 1

1

2

1 1

1

















Π

Π

Π

+

Π

Π

Π

=

Π

Π

Π

+

Π

Π

Π

Π =

−

EMPD

EMPD

air sat

surf EMPD deep d

d

x

p

d

dw

k d

δ

μ

φ (31)

After some algebra, we end up with a relationship for Π4 based on the other three Π groupings:

( ) 3 3 1

2 1

4 Π 1+ Π Π

Π Π Π = (32)

Thus, three parameters are needed to fully define the EMPD model inputs. In the building energy 

model, we would like to have realistic material inputs, rather than the empirical Π groupings. We 

can assume values for some variables and calculate three empirical values. Here, we assume 

values for dw/dφ, and μ, and then we calculate the total surface area (A), the surface-layer EMPD 

thickness (dEMPD), and the deep-layer EMPD thickness (dEMPD-deep).

3.3 Realistic Load Test Case

With these empirical parameters calculated, their accuracy was assessed by using them in a 

model and comparing the model’s output with measured data. We use not only the EMPD 

model, but also the effective capacitance model for comparison. The measured data were taken 
24

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from a 24-day test (December 21, 2013 to January 14, 2014), which included enough variation in 

the weather to provide a reasonable assessment of model accuracy. The heaters and humidifier 

simulated occupants and internal gains, while the dehumidifier was turned off, and the heaters 

and air conditioner controlled the zone temperature to between 21.1°C (heating set point) and 

25°C (cooling set point). The internal gain profile was based on the Building America House 

Simulation Protocols [15]. We also added internal gains that mimicked solar gains through 

windows, because the windows were still covered to prevent condensation. The solar gains 

through the windows were calculated assuming a relatively clear day and a solar heat gain 

coefficient of 0.3.

To isolate the moisture buffering model, we simplified the sensible energy calculations by setting 

the zone temperature in the model equal to the measured value at each time step. This eliminates 

any uncertainty with the heat transfer model, which is not being evaluated. We also assumed a 

high mass transfer coefficient at the material surfaces, because the fans operated continuously.

Since we specified the zone temperature in the model, we did not calculate the loads required to 

maintain the temperature set point. We did, though, need to calculate the moisture removal by 

the air conditioner, as this impacts the moisture balance. For this, we used the rated air 

conditioner capacity with an assumed rated sensible heat ratio, and then calculated the latent 

removal at each time step using the bypass-factor method [16]. We prefer this approach to using 

the measured latent removal directly, because the modeled latent removal is a function of the 

zone humidity, and the modeled zone humidity will not, in general, match the measured zone 

humidity at each time step, especially for the inaccurate EC model.

Other inputs into the model include the ambient humidity ratio, used to calculate the latent 

infiltration exchange, the barometric pressure, used to calculate various psychrometric functions, 

and the zone volume.

4 Results and Discussion

4.1 Incremental Whole-House Buffering Tests

The results of the whole-house incremental tests are shown in Figures 17 and 18 for the 24-hour 

tests and 2-week tests, respectively. They show the results for each level of materials. We 

averaged the material absorption during the humidification steps with the material desorption 

during the dehumidification steps to obtain the curves shown in the figures. This averaging 

forces the line to return to zero at the end of the dehumidification step. For clarity, these plots do 

not include uncertainty bars; the uncertainty of these experiments is discussed in Section 4.2.

Twenty-four-hour tests (Figure 17): The first case for the 24-hour tests is an empty house, which 

includes the buffering effects of the exterior walls and the ceiling. Temperature and RH sensors 

between the gypsum board and the concrete blocks of the exterior walls indicated that the 

moisture penetrated the gypsum board and was absorbed by the concrete blocks. Thus, the blocks 

are responsible for at least part of the absorption seen in the empty house test.

After the empty house test, we incrementally looked at the effects of various materials in the 

space. The vapor barrier was removed from the floor so that the concrete slab would absorb 

moisture. This nearly doubled the moisture absorption from the empty house test, with 3.7 kg of 
25

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moisture being absorbed. Adding carpet gives the next line, which shows that carpet absorbs 

moisture quickly, based on the faster absorption of the carpet compared to the bare slab for the 

first 3 hours. However, the carpet slows the moisture absorption into the slab, so that at the end 

of the humidification step, the bare slab was absorbing moisture more quickly than the slab with 

carpet. Adding carpet increased the cumulative absorption over 12 hours by 0.5 kg. The next two 

steps (adding furniture and then interior walls) each increased the moisture absorption by 

roughly 1.7 kg. 

