A comparison of measured indoor relative humidity data with results from predictive models

Publisher’s version / Version de l'éditeur:

Vous avez des questions? Nous pouvons vous aider. Pour communiquer directement avec un auteur, consultez la

première page de la revue dans laquelle son article a été publié afin de trouver ses coordonnées. Si vous n’arrivez

Questions? Contact the NRC Publications Archive team at

PublicationsArchive-ArchivesPublications@nrc-cnrc.gc.ca. If you wish to email the authors directly, please see the first page of the publication for their contact information.

https://publications-cnrc.canada.ca/fra/droits

L’accès à ce site Web et l’utilisation de son contenu sont assujettis aux conditions présentées dans le site LISEZ CES CONDITIONS ATTENTIVEMENT AVANT D’UTILISER CE SITE WEB.

Research Report (National Research Council of Canada. Institute for Research in Construction), 2007-05-22

READ THESE TERMS AND CONDITIONS CAREFULLY BEFORE USING THIS WEBSITE.

https://nrc-publications.canada.ca/eng/copyright

NRC Publications Archive Record / Notice des Archives des publications du CNRC :

https://nrc-publications.canada.ca/eng/view/object/?id=87611a33-e1d7-488f-8084-881f96e700cb https://publications-cnrc.canada.ca/fra/voir/objet/?id=87611a33-e1d7-488f-8084-881f96e700cb

Archives des publications du CNRC

For the publisher’s version, please access the DOI link below./ Pour consulter la version de l’éditeur, utilisez le lien DOI ci-dessous.

https://doi.org/10.4224/20377111

Access and use of this website and the material on it are subject to the Terms and Conditions set forth at

A comparison of measured indoor relative humidity data with results from predictive models

A C o m p a r i s o n o f M e a s u r e d I n d o o r R e l a t i v e H u m i d i t y

D a t a w i t h R e s u l t s f r o m P r e d i c t i v e M o d e l s

R R - 2 3 1

C o r n i c k , S . M . ; K u m a r a n , M . K .

J u n e

2 0 0 7

The material in this document is covered by the provisions of the Copyright Act, by Canadian laws, policies, regulations and international agreements. Such provisions serve to identify the information source and, in specific instances, to prohibit reproduction of materials without written permission. For more information visit http://laws.justice.gc.ca/en/showtdm/cs/C-42

Les renseignements dans ce document sont protégés par la Loi sur le droit d'auteur, par les lois, les politiques et les règlements du Canada et des accords internationaux. Ces dispositions permettent d'identifier la source de l'information et, dans certains cas, d'interdire la copie de documents sans permission écrite. Pour obtenir de plus amples renseignements : http://lois.justice.gc.ca/fr/showtdm/cs/C-42

A Comparison of Measured Indoor Relative Humidity Data with Results

from Predictive Models

National Research Council of Canada Institute for Research in Construction Research Report RR-231

Author:s S. M. Cornick. and M. K. Kumaran Research Officer

Date: May 24, 2007 Pages: 44

Table of Contents

Summary... 5

Introduction... 6

Interior Relative Humidity Models ... 7

European Indoor Class Model ... 7

BRE Model ... 9 ASHRAE 160P Method... 10 Field Measurements... 12 Prince Rupert BC ... 12 Inuvik NT... 14 Carmacks YT ... 14 CCHT Reference House ... 14 Modeling Assumptions ... 15

Determination of Ventilation Rates ... 15

Infiltration Model... 16 Stack-induced infiltration... 16 Wind-induced infiltration... 19 Combined infiltration... 19 Sensitivity Analysis ... 20 Error Analysis ... 22

Results and Discussion... 23

Overall Discussion... 23 Prince Rupert BC... 26 Inuvik NT... 27 Carmacks YT... 29 Ottawa ON ... 31 Conclusions... 35 Acknowledgements ... 35 Appendix... 36 References... 42

List of Figures

Figure 2 – Long-term mean monthly temperature for locations with field data. Sampling periods are boxed. ... 13

Figure 3 – Long-term mean monthly vapour pressure for locations with field data. Sampling periods are boxed... 13

Figure 4 – Typical example of the houses surveyed, a) Prince Rupert BC, b) Inuvik NT, and c) Carmacks YT. ... 15

Figure 5 – Comparing 24h running averages smoothes out the results but does not necessarily lead to decreased error (MBE and MAE). ... 23

Figure 6 – Sensitivity of the ASHRAE Intermediate and BRE models to variations in ventilation rates... 24

Figure 7 – Sensitivity of the ASHRAE Intermediate and BRE models to variations in moisture generation rates. ... 25 Figure 8 – Sensitivity of the BRE models to variation in the moisture transfer coefficient

and surface relative humidity... 26 Figure 9 – Comparison of the predictions of the four models with measured data over

time for house number 5 in Prince Rupert BC; a) bathroom, b) main floor storage room. ... 28 Figure 10 – Predicted versus measured data for each of the four models for both rooms of

house 5 in Prince Rupert BC... 29 Figure 11 – Comparison of the predictions of the four models with measured data over

time for house number 3 in Inuvik NT; a) bathroom, b) kitchen... 30 Figure 12 – Predicted versus measured data for each of the four models for both rooms of

house 3 in Inuvik NT. ... 31 Figure 13– Comparison of the predictions of the four models with measured data over

time for house number 5 in Carmacks YT; a) living room, b) kitchen... 32 Figure 14 – Predicted versus measured data for each of the four models for both rooms of

house 5 in Carmacks YT... 33 Figure 15 – Comparison of the predictions of the four models with measured data over

time for the CCHT reference house in Ottawa ON; a) main floor, b) second floor. 34 Figure 16 – Predicted versus measured data for each of the four models for both floors of

List of Tables

Table 1 – Residential design moisture generation rates from ASHRAE 160P... 11

Table 2 – Basic geographic and climate data for locations with field data. ... 14

Table 3 – Physical characteristics of the eight houses surveyed in Prince Rupert BC. .... 17

Table 4 – Physical characteristics of the eight houses surveyed in Inuvik NT... 17

Table 5 – Physical characteristics of the eight houses surveyed in Carmacks YT. ... 18

Table 6 – Physical characteristics of CCHT, Ottawa ON... 18

Table 7 – Parameters for Standard Terrain Classifications. ... 20

Table 8 – Local Shielding Parameters. ... 20

Table 9 – Shielding parameters used for this study. ... 20

Table 10 – Variations in kn and RHsN for a sensitivity analysis... 21

Table A 1 – Errors from measured data from the Prince Rupert BC houses for the four different models tested... 36

Table A 2 – Errors from measured data from the Inuvik NT houses for the four different models tested... 38

Table A 3 – Errors from measured data from the Carmacks YT houses for the four different models tested... 40

Table A 4 – Errors from measured data from the CCHT reference house in Ottawa ON for the four different models tested... 42

A Comparison of Measured Indoor Relative Data with Results

from Predictive Models

S. M. Cornick and M. K. Kumaran

Institute for Research in Construction, National Research Council Canada, 1200 Montreal Road, Building M24, Ottawa, ON, K1A 0R6.