The total moisture absorbed (7.6 kg) for the final case is roughly 2.7 times higher than the 

change in moisture in the zone air. This final case is used in Section 4.3 to derive the overall 

buffering properties of the house.

Two-week tests (Figure 18): The 2-week tests started with a dehumidification step. We again 

averaged the measured moisture desorption during dehumidification and the measured 

absorption during humidification. For the final test (interior walls + furniture + carpet), the 

materials absorbed 37 kg of moisture. This is 13 times higher than the change in moisture in the 

zone air. This final test is used to derive the third lumped parameter for the moisture buffering 

model (Eq. (25)), as discussed in Section 4.3.

Figure 17. Cumulative moisture sorption for 24-hour cycle tests

0

1

2

3

4

5

6

7

8

0 4 8 12 16 20 24

Cumulative moisture absorption (kg)

Time (hr)

empty

slab

carpet

furniture (+ carpet)

walls (+ furniture & carpet)
26

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Figure 18. Cumulative moisture sorption for 2-week cycle tests

4.2 Uncertainty Analysis

To improve the readability of the figures, we omitted uncertainty bars from most of the previous 

graphs. Instead, we show the percent uncertainty versus time for these measurements in Figure 

19. The uncertainty is split into two cases: (1) the uncertainty when the ambient humidity ratio is 

close to the indoor humidity ratio; and (2) the uncertainty when the ambient humidity ratio and 

indoor humidity ratio differ significantly. Case (1) is typical of a humidification step (when the 

indoor humidity is high); case (2) is typical of a dehumidification step (when the indoor humidity 

is low). The actual cases plotted in Figure 19 are: (1) the humidification step of the 2-week tests 

with a fully furnished house; and (2) the dehumidification step during the 2-week tests with 

furniture and carpet.

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336

Cumulative moisture absorption (kg)

Time (hr)

empty

slab

furniture (+ carpet)

interior walls (+ furniture & carpet)
27

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Figure 19. Percent uncertainty in the calculated material moisture sorption

The percentage uncertainty during the first hour is high in both cases. This is partially due to the 

slightly higher absolute uncertainty during the beginning of these tests, but more due to the lower

absolute material absorption during the beginning of the tests, leading to high percent

uncertainty. At around 12 hours, a key time for data analysis for the 24-hour tests, the 

uncertainty is less than 3% for case (1) and 9% for case (2). The uncertainty is around 5% for 

case (1) for time periods at one week (important for the 2-week test). For case (2), the 

uncertainty at one week approaches 35%, which is primarily due to the uncertainty in the 

measurement of the infiltration moisture.

This is illustrated in Figures 20 and 21, which show the apportionment of the overall uncertainty 

for cases (1) and (2), respectively, to each individual measurement uncertainty. 

0

5

10

15

20

25

30

35

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Percent uncertainty in 

Mv,matl

Time (hr)

Case (2)

ωambient - ωzone = small

Case (1)

ωambient - ωzone = large
28

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Figure 20. Percent contribution of each measurement uncertainty to the overall uncertainty in the 

calculated material sorption. Case (1): slight difference between zone and ambient humidity ratio.

Figure 21. Percent contribution of each measurement uncertainty to the overall uncertainty in the 

calculated material sorption. Case (2): large difference between zone and ambient humidity ratio.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Contribution to uncertainty (%)

Time (hr)

RHzone

RHambient

Tzone

Tambient

Vzone

CCO2-ambient

CCO2-zone

mCO2 injection

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 12 24 36 48 60 72 84 96 108 120 132 144 156 168

Contribution to uncertainty (%)

Time (hr)

RHzone RHambient

Tzone

Tambient

Vzone

CCO2-ambient

CCO2-zone

mCO2 injection
29

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For case (1), the uncertainty for the initial day is driven by the zone RH measurement. For longer 

periods, the uncertainty in the infiltration starts to dominate, which is due to both the uncertainty 

in the humidity ratio difference between the zone and ambient, as well as the infiltration rate 

(ṁair,inf). For case (2), the uncertainty in the tracer gas measurements (primarily the CO2 injection 

rate) contribute to nearly 80% of the overall uncertainty after only 24 hours. Since the humidity 

ratio difference between the zone and the ambient is large, the uncertainty in the actual 

infiltration rate is more important than for case (1). These results show that uncertainty could be 

reduced by using a more accurate mass flowmeter. Because this instrument’s uncertainty is a 

percentage of full scale, it could be improved by simply using a smaller mass flowmeter and 

measuring closer to the upper end of the instrument range.

The uncertainty data are carried through to the overall uncertainty in the empirically derived 

parameters. These are presented with the parameter values in Section 4.3.

4.3 Empirical Parameter Derivation

The Mv,matl data for the 24-hour and 2-week tests can be used to derive the parameters for use in 

building energy models. The data for these two tests are shown again in Figures 22 and 23, along 

with the least-squares fit based on Eq. (23) for Figure 22 and Eq. (25) for Figure 23. 

The parameters for these least-squares fit curves are shown in Tables 5 and 6. The moisture 

buffering of the house is fully characterized with any three of these parameters, which can be 

used as inputs in building simulations. For Table 6, we assume values for the vapor resistance 

factor and the slope of the sorption curve. These values are arbitrary, because it is the overall 

groupings that are important, but using these values (typical of gypsum and wood-based 

materials) give meaningful numbers to the area and penetration depths.

Table 5. Empirically Derived Parameters (Π Groupings)

Π1 (kg m-3 RH-1

) Π2 (s-1) Π3 (kg m-3 RH-1) Π4 (s-1)

31.0 ± 0.414 4.27E-05 ± 0.31E-05 183 ± 34 1.05E-06 ± 0.276E-06

Table 6: Example of Empirically Derived Material Properties

μ dw/dφ (kg m-3

) A (m2) dEMPD (m) dEMPD-deep (m)

8.0 † 10.0 † 161.8 ± 8.0 0.0191 ± 0.0007 0.113 ± 0.016

† assumed
30 

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Figure 22. Empirical fit for 24-hour data for all materials in whole-house test 

Figure 23. Empirical fit for 2-week data for all materials in whole-house test 

 

0

1

2

3

4

5

6

7

8

9

0 2 4 6 8 10 12 14 16 18 20 22 24

Cumulative moisture transfer (kg)

Time (hr)

Measured whole-house data

Empirical curve fit

-40

-35

-30

-25

-20

-15

-10

-5

0

5

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336

Cumulative moisture transfer (kg)

Time (hr)

Measured whole-house data

Empirical curve fit
31

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4.4 Using the Calibrated Model

The realistic-load test case is used to validate the model and its inputs. The ambient conditions 

during this test varied as shown in Figure 24. During the cooler periods (hour 315 to 340 and 

hour 405 to 440), the air conditioner was off for several days. This affects the RH, because the 

air conditioner is the primary means of removing moisture from the zone.

Figure 24. Measured temperature and humidity ratio for the building zone

and ambient air during the realistic-load test case

To assess model accuracy, we compare the measured and modeled RH. This is shown in Figure 

25 for the EMPD model, Figure 26 for the EC model, and Figure 27 for the EMPD model with 

no deep layer. The uncertainties for these plots are: 1.7% RH (measured), 0.73% RH (EMPD 

model), 0.65% RH (EC model), and 0.71% (EMPD model with no deep layer). The uncertainty 

for the EC model assumes there is no uncertainty in the actual EC value, since this is simply 

prescribed, but Figure 26 shows the sensitivity to this value with results for EC = 3 and EC = 10.

These figures illustrate how the EMPD model, when using a deep layer, matches the data fairly 

well, while the EC model does not. The coefficient of determination (R2

), a way to quantify the 

model accuracy, is R2 = 0.81±0.03 for the EMPD model with a deep layer. Table 7 shows this 

value compared to the EC model, which has a maximum R2 of 0.52 (EC = 5). This shows that 

the EC model, regardless of what EC value is used, cannot be calibrated; it is incapable of 

matching the measured data.

The reasons for this can be seen in Figure 26. Using EC = 10 results in overdamping of the daily 

fluctuations in RH. Using EC = 3 is better for these high-frequency fluctuations, but it results in 

underdamping of the lower frequency moisture loads (288 hours < t < 480 hours).