Summary

Building simulation models, such as HAM models, require information on the interior boundary conditions. It is important to properly model the interior conditions if meaningful conclusions are to be drawn from modeling studies. When measured data is available it can be used directly as input for the interior boundary conditions. More generally however information or measurements on interior conditions are lacking and interior conditions and are often simulated using predictive models. The focus of this study was to examine the reliability of models that are available in the open literature for simulating the interior moisture conditions, comparing the predicted interior relative humidity to measured data. Four models, for predicting the indoor relative humidity in houses were tested against measured relative humidity data for 25 houses. The models considered were primarily developed as design tools. The models tested were the European Indoor Class Model, the BRE model, and the ASHRAE 160P simple and intermediate models. The RH in each house was measured in two different locations producing 50 data sets. The houses were typical of older North American construction methods. In assessing the models it should be noted that only 1 month of measured data used for comparison with predicted results. The month used was typical of the most extreme conditions occurring at the measurement sites. Hourly predictions were made using the four models and compared with the average hourly observations.

The ASHRAE intermediate model seemed to be the most robust exhibiting lower errors when compared to measured data. The European Indoor Class also performed well and can be used when data regarding moisture generation and/or air change rates is not available. As a design tool however it is not universally conservative in estimating the indoor RH. The BRE is problematic and generally exhibits large positive errors for most of the houses surveyed. It was found to be not reliable for the North American houses investigated in the comparisons. This model should be used with caution as the α and

β coefficients are probably not appropriate for the type of houses monitored, as was noted by Jones. The ASHRAE simple model also exhibited large positive errors and does not trend well with the measured conditions. This model was developed for design purposes and should be used as last resort even as a design tool. For colder climates the model overestimates of the design RH. Models that greatly overestimate the design loads should be used with caution as they may lead to complicated inefficient designs. For models that use ventilation rates as a primary input it is imperative that these be determined accurately, as these models are very sensitive to changes in the ventilation rates especially at lower range.

Introduction

There is a current trend in modeling and simulation to consider the performance of the whole building. Simulations can be conducted for a variety of reasons including design of building envelopes, performance assessment, and forensic or research investigations. When simulations are used for design the loads should be conservative to provide a factor of safety. If however the design loads are greatly overestimated there is a potential to winnow the choice of designs leading to over designed, inefficient, complex, and costly designs. When using simulation tools to investigate the performance of the building envelope or investigative work the setting of the exterior and interior boundary conditions are critical. Exterior boundary conditions are generally obtained from various sources of weather or climatic data and are not considered here. When considering the performance of the building envelope two important interior conditions are the temperature and the moisture content of the interior air. The interior moisture load plays an important role in occupant comfort, health and safety, as well the durability of the building envelope. For example, the effect of inside air relative humidity on the performance of the envelope has been analysed by Ojanen et. al. [1, 2, 3, 4]. Numerical analyses for air exfiltration cases suggest a significant effect of the inside air relative humidity, greater than the air-leakage rate, on the accumulation of moisture in walls in cold climates. The indoor conditions for these studies were held constant. These studies demonstrated the importance of properly modeling the interior conditions if meaningful conclusions are to be drawn from modeling studies. When measured data are available it can be used directly as input for the interior boundary conditions. More generally, however, information on measurements of interior conditions is lacking and is often simulated using predictive models. Often the interior boundaries conditions are modeled by either assuming constant conditions or using the simple HVAC set points. More detailed models simulating the interior conditions are available. These models use readily available data, such as the ambient temperature and atmospheric moisture content, occupancy and use information, in addition to some basic building characteristics.

The focus of this study was to examine the reliability of four selected models for simulating the interior moisture conditions comparing the predicted interior relative humidity to measured data. The measured field data were obtained from four locations in three very different climate conditions. The climate types were; 1) a cool marine type climate (Prince Rupert British Columbia), 2) a very cold (arctic) type climate (Inuvik Northwest Territories and Carmacks Yukon Territory), and 3) a typical temperate continental climate (Ottawa Ontario). The type of buildings and occupancies considered here were residential; all single-family homes were either fully detached or row houses. The interior temperature and relative humidity of the surveyed houses were monitored as part of project to examine engineered building envelope systems to accommodate high performance insulation with outdoor/indoor climate extremes. A summary of the field measurement protocol, results and analysis, is provided by Rousseau et. al.[5].

Interior Relative Humidity Models

Models that predict the interior relative humidity conditions inside occupied spaces must account for the contribution and removal of moisture from the interior. In general the models must account for the contribution of the occupant’s respiration, perspiration, and activities that add moisture to the space; washing and cooking for example. Account must be made of the contribution due to ventilation and air leakage from the exterior environment, i.e. exterior air. Removal of moisture through ventilation or air leakage must also be taken in to consideration when estimating the moisture balance. Other factors affecting the indoor relative humidity include but are not limited to humidification and dehumidification. “Accidental” sources, such as rainwater penetration are generally not considered.

Tsuchiya[6] extended indoor relative humidity models by considering the absorption and desorption by the materials comprising the building interior surfaces. Tsuchiya’s model was reviewed by Kusuda [7] and demonstrated good concurrence with measured results and model predictions.

Many procedures have since been proposed to predict the indoor relative humidities. Jones [8] surveyed several interior RH models. Essentially all the models reviewed by Jones are variations on Tsuchiya’s [6] equations. Some such as the BRE model [9] include a moisture generation rate, a ventilation component, and absorption/desorption component. Others simplify by combining the various components into constants that are based on surveys of many houses.