0

5

10

15

20

25

30

35

0 48 96 144 192 240 288 336 384 432 480 528 576

Temperature [C]

Time [hr]

0

0.005

0.01

0.015

0.02

0 48 96 144 192 240 288 336 384 432 480 528 576

Humidity ratio

Time [hr]

Tambient

Tzone

ωzone

ωambient
32 

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Figure 25. Model-predicted RH for the EMPD model compared to the 

measured RH during the realistic-load test case 

Figure 26. Model-predicted RH for the EC model, with EC = 3 and EC = 10, 

compared to the measured RH during the realistic-load test case 

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 48 96 144 192 240 288 336 384 432 480 528 576

Relative humidity

Time [hr]

Measured RH

Modeled RH (EMPD w/ deep layer)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 48 96 144 192 240 288 336 384 432 480 528 576

Relative humidity

Time [hr]

Measured RH

Modeled RH (EC = 10)

Modeled RH (EC = 3)
33 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. 

Figure 27. Model-predicted RH for the EMPD model without a deep layer, 

compared to the measured RH during the realistic-load test case 

Table 7. Coefficient of Determination (R2

) for the Model Based on the 

Realistic-Load Test Case; Uncertainty for EMPD Model Is ±0.03 

Model R2

EMPD 0.81

EMPD (no deep layer) 0.64

EC = 3 0.29

EC = 5 0.52

EC = 8 0.46

EC = 10 0.40

EC = 15 0.26

The EMPD model with only the surface layer also underdamps the lower frequency moisture 

loads, but it has a better R2 (0.64) than the EC model. These results indicate that, at least for 

houses with similar construction to that tested here, a deep layer is required for an accurate 

model. 

The low uncertainty in the RH predicted by the EMPD model, despite the sizable uncertainties 

discussed in Section 4.2, indicates that the EMPD model is insensitive to small changes in its 

inputs. But what about larger changes? We were careful to eliminate uncertainties in the 

experiments, such as using an accurate scale for measuring moisture addition and removal, 

minimizing infiltration, and keeping the air conditioner ducts in conditioned space. If we 

introduced more uncertainty, how would that affect our final “calibrated” model? To explore this 

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 48 96 144 192 240 288 336 384 432 480 528 576

Relative humidity

Time [hr]

Measured RH

Modeled RH (EMPD w/out deep layer)
34

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question, we looked at the sensitivity of the final R2 value to larger uncertainties of the 

determined parameters (A, dEMPD, and dEMPD-deep). There are only three independent parameters, 

so looking at the uncertainty of other parameters (e.g., sorption curve) is not meaningful. This 

does not answer this question definitively, because we have only 3.5 weeks of monitored data on 

just one house. But it gives a good initial assessment of the sensitivity of the model to its inputs.

To calculate the sensitivity, we changed the values of the three inputs by 10 standard deviations 

in both directions (±25% for A, ±20% for dEMPD, and ±70% for dEMPD-deep) and calculated the 

change in R2. The largest change (Table 8) is from R2 = 0.81 to R2 = 0.74 for a 25% smaller 

material surface area.

The effect of the deep layer thickness changing by ±70% has little effect on R2

. So the deep layer 

is important (eliminating the deep layer reduces R2 from 0.81 to 0.64), but the value for the deep 

layer thickness is less important.

Table 8. Sensitivity of Results to a 10-Standard-Deviation Change in Each Input Parameter

Case R2

Baseline 0.81

1.25A 0.79

0.75A 0.74

1.2dEMPD 0.83

0.8dEMPD 0.77

1.7dEMPD-deep 0.78

0.3dEMPD-deep 0.81

This shows that the model is relatively insensitive to the accuracy of these inputs. Although 

estimating the values based solely on house characteristics, which may provide an order of 

magnitude estimate, is still not an option, it may allow for less rigorous measurement techniques 

without much sacrifice in accuracy. It also means a limited dataset, based on tests on a handful of 

houses, may be adequate to develop correlations for the model inputs based on house size, 

construction materials, and level of furnishings.

5 Conclusions

This study validated a method for calculating material moisture sorption by measuring all other 

moisture transport terms during well-defined RH cycles. This allows us to derive moisture model 

inputs for building simulations by testing houses in the field. The results of the house tested in 

this study showed that using these derived model inputs in a building simulation accurately 

predicted the RH in the house during a test under Building America operation protocols. 

The EMPD model can be fully defined with three independent parameters that are groups of 

material properties and geometric inputs. By assuming values for the material properties, we can 

obtain more intuitive inputs: the surface area of the material, the surface-layer thickness, and the 

deep-layer thickness. 
35

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The method is less accurate over longer time periods, but the model was still accurate for two 

reasons: (1) the first two model parameters were derived based on data over short periods; and 

(2) the model is relatively insensitive to the third parameter, which is derived based on data over 

longer periods. The key driver in the accuracy was the uncertainty in the infiltration 

measurement; improving this measurement would provide the largest reduction in uncertainty.

That being said, the final modeling results were relatively unaffected by these uncertainties. This 

means simpler measurement techniques may be possible without sacrificing accuracy. For 

example, a simple model of infiltration, based on a one-time infiltration measurement, could be 

used instead of continuously monitoring infiltration. These questions require further analysis to 

understand its importance for different house characteristics (e.g., for leakier houses than the 2.5-

ACH50 house used here).

This study provided data for just one house construction, and a few levels of furnishings. This 

method could be used in houses of other constructions (e.g., wood frame), to determine how the 

moisture buffering of these homes differ. Several tests could be used to develop a dataset to 

provide guidance on moisture buffering model inputs for different home constructions and level 

of furnishings.

Some questions were not addressed in this study, and may need further research:

• How humidity distribution from room to room affects the measurement.

• How sensitive the results are to varying degrees of air conditioner duct leakage.

• The accuracy of the method when measuring air conditioner condensate with a less 

accurate measurement, such as a tipping bucket. This may be required in cases using the 

home’s existing air handler.
36

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References

[1] Woods, J., J. Winkler, D. Christensen, Moisture modeling: Effective moisture penetration 

depth versus effective capacitance, in Thermal Performance of the Exterior Envelopes of Whole 

Buildings XII International Conference. 2013: Clearwater, FL.

[2] Rudd, A. and H. Henderson, Monitored indoor moisture and temperature conditions in 

humid-climate US residences, ASHRAE Transactions. 113 (2007) 435-49.

[3] Henderson, H., D. Shirey, C.K. Rice, Can conventional cooling equipment meet 

dehumidification needs for houses in humid climates?, in 2008 ACEEE Summer Study on Energy 

Efficiency in Buildings. 2008: Pacific Grove, CA.

[4] Kuenzel, H.M., A. Karagiozis, A. Holm, WUFI ORNL/IBP A Hygrothermal Design Tool 

for Architects and Engineers. 2001, Chapter ASTM Manual 40 in Moisture Analysis of 

Buildings.

[5] Combined Heat and Moisture Transfer (HAMT) Model, EnergyPlus Engineering 

Reference. 2013, US Department of Energy. p. 47-52.

[6] Kerestecioglu, A., M. Swami, A. Kamel, Theoretical and computational investigation of 

simultaneous heat and moisture transfer in buildings: "Effective penetration depth" theory, 

ASHRAE Transactions. 96 (1990) 447-54.

[7] Cunningham, M.J., Effective penetration depth and effective resistance in moisture 

transfer, Build. Environ. 27 (1992) 379-86.

[8] Cunningham, M.J., The moisture performance of framed structures - a mathematical 

model, Build. Environ. 23 (1988) 123-35.

[9] Woods, J., J. Winkler, D. Christensen, Evaluation of the effective moisture penetration 

depth (EMPD) model for estimating moisture buffering in buildings. National Renewable Energy 

Laboratory, TP-5500-57441, 2013. 

[10] Janssen, H. and S. Roels, Qualitative and quantitative assessment of interior moisture 

buffering by enclosures, Energ. Buildings. 41 (2009) 382-94.

[11] Abadie, M.O. and K.C. Mendonca, Moisture performance of building materials: From 

material characterization to building simulation using the Moisture Buffer Value concept, Build. 

Environ. 44 (2009) 388-401.

[12] Rode, C. and K. Grau, Moisture buffering and its consequence in whole building 

hygrothermal modeling, Journal of Building Physics. 31 (2008) 333-60.

[13] Vereecken, E., S. Roels, H. Janssen, In situ determination of the moisture buffer potential 

of room enclosures, Journal of Building Physics. 34 (2011) 223-46.
37

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

[14] Vieira, R. and J. Sherwin, Flexible Residential Test Facility Instrumentation Plan. Flordia 

Solar Energy Center for DOE Building America Program, 2011. 