Of the procedures for calculating indoor relative humidities four models were considered in the present work. The criteria for selection were ease of application and availability of climatic data. The four models selected were:

1. BRE model [9]

2. European Indoor Class Models10 (CEN 2005) 3. ASHRAE 160P Model [11]

4. ASHRAE 160P Simplified Method [11]

European Indoor Class Model

The Class model [10] is fairly straightforward. It assumes that the amount of atmospheric moisture indoors, expressed in terms of vapour pressure, is a function of the outdoor vapour pressure. Depending on the class of the building to be modeled a specified amount of internally generated moisture is added to the external vapour pressure. The amount of additional moisture load is modified according to the mean monthly ambient temperature, accounting for the effect of air changes. At colder temperatures the moisture surcharge is assumed to be at maximum while for warmer temperatures ventilation is assumed to remove most of the internally generated moisture. Between the two temperature thresholds linear interpolation is used to determine the moisture surcharge. The model is described below.

100 ) ( ) ( 100 ) ( ) ( sat e sat i i p p p p p ₌ +Δ = ϕ (%) Equation 1 Where: ϕi is the indoor RH in %

pi is the indoor vapour pressure, Pa

psat is the indoor saturation vapour pressure, Pa

pe is the outdoor vapour pressure at the mean monthly temperature, Pa

Δp is the indoor-outdoor vapour pressure difference (pi - pe) for the class

of building in question, Pa

The procedure defines five classes of buildings. The classes represent different levels of moisture generation rates related to the occupancy and use of the building. The classes are:

1. Class 1 – very low moisture generation (e.g., storage areas, warehouses) 2. Class 2 – low moisture generation (e.g., offices or shops)

3. Class 3 – moderate moisture generation (e.g., dwellings with low occupancy) 4. Class 4 – high moisture generation (e.g., dwellings with high occupancy,

sports halls, kitchens, canteens; buildings heated with gas heaters and no flues)

5. Class 5 – very high moisture generation (e.g., swimming pools; laundries; breweries)

The main model inputs are the mean monthly temperature, T_Month °C, and the class of the building based on use and occupancy, Classn. More information on this model is given by

Djebbar [12], Sandberg [13], and ISO [10]. The indoor/outdoor vapour pressure gradient Δp, (pi - pe), can be determined from Figure 1. A simple method for determining Δp used

to program the Class Model is as follows: 0

=

Δp Pa if mean monthly outdoor temperature is greater than 20ºC

(

)

270 −

=

Δp Class_n Pa if the mean monthly outdoor temperature is below 0ºC

(

)

(

)

270 − − −

=

Δp Class_n T_Month Class_n Pa if the mean monthly outdoor

0 270 540 810 1080 -10 -5 0 5 10 15 20 25

Mean Monthly Temperature, ºC

Indoor-Outdoor Vapour Pressure Gradient

Δ

p, Pa

Class 1 Very Low Class 2 Low Class 3 Moderate Class 4 High Class 5 Very High

Typical Winter Conditions

Figure 1 – Moisture surcharge to be added to external vapour pressure for predicting indoor RH.

BRE Model

The BRE Model is based on the mass difference between the moisture generation rate and the moisture gain or loss due to ventilation. Moisture absorption and desorption by interior finishes and furnishings are accounted for by a moisture admittance model. Jones [9] describes the BRE model. The indoor vapour pressure can be calculated using the following equation:

(

) (

[

)(

)

]

(

)

pi is the interior vapour pressure, Pa pe is the exterior vapour pressuree, Pa

psat is the saturation vapour pressure of the interior, Pa

ptot is the total mix pressure, assume 100 KPa, 1000 mb, or 100, 000 Pa I is the ventilation rate, Air Changes/h

Qg is the moisture generation rate, kg/h v is the volume of the room, m3

ρair is the density of air; assumed to be 1.2 kg/m3

The ventilation rate can be calculated from:

v Q

I = total _{…Air changes/h Equation 3}

Where:

Qtotal is the total volumetric flow rate of air into the space, m3/h v is the volume of the room or building. m3

Finally the indoor relative humidity is simply calculated as the ratio of the indoor vapour pressure and the indoor saturation vapour pressure at the indoor temperature.

100 sat i i p p = ϕ …(%) Equation 4 Where: ϕi is the indoor RH, (%)

pi is the vapour pressure of the interior, Pa

psat is the saturation vapour pressure of the interior, Pa

The main model inputs are 1) the average moisture generation rate, 2) the average air change rate, 3) the volume of the space, 4) the average interior and exterior hourly temperatures, 5) the average hourly exterior vapour pressure mean monthly temperature, and 6) the moisture admittance factors, α and β. More information on this model is given by Jones [9], Christian [14], Djebbar [12], Loudon [15], El Diasty [16], and Oreszczyn [17]. The BRE model is fairly simple to code and is easily implemented in a spreadsheet application.

ASHRAE 160P Method

ASHRAE Standard 160P, Design Criteria for Moisture Control in Buildings [11], is a proposed standard that specifies the criteria for performance-based design and mitigating moisture damage to the building envelope. Part of the standard specifies the criteria for inputs to various calculation procedures and simulation tools. The proposed standard has three procedures for calculating the indoor relative humidity, 1) the simplified method, 2) the intermediate method, and 3) the full parameter method, which is not addressed here. The houses surveyed did not feature designed mechanical ventilation, rather ventilation equipment was manually operated with the expectation furnace fans. Similarly since the sampling period was during the winter, cooling the dehumidification equipment if present, was not operating [11]. Two paths outlined in 160P were followed, the Indoor

Design Humidity, Simplified Method (Simple method) and Indoor Design Humidity

without Dehumidification or Air-conditioning (Intermediate method). The simplified method is given below.

ϕi = 40% if To,daily <= -10°C

40% + (To,daily + 10) if -10°C< To,daily<20°C…(%) Equation 5 70% if To,daily => 20°C

Where:

ϕi is the indoor RH, (%)

To,daily is Daily average outdoor temperature. °C

The intermediate method is outlined below.

n ventilatio h o i Q m c p p • + = _,24 …(Pa) Equation 6 Where

pi is the indoor vapour pressure, Pa

po,24h is the 24-hour running average outdoor vapour pressure, Pa

c is a constant equal to 1.36 x105 m2/s2

•

mis the design moisture generation rate, kg/s

Qventilation is the design ventilation rate, m3/s

Design values for residential moisture generation

•

m are based on the expected number of occupants. For design purposes a minimum of two occupants is assumed, with an additional occupant for each bedroom in addition to the master bedroom. Design moisture generation rates are given in Table 1 below from ASHRAE 160P [11]. The ventilation rate can be determined from the air change rate.