[15] Hendron, R. and C. Engebrecht, Building America House Simulation Protocols. National 

Renewable Energy Laboratory, TP-5500-49426, 2010. 

[16] Threlkeld, J.L., Cooling and Dehumidying Coils, in Thermal Environmental Engineering. 

1970, Prentice-Hall: Englewood Cliffs. p. 254-70.
38

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Appendix

This appendix derives the equations used to calculate the material’s moisture properties for the 

surface layer (Eqs. (23-24) and the deep layer (Eq. (25)).

Surface-layer properties: The surface layer equations are derived from the differential equation 

based on a mass balance for the surface layer:

( ) ( ) ( )





 





 = t − w t

d

dw k A

dt

dw t

Ad surf zone surf

surf

EMPD φ

φ (A.1)

We start by converting this to the standard format for a first order, linear differential equation:

p(t)w q(t) dt

dw

surf

surf + = (A.2)

Where

( )

EMPD

surf

d

k

p t = (A.3)

( ) (t) d

d

dw k

q t zone

EMPD

surf

φ φ = (A.4)

We assume the material properties are constant with time. The solution to this equation is:

( )

( ) ( )

exp(pt)

q t exp pt dt C

w t

t

surf

+

=

∫

0 (A.5)

At this point, we split the problem into two parts: the ramping period and the steady-state period.

Ramping period: During the ramping period, the zone RH is:

(t) ( ) m t ZONE = ZONE + r φ φ 0 (A.6)

where mr is the rate of increase in the zone RH during this period, which is approximately 

constant with time, but can differ from one test to the next:

( )

0

0

1 −

− = ∆

∆ = t t

m

ZONE,f ZONE

r

φ φ φ (A.7)

where t1 is the time at which the RH equals its steady-state value. For this period, Eq. (A.5) 

becomes:
39

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( )

( ( ) ) ( )

exp(pt)

m t exp pt dt C

w t

t

ZONE r

SURF

+ +

=

∫

0

α φ 0

(A.8)

where α is:

EMPD

surf

d

d

dw k

φ α = (A.9)

Solving the integral leads to:

( ) ( ) ( ) C exp( pt)

p

m

p

m t

p

m

p

w t r

r ZONE

r

SURF ZONE  −



 





+















+ − + 













 = 0 − + φ 0 α φ α

(A.10)

Substituting in the equations for α and p gives:

( ) ( )

( ) 















−

















+















− +

 +



 



 = − +

t

d

k

C exp k

m d

d

dw

m t

k

m d

d

dw

w t

EMPD

surf

surf

r EMPD

ZONE

r

r EMPD

SURF ZONE

0

0

φ φ

φ φ

(A.11)

The initial condition ( ) ( )





 





 0 = 0 SURF ZONE d

dw

w φ

φ

is used to solve for C, which gives the surface 

moisture content during the ramping period:

( ) ( ) 















+ − 













 = − + t

d

k

exp k

d

m

d

dw

m t

k

d

m

d

dw

w t

EMPD

surf

surf

EMPD

r r

surf

EMPD

SURF ZONE r φ φ φ

0 1 0 < t ≤ t (A.12)

This is converted to the cumulative moisture transfer with:

( ) ( ) ( ) ∫ ∫ 





 





 = = −

t

surf ZONE SURF

t

v,SURF v,SURF t w t dt

d

dw M t m dt k A

0 0

φ

φ  1 0 < t ≤ t (A.13)

where ṁSURF(t) is the instantaneous moisture transfer rate. Substituting Eq. (A.12) for wSURF and 

(A.6) for φZONE(t) and simplifying gives:

( ) ∫ 





























 = − −

t

EMPD

surf

v,SURF EMPD r t dt

d

k

m exp d

dw M t Ad

0

1

φ 1 0 < t ≤ t (A.14)
40

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Integrating leads to the final equation for the cumulative moisture transfer during the ramping 

period (Eq. (23) in the report):

( ) 













































 − = − − t

d

k

exp k

d

m t

d

dw M t Ad

EMPD

surf

surf

EMPD

v,SURF EMPD r 1

φ 1 0 < t ≤ t (A.15)