3600

Iv

Q_ventliation = …m3/s Equation 6

Where:

I is the ventilation rate, using the ASHRAE Simplified residential model [18], Air Changes/h

v is the volume of the building, m3

Table 1 – Residential design moisture generation rates from ASHRAE 160P

Number of

Occupants

Moisture generation rate

1 bedroom 2 8 L/day 0.9 x 10-4 kg/s

2 bedrooms 3 12 L/day 1.4 x 10-4 kg/s

3 bedrooms 4 14 L/day 1.6 x 10-4 kg/s

4 bedrooms 5 15 L/day 1.7 x 10-4 kg/s

Additional bedrooms per additional bedroom

The main model inputs are for the simplified method the daily average outdoor temperature and for the intermediate method: 1) the average moisture generation rate, 2) the average ventilation rate, 3) the volume of the space, 4) the average interior hourly temperature, and 5) the 24 hour running exterior vapour pressure.

Field Measurements

In 2005 and 2006, surveys of indoor and outdoor conditions of relative humidity and temperature in twenty-four Canadian houses were carried out [5]. This activity was part of a project to develop durable, energy-efficient wall assemblies that can accommodate extreme outdoor and indoor climates in Canadian northern coastal and in northern regions [19]. The surveys were carried to help in defining the effect of factors such as outdoor climate, occupant’s activities and house characteristics on the levels of indoor temperature and relative humidity. The data collected will be used for numerical modeling and laboratory studies to predict the hygrothermal response of promising wall assemblies. The three locations surveyed were Prince Rupert BC, Inuvik NT and Carmacks. YT. For two of the locations local airport weather data was available as well. For Carmacks YT the meteorological station at the Whitehorse YT airport was used as a surrogate station. A fourth set of interior temperature and relative humidity conditions was obtained from the Canadian Center for Housing Technology (CCHT) [20] reference house, located in Ottawa ON. A meteorological station located at the Institute for Research in Construction as well as local airport data was available for the analysis. Some basic information and climate parameters for these locations are given in Table 2, Figure 2 and Figure 3.

For each of the twenty-four houses hand-size relative humidity and temperature sensors and data loggers were placed in two areas (usually a bathroom and another location) of the tenant living spaces for a month period, capturing conditions every three minutes. Hourly averaged values for temperature and relative humidity were used for this analysis. One similar sensor was placed outside one of the houses in each region surveyed. The instruments were calibrated before being deployed and checked again after the survey program was completed. Half of the houses experienced moisture problems, ranging from condensation on window glass and frame to mould growth on interior finish. Information on the field measurements for the PERD-79 project can be found in Rousseau et. al. [5].

Prince Rupert BC

Eight houses in Prince Rupert BC were monitored. The survey sample included only two-storey row housing constructed in the 1980’s. Half the houses were reported to exhibit moisture related problems. The results of the field monitoring for these houses is given in Report B1239.1.1 “Summary of the Prince Rupert Monitoring,” [5]. The house characteristics are given in Table 3. A typical example is shown in Figure 4 a).

Long-term Mean Daily Temperatures -30.0 -20.0 -10.0 0.0 10.0 20.0 30.0

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Temperature, °C Prince Rupert A Inuvik A Ottawa A Carmacks CS* Surrogate Sampling periods

Figure 2 – Long-term mean monthly temperature for locations with field data. Sampling periods are boxed.

Long-term Mean Daily Vapour Pressure

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

Average Vapour Pressure, Kpa Prince Rupert A

Inuvik A Ottawa A

Carmacks CS* Surrogate Sampling periods

Figure 3 – Long-term mean monthly vapour pressure for locations with field data. Sampling periods are boxed.

Table 2 – Basic geographic and climate data for locations with field data.

Station Name CARMACKS CS* INUVIK A PRINCE RUPERT

AWOS

Ottawa A

Province Yukon Territory Northwest Territories British Columbia Ontario

Latitude 62.12 68.3 54.29 45.32 Longitude -136.19 -133.48 -130.44 75.67 Elevation, m 542.9 68.3 35.4 114 Annual Mean, ºC -0.7* -8.8 7.1 6 Annual Max, ºC. 4.5* -3.9 10.5 10.9 Annual Min., ºC -5.9* -13.6 3.8 1.1 Mean Annual Precipitation, mm 267.4* 248.4 2593.6 943.5

Mean Annual Wind Speed, Km/h

12.7* 9.7 13.1 12.9

* – Whitehorse A was used a surrogate station for Carmacks CS for long-term data and RH.

Inuvik NT

Eight houses in Inuvik were monitored. The survey sample included a mix of row housing and fully detached houses. The homes were also a mix of single and two-storey homes constructed between 1975 and 1986. Half the houses were reported to exhibit moisture related problems. The results of the field monitoring for these houses is given in Report B1239.1.2 “Summary of the Inuvik Monitoring” [5]. The house characteristics are given in Table 4. A typical example is shown in Figure 4 b).

Carmacks YT

Eight houses in Carmacks were monitored. The survey sample included only one-storey single and fully detached houses, although one was a mobile home. Two of the homes were constructed in the late 1970’s. The remaining houses were constructed after 1995. Half the houses were reported to exhibit moisture related problems. The results of the field monitoring for these houses is given in Report B1239.1.3 “Summary of the Carmacks Monitoring” [5]. The house characteristics are given in Table 5. A typical example is shown in Figure 4 c).

CCHT Reference House

The Canadian Center for Housing Technology [20] features twin research houses to evaluate the whole-house performance of new technologies in side-by-side testing. One house is used to test research hypotheses while the other is maintained as a reference. Data for this study was obtained from the reference house. Both houses are intensively monitored with simulated occupancy profiles. The houses are equipped with a data acquisition system consisting of over 250 thermocouples, 9 RH sensors, and 23 meters (gas, water and electrical) that capture a detailed history of the house performance in terms of temperature, humidity and energy and water consumption. The sensors are read every 5 minutes. A complete set of weather data is available from a nearby weather

tower. Weather data are collected at 10-minute intervals. The house characteristics are given in Table 6.

(a) (b) (c)

Figure 4 – Typical example of the houses surveyed, a) Prince Rupert BC, b) Inuvik NT, and c) Carmacks YT.

Modeling Assumptions

The following assumptions were made in applying the models tested:

1. The entire house volume is being modeled not the individual rooms. It is more common in survey information of this type to have gross measurements and not the areas of individual rooms.

2. The air change rate and or ventilation rates apply to the whole volume of house. As well the air leakage through the envelope is assumed to occur at a constant rate per area through the floor, exterior walls, and ceiling. The air change rate was based on the method given by ASHRAE [18]. (See below)

3. The moisture generation rate, determined from the occupancy using slightly modified rates from ASHRAE 160P are assumed to apply to the whole volume. The use and occupancy needed for the Class Models are assumed to apply to the whole volume of the house.

4. The interior temperature of the space is the temperature at sensor.

5. The exterior temperature and atmospheric moisture is measured locally using the exterior sensor. Local airport data were used where appropriate if available.

Determination of Ventilation Rates

In order to use the BRE and ASHRAE 160P models it was necessary to estimate the hourly air change rate (ACH) or ventilation rate, Qventilation, for each of the houses. For the

Class Models a qualitative assessment of the use and occupancy was all that was required. The LBL model was used in this work, a simplified version of which is given in the ASHRAE Handbook of fundamentals [18]. The original model can be found in a paper by Sherman and Grimsrud [21]. There was no continuously operated mechanical ventilation for the surveyed houses, except for the CCHT reference house. The basic model is presented below.

Infiltration Model

Stack-induced infiltration

The stack-induced infiltration was calculated from the following formulas.

0 * T T Lf Q_s = _{s i}− m3/s Equation 7 i s s f gH T f* = / Equation 8

( )(

)

_[

[

]

_]

Alternatively, if the neutral pressure is not known, fs is also defined by:

( )(

)

₍

₎

(

)

(

)

Qs = infiltration flow rate due to stack effect, m3/s L = effective leakage area of the house @ 4 Pa, m2 Ti = indoor temperature, K

To = outdoor temperature, K fs = dimensionless stack parameter f*s = reduced stack parameter, √m2/s2/ K g = acceleration due to gravity, 9.806 m/s2

H = house height (distance from grade to upper ceiling), m βo = ratio of the neutral pressure height to house height, h = height of the neutral pressure level above grade, m

R = fraction of the total effective leakage area located in the floor and

ceiling of the house,

X = difference between the fractions of the total effective leakage area

located in the ceiling and the floor,

Lc = effective leakage area in the upper ceiling, m2

Table 3 – Physical characteristics of the eight houses surveyed in Prince Rupert BC.

Location a Location b Heating System Ventilation Class Volume m3 _{ACH @}

50 Pa Occupancy Moisture Generation Rate (ASHRAE 160P) L/day, Kg/day ACH (ASHRAE) Qventilation, m3/h α, β

House 1Main Floor Closet

Upstairs Bedroom Electric Baseboard

Kitchen - Manual, Bathroom - humidistat.

3 267 5.01 2 8 0.431 115.02 0.6, 0.4

House 2 Bathroom Main Floor Storage

Hydronic Kitchen - Manual,

Bathroom - humidistat.

3 244 7.35 3 12 0.649 158.25 0.6, 0.4

House 3 Bathroom Unknown Electric

Baseboard

Kitchen and Bathroom, manual

3 250 6.3 8 19 0.549 137.23 0.6, 0.4

House 4 Bathroom DHW Tank Room Electric Baseboard

Kitchen - Manual, Bathroom - humidistat.

3 254 6.2 6 17 0.534 135.61 0.6, 0.4

House 5 Bathroom Main\Floor

Storage

Hydronic Kitchen - Manual,

Bathroom - humidistat.

3 234 9.9 2 8 0.813 190.26 0.6, 0.4

House 6 Entrance Closet Bathroom Unknown Kitchen - Manual 3 210 6.36 3 12 0.548 115.16 0.6, 0.4

House 7 Bathroom Entrance Closet Electric Baseboard

Kitchen - Manual 3 251 5.3 4 14 0.459 115.25 0.6, 0.4

House 8 Coat Closet Bathroom Electric Baseboard

Kitchen - Manual 3 225 6.7 2 8 0.509 114.60 0.6, 0.4

Table 4 – Physical characteristics of the eight houses surveyed in Inuvik NT.

Location a Location b Heating System Ventilation Class Volume m3 _{ACH @}

50 Pa Occupancy Moisture Generation Rate (ASHRAE 160P) L/day, Kg/day ACH (ASHRAE) Qventilation, m3/h α, β

House1 Bathroom Kitchen Hydronic/Gas Kitchen and Bathroom, manual

3 172 6.88 4 14 0.542 93.47 0.6, 0.4

House 2 Bathroom Kitchen Hydronic/Gas Kitchen and Bathroom, manual

3 367 3.6 5 15 0.425 155.85 0.6, 0.4

House 3 Bathroom Kitchen Hydronic/Gas Kitchen and Bathroom, manual

3 231 6.29 3 12 0.53 122.46 0.6, 0.4

House 4 Bathroom Kitchen Hydronic/Gas Kitchen and Bathroom, manual

3 264 10.37 5 15 1.08 285.12 0.6, 0.4

House 5 Bathroom Kitchen Hydronic Kitchen and Bathroom, manual

3 243 10.88 3 12 0.854 207.49 0.6, 0.4

House 6 Kitchen Bathroom Forced Air/Gas Kitchen and Bathroom, manual

3 274 12.22 3 12 1.06 290.10 0.6, 0.4

House 7 Bathroom Kitchen Forced Air/Gas Kitchen and Bathroom, manual

3 225 12.25 5 15 1.27 286.04 0.6, 0.4

House 8 Kitchen Bathroom Hydronic Kitchen and Bathroom, manual

Table 5 – Physical characteristics of the eight houses surveyed in Carmacks YT.

Location a Location b Heating System Ventilation Class Volume m3 _{ACH @}

50 Pa Occupancy Moisture Generation Rate (ASHRAE 160P) L/day, Kg/day ACH (ASHRAE) Qventilation, m3_/h α, β

House 1 Bedroom Storage Room Wood Stove Kitchen - Manual 3 344 7.8 6 17 _{0.78 268.78} 0.6, 0.4

House 2 Living Room Bathroom Wood Stove Kitchen - Manual 3 238 19 1 3 _{1.29 307.44} 0.6, 0.4

House 3 Bedroom Kitchen Wood Stove Kitchen - Manual 3 183 9.6 3 12 _{1.30 238.33} 0.6, 0.4

House 4 Kitchen Bedroom Wood Stove Kitchen - Manual 3 193 13.6 2 8 _{1.23 237.24} 0.6, 0.4

House 5 Kitchen Living Room Wood Stove Kitchen - Manual 3 204 8.9 5 15 _{1.24 251.97} 0.6, 0.4

House 6 Kitchen Hall Wood Stove Kitchen - Manual 3 157 12 4 14 _{1.45 227.60} 0.6, 0.4

House 7 Kitchen Living Room Wood Stove Kitchen - Manual 3 195 7.9 2 8 _{1.12 217.76} 0.6, 0.4

House 8 Kitchen Living Room Oil/Forced air Kitchen - Manual 3 196 5 6 17 _{0.40 77.47} 0.6, 0.4

Table 6 – Physical characteristics of CCHT, Ottawa ON.