Steady-state period: During the steady-state period, the zone RH is constant at its final value 

φZONE,f. Eq. (A.5) becomes:

( )

( )

exp(pt)

exp pt dt C

w t

t

t

ZONE,f

SURF

+

=

∫

1

αφ (A.16)

Solving the integral leads to:

( ) exp( p(t t )) C exp( pt)

p p

w t SURF = ZONE,f − φ ZONE,f − − 1 + − α φ α

(A.17)

In this case, the initial condition is wSURF(t1), which is calculated from the ramping period 

equation for t = t1. This gives C = wSURF(t1), and the surface moisture content during the steadystate period becomes:

( ) ( ) ( )















− − 





 





 = + 1 − 1 t t

d

k

exp d

dw

w t

d

dw

w t

EMPD

surf

SURF ZONE ,f SURF φ ZONE ,f φ φ

φ 1 t > t (A.18)

This is converted to the cumulative moisture transfer by adding the total cumulative moisture 

transfer during the steady-state period (after time t1) to the cumulative moisture transfer at the 

end of the ramp period:

( ) ( ) ( ) ( ) ∫ 





 





 = + −

t

t

v,SURF v,SURF surf ZONE SURF t w t dt

d

dw M t M t k A

1

1 φ

φ (A.19)

Substituting in Eq. (A.18) for wsurf(t) and φZONE,f for φZONE(t), and simplifying leads to:

( ) ( ) ( ) ( ) ∫ 















− − 



 





 = + −

t

t EMPD

surf

v,SURF v,SURF surf EMPD ZONE,f SURF t t dt

d

k

w t exp d

dw M t M t k Ad

1

1 φ 1 1 φ (A.20)

Evaluating the integral from t1 to t gives the final equation for the cumulative moisture transfer to 

the surface layer for the steady-state period:
41

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

( ) ( ) ( ) ( ) 



 



















 − − − 





 





 = 1 + − 1 1 1 t t

d

k

w t exp d

dw M t M t Ad

EMPD

surf

v,SURF v,SURF EMPD φ ZONE,f SURF φ 1 t > t (A.21)

Deep-layer properties: The deep-layer properties are derived based on a moisture balance on 

the deep layer:

( ) k A(w (t) w (t)) dt

dw t

Ad deep surf deep

deep

EMPD−deep = − (A.22)

which can be rearranged to:

( ) ( ) w (t) d

k

w t

d

k

dt

dw t

surf

EMPD deep

deep

deep

EMPD deep

deep deep

− −

+ = (A.23)

Again, Eq. (A.5) is the solution to this differential equation. At this point, we simplify the 

equation by assuming that the surface layer absorbs moisture much more quickly than the deep 

layer. We have assured this to be true based on the definitions of the surface and deep layers: the 

surface layer becomes saturated after 12 hours; the deep layer becomes saturated after 168 hours. 

In other words, the resistance and capacitance of the surface layer affect only the first 7% of the 

absorption period for the deep layer. This has a minimal impact on our data analysis method (see 

Figure 23). Based on similar arguments, we also assume that the ramping period is negligible for 

the deep layer. These assumptions lead to:

( ) ( ) ZONE,f

EMPD deep

deep

deep

EMPD deep

deep deep

d

d

dw k

w t

d

k

dt

dw t

φ φ

− −

+ = (A.24)

We recognize this as the same form as the equation for the surface layer. Thus, the final equation 

for wdeep(t) and Mv,deep(t) are:

( ) 





























 − − 





 





 = + −

−

t

d

k

exp d

dw

d

dw

d

dw

w t

EMPD deep

deep

DEEP ZONE,f ZONE,f ZONE,i φ 1

φ φ

φ φφ (A.25)

( ) ( ) 





























 = − − −

−

− t

d

k

exp d

dw M t Ad

EMPD deep

deep

v,DEEP EMPD deep φ ZONE,f φ ZONE,i 1

φ (A.26)

Because the tests are measuring the absorption by both the surface layer and the deep layer, we 

compare the total moisture absorption to the data during the deep-layer tests. This total moisture 

absorption is:

( ) ( ) ( ) 





























 − = + − −

−

− t

d

k

exp d

dw M t M t Ad

EMPD deep

deep

v,TOTAL v,SURF EMPD deep φ ZONE,f φ ZONE,i 1

φ (A.27)