Location a Location b Heating System Ventilation Class Volume m3 _{ACH @}

50 Pa Occupancy Moisture Generation Rate (ASHRAE 160P) L/day, Kg/day ACH (ASHRAE) Qventilation, m3/h α, β

CCHT Main Floor Second Floor Gas/Forced air Heat recover ventilator @ 35 L/s supply

2 790 1.611 1* _{3 0.204 161.05 0.6, 0.4}

For the surveyed houses the effective leakage area at 4 Pa, L, was calculated from the C and n coefficients derived from blower fan door tests carried out on each house. The indoor temperature, Ti, was assumed to be 21ºC while the outdoor temperature, To, was

the mean ambient temperature during the sampling period. The house height, H, was taken as the floor to ceiling height reported by the contractor. There was no information on the level of the neutral pressure plane consequently the stack parameter was based on the ratios of the gross floor, ceiling, and exterior wall areas reported by the contractor assuming constant leakage through all the surface areas.

Wind-induced infiltration

The wind-induced infiltration was calculated from the following formulas.

' * U Lf Q_w = _w m3/s Equation 11 t w C R f f* = _'(1− ₎(1/3) Equation 12 ' ) / ' ( ' ) / ( γ γ α α ref ref t H H H H f = Equation 13 Where:

Qw = infiltration flow rate due to wind, m3/s U’ = measured wind speed, m/s

f*w = dimensionless reduced wind parameter, ft = terrain factor, dimensionless,

C’ = generalized shielding coefficient for the house, H is the height of the building or point of interest, m, H’ is the wind speed measurement height, m,

Href is a reference height, m

α, γ are the terrain parameters for the building site, α’, γ’ are the terrain parameters for the measurement site.

For the surveyed houses the measured wind speed, U’, was taken from climate normal data for the month. If the measurement period split two months the average of the two months was taken. The assumed measurement and reference heights, H’ and Href, were 10

m. The height of interest was assumed to be the house height; H. Table 7 and Table 8 define the shielding and terrain parameters for modifying the reference wind speed. The shielding and terrain parameters used for calculating the wind-induced infiltration are given in Table 9.

Combined infiltration

Finally the combined stack- and wind-induced infiltration and the contribution from mechanical ventilation can be estimated from:

2 2 2 v w Q Q Q Q s + + = m3/s Equation 14 Where:

Q = total combined infiltration flow rate for the house, m3/s

Qv = mechanical ventilation term, m3/s.

Table 7 – Parameters for Standard Terrain Classifications.

Class γ α Description

I 0.10 1.30 Ocean or other body of water with at least 5km of unrestricted expanse

II 0.15 1.00 Flat terrain with some isolated obstacles (buildings or trees well separated)

III 0.20 0.85 Rural areas with low buildings, trees, etc.

IV 0.25 0.67 Urban, industrial, or forest areas

V 0.35 0.47 Center of large city

Table 8 – Local Shielding Parameters.

Class C’ Description

I 0.324 No obstructions or local shielding

II 0.285 Light local shielding with few obstructions

III 0.240 Moderate local shielding, some obstructions within two house heights

IV 0.185 Heavy shielding, obstructions around most of the perimeter

V _{0.102 Very heavy shielding, large obstructions surrounding the perimeter within two}

house heights.

Table 9 – Shielding parameters used for this study.

Location Local shielding, C’ Terrain, α Terrain γ Terrain, α’ Terrain γ’

Prince Rupert BC III IV IV III III

Inuvik NT II III III III III

Carmacks YT III III III III III

Ottawa ON III III III III III

Sensitivity Analysis

Two models, the BRE and ASHRAE intermediate models, were investigated for sensitivity to input parameters. Parameters common to both models, the ventilation rate (ACH) and the moisture generation rate were varied to examine the changes in MBE from the measured results. As well for the BRE model the sensitivity of the model to the moisture admittance factors, α and β, was investigated

In examining the sensitivity to air leakage the moisture generation rates and the moisture admittance factors were kept the same as in the main study. These can be found in Table 3, Table 4, Table 5, and Table 6. The ventilation rate was varied from 0 to 16 ACH, doubling the rate in each step (0, 0.5, 1, 2, 4, 8, and 16). The MBE was calculated for each room for each step. The effect of changing the moisture generation rate was examined in a similar fashion. The air leakage rates and the moisture admittance factors

were kept the same as in the main study. The moisture generation rate was varied from 0 to 20 Kg/day, incrementing the rate in steps of 4 Kg/day (0, 4, 8, 12, 16, 20, and 16). The sensitivity of the BRE model to the moisture admittance factors, α and β, requires some further elaboration. The desorption coefficient, β, was linked to the absorption coefficient α (see the Equations below).

v A k_{n n} ρ α =

∑

∑

kn is the mass transfer coefficient at the surface of surface n, Kg/m2·h An is the surface area of surface n, m2

ρ is the density of air (assume 1.2), Kg/m3,

v is the volume of the space, m3

RHsN is the surface relative humidity at surface n.

kn, An, and RHsN refer to areas of like materials. For this study all the materials were

assumed to be similar. Thus the relationship of β to α is reduced to:

β = RHsNα Equation 17

The basic input parameters for calculating the moisture admittance factors are then, the moisture transfer coefficient, the surface relative humidity, the surface area and the volume of the space. The volume of the spaces is given in Table 3, Table 4, Table 5, and Table 6. An estimate of the surface area was obtained by assuming a 2 to 1 aspect ratio for the floor plan. The storey height was assumed to be either 4.9 m for a two-storey house or 2.45 m for a bungalow. For both Prince Rupert and Carmacks house #5 was used for the sensitivity analysis, while for Inuvik house #3 was used. Jones [9] suggested a range of possible values for the mass transfer coefficient. The variations for kn and RHsN

are given in Table 10. When varying the moisture transfer coefficient the surface relative was held at a constant value of 0.7. Similarly while varying the surface relative humidity the moisture transfer coefficient was assumed to be 0.5 Kg/m2·h. Thus for each house a pair of moisture admittance factors can be generated for each variation in the moisture transfer coefficient and surface relative humidity.

Table 10 – Variations in kn and RHsN for a sensitivity analysis.

Parameter Values

RHsN 0.3 0.5 0.7 0.9

Error Analysis

In analysing the reliability of the selected models several error measures were used, specifically the mean bias and mean absolute error, the root mean squared error, the root mean squared systematic and unsystematic error, and the normalized root mean squared error. The definition of these error measured are given below.

P = Mean of the predicted hourly averages [RΗ%]. O= Mean of the observed hourly averages [RΗ%].

MBE = Mean Bias Error or the first moment of the distribution of differences. This shows

the general bias of the model predictions [RΗ%].

i n i i O P n MBE=

∑

MAE = Mean Absolute Error. This gives the average difference between Predicted and

Observed values without respect to over or under prediction [RΗ%].

i n i i O P n MAE=

∑

RMSE = Root Mean Square Error [RΗ%].

(

)

∑

RMSEs and RMSEu = Systematic & Unsystematic RMSE - these describe the proportion

of error attributable to systematic errors (those contained within the model) whilst unsystematic errors are generally 'noise'. In a 'good' model RMSEs should approach zero

[RΗ%].

(

)

∑

(

)

∑

∑

∑

NMSE = Normalised Mean Square Error [RΗ%].

(

)

∑

Results and Discussion

Overall Discussion

Generally the models track the indoor conditions except that the hourly variations are not captured. This is due to the fact that the moisture generation rates and ventilation rates are specified as average rates. A seemingly better trend is observed when running twenty-four averages for observed and predicted values are compared. In some circumstances this reduced the errors (MAE, MBE, and RMSE) but it did not change the overall bias of the models (See Figure 5). Another way of achieving better results would be to include variations in the moisture generation and air change rates. This however presumes that much more information is available, such as wind speed and direction or the occupant’s schedules and habits. This was not investigated.

Carmacks YT; House 5

0 10 20 30 40 50 60 70 80 90 100 1/_13/ 06 0: 00 1/_18/ 06 _0: 00 1/ 23/₀₆ 0:0 0 1/₂₈ /0 6 0:0 0 2/2/_{06 0:00} 2/7/₀₆ 0:00 2/_12/ 06 0: 00 2/_17/ 06 0: 00 2/_22/ 06 0:0 0 2/ 27/₀₆ 0:0 0 Time, h RH, % Observed BRE Model BRE 24 running avg. Observed 24 running avg.

Living Room

Figure 5 – Comparing 24h running averages smoothes out the results but does not necessarily lead to decreased error (MBE and MAE).

Overall the models examined have tendency to overestimate the indoor conditions except for the Class model, which for the houses surveyed over or underestimates depending on the house. The ASHRAE intermediate model seemed to perform the best in terms of MBE, MAE, and RSME. Of the parameters used in this model the most sensitive parameter is the ventilation rate. Large changes occur over a small range of ventilation rates at the lower range (see Figure 6). Larger ventilation rates tend to bring the indoor air to outdoor conditions and the error trends towards a constant value with increasing ventilation rates. The ASHRAE intermediate model is less sensitive to changes in the moisture generation rates, especially at high ventilation rates (see Figure 7).

-40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ventilation rate, air changes/h

M

ean bias error, %RH

ASHRAE Intermediate Model BRE Model

Figure 6 – Sensitivity of the ASHRAE Intermediate and BRE models to variations in ventilation rates.

The Class model performs surprisingly well for such a simple model. This was probably due to the fact that most houses monitored were close to the average house characteristics on which the Class model is based. The closer the house to the typical surveyed house the better the result, except for the CCHT reference house. The CCHT reference house was built to a high level of energy efficiency and consequently is very tight house from an air leakage perspective. This house is probably far from the typical house used in developing the Class model.

-40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00 0 2 4 6 8 10 12 14 16 18 20

Moisture generation rate, kg/d

Mean bias error, %RH

ASHRAE Intermediate Model BRE Model

1.24 ACH 0.204 ACH

Figure 7 – Sensitivity of the ASHRAE Intermediate and BRE models to variations in moisture generation rates.

The BRE model generally overestimates and is clearly problematic. This can be seen by examining the formulation given in Equation 2. Suppose that the contribution of the exterior environment and the moisture generation were zero – the first and second terms in Equation 2. The last term represents the contribution of the interior surfaces and in this case is the only contributing factor to the interior RH. The values of α = 0.6 and β = 0.4 were suggested by Jones [9]. The range of calculated air change rates in the monitored houses was from 0.204 to 1.45. Thus the contribution of this term in the BRE model ranges from 0.50psat (50% RH) to 0.20 psat (20% RH). This represents a baseline relative

humidity regardless of the contribution of the occupants or the exterior air. For the houses in Inuvik and the CCHT reference house this baseline RH was already above the measured RH. The BRE is sensitive to the β parameter, the desorption factor. Changes in this parameter, which is a function of the assumed RH at the desorbing surface can have large effects on the predicted RH, especially at lower ventilation rates (see Figure 8). The model is less sensitive to the α parameter, the absorption factor, which tends to dampen the effect of ventilation air on the interior RH. Clearly the α, β coefficients are not appropriate for the majority of the North American houses monitored, as was noted by Jones [9]. The most sensitive parameter in the BRE however is the ventilation rate. The effect of changes in ventilation rates is the same as the ASHRAE intermediate model (see Figure 6). The BRE model less sensitive to changes in the moisture generation rates (see Figure 7).

-40.00 -20.00 0.00 20.00 40.00 60.00 80.00 100.00 0 0.2 0.4 0.6 0.8 1 1.2 kn, kg/m 2 h; RHsN, kg/kg

Mean bias error, %RH

RHsN, k = 0.5 kn, RHs = 0.7

BRE Model

Figure 8 – Sensitivity of the BRE models to variation in the moisture transfer coefficient and surface relative humidity.

The ASHRAE simplified model is based on work conducted in Europe where it was considered to be within the recommended indoor humidity levels. This model was meant for design purposes and therefore overestimating the design loads is conservative. Comparing the ASHRAE simple model with measured result clearly indicates that it consistently overestimates the indoor RH. The model also fails to track well with exterior conditions that have an effect on the interior environment. The commentary in ASHRAE 160P states this clearly, “The simplified method may also produce high values for dry climates, even with air-conditioning. Again, the intermediate or full-parameter analysis would be preferable.” Given that ASHRAE simple model in many causes considerably overestimates the indoor RH it should only be used when no other information is available. It is not appropriate for use in cold climates where the 40% RH baseline is too high Conservative loads estimates may preclude cheaper and more efficient designs. The following discuss the performance of the models for the for locations where measured data was obtained.

Prince Rupert BC

The Prince Rupert climate is cool and wet. The air change rate (ACH) calculated for the houses monitored ranged from 0.33 to 0.62 ACH. Occupancy varied between 2 and 8 persons. Of the 4 models tested the Class model showed the best concurrence generally showing the lowest MBE. The class model, however, consistently underestimated the

relative humidity in the space. The ASHRAE intermediate model also showed good concurrence but generally overestimated the relative humidity in the space. The BRE model showed large errors from the measured results and tended to overestimate, as does the ASHRAE simple model. The same results are obtained from examining the MAE, the Class model giving the lowest MAE overall, the ASHRAE intermediate gave the next best results with the BRE and ASHRAE simple models showing large errors. Large RSME errors indicate considerable variability in the predicted results from the measured data, the Class model again giving the best results for the Prince Rupert houses. The ASHRAE intermediate, BRE, ASHRAE simple models have large systematic errors compared to the noise in the models while the Class model shows about the same amount of systematic error as the noise in the model. There was little effect from switching from locally measured weather data to the airport or meteorological station weather data. House 5 was a typical example showing good concurrence for the Class and ASHRAE models. The other models consistently overestimate the interior conditions. The results are shown in Figure 9 and Figure 10. The error data are presented in the Appendix (See Table A 1).

Inuvik NT

The Inuvik climate is very cold and dry. The air change rate (ACH) calculated for the houses monitored ranged from 0.452 to 1.27 ACH. Occupancy varied between 3 and 5 persons. Of the 4 models tested the ASHRAE intermediate model showed the best concurrence generally showing the lowest MBE for the eight houses in Inuvik. The ASHRAE intermediate model for some cases underestimated and for the rest overestimated the relative humidity in the space. The Class model also showed good concurrence but generally overestimated the relative humidity in the space. The BRE model showed large errors from the measured results and consistently overestimated, as did the ASHRAE simple model. The same results are obtained from examining the MAE, the ASHRAE intermediate model giving the lowest MAE overall, the Class model the next best results, with the BRE and ASHRAE simple model showing large errors. Large RSME errors indicate considerable variability in the predicted results from the measured for the BRE model and ASHRAE simple models. The best RMSE results were obtained from using the ASHRAE intermediate model, followed by the Class model for the Inuvik houses. The BRE and ASHRAE simple models have large systematic errors compared to the noise in the models while the ASHRAE intermediate and Class models have about the same amount of systematic error as the noise in the model. There was little effect from switching from locally measured weather data to the airport or meteorological station weather data. House 3 is a typical example showing good concurrence for the Class and ASHRAE intermediate models. The other models consistently overestimated the interior conditions. The results are shown in Figure 11 and Figure 12. The error data are presented in the Appendix (See Table A 2).

Prince Rupert BC; House 5 0 10 20 30 40 50 60 70 80 90 100 4/₁₈ /05 0 :0₀ 4/ 23/ 05 0: 00 4/28 /05 0 :00 5/ 3/05 0 :00 5/_8/ 05 0: 00 5/13/ 05 0: 00 5/18/ 05 0: 00 5/23/ 05 0: 00 5/28/ 05 0: 00 Time, h RH , % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Bathroom

(a)

Prince Rupert BC; House 5

0 10 20 30 40 50 60 70 80 90 100 4/ 18 /05 0 :0₀ 4/ 23/ 05 0: 00 4/28 /05 0 :00 5/ 3/05 0 :00 5/ 8/ 05 0: 00 5/13/ 05 0: 00 5/18/ 05 0: 00 5/23/ 05 0: 00 5/28/ 05 0: 00 Time, h RH , % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Main Floor Storage

(b)

Figure 9 – Comparison of the predictions of the four models with measured data over time for house number 5 in Prince Rupert BC; a) bathroom, b) main floor storage room.

0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % Pre d ic te d R H , % Bathroom Main Floor Storage

Class Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % P red ic te d R H , % Bathroom Main Floor Storage

ASHRAE Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % Pre d ic te d R H , % Bathroom Main Floor Storage

BRE Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % P re d ic te d R H , % Bathroom Main Floor Storage

ASHRAE Simple Model

Figure 10 – Predicted versus measured data for each of the four models for both rooms of house 5 in Prince Rupert BC.

Carmacks YT

The Carmacks climate is very cold and dry. The air change rate (ACH) calculated for the houses monitored ranged from 0.395 to 1.45 ACH. Occupancy varied between 1 and 6 persons. Of the 4 models tested the Class model showed the best concurrence generally showing the lowest MBE for the eight houses in Carmacks. The Class model underestimated for the most part the relative humidity in the space, 9 of the 15 rooms. The BRE model also showed good concurrence but in most cases overestimated the relative humidity in the space depending on the house. The ASHRAE intermediate model sometimes showed large errors from the measured results and generally underestimated, as did the ASHRAE simple model. The same results are obtained from examining the MAE, the Class model giving the lowest MAE overall, the BRE model the next best results with the ASHRAE intermediate and simple models showing larger errors. Large RSME errors indicate considerable variability in the predicted results from the measured for the ASHRAE intermediate and simple models. The best RMSE results were obtained from using the BRE model, followed by the Class model for the Carmacks houses. The ASHRAE simple model showed large systematic error when compared to the noise in the model while the other models exhibited about the same or less amount of systematic error than the noise in the model. There was little effect from switching from locally measured weather data to the airport or meteorological station weather data. House 5 is a typical example showing, in this case, the best concurrence for the BRE model. The results are shown in Figure 13 and Figure 14. The error data are presented in the Appendix (See Table A 3).

Inuvik NT; House 3 0 10 20 30 40 50 60 70 80 90 100 11 /14/ 05 0: 00 11/ 19/₀₅ 0 :00 11/ 24/₀₅ 0: 00 11/ 29/₀₅ 0: 00 12/4 /0_{5 0} :0₀ 12/9_/0 5 0: 00 12 /1_4/ 05 0: 00 12 /19/ 05 0: 00 12 /24/₀₅ 0 :00 Time, h RH , % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Bathroom (a) Inuvik NT; House 3 0 10 20 30 40 50 60 70 80 90 100 11 /14 /05 0 :00 11/₁₉ /0 5 0_:0 0 11/₂₄ /0 5 0 :0 0 11/2 9/0 5 0: 00 12/4 /05 0 :0₀ 12 /9/05 0:0₀ 12/1 4/05 0_:0 0 12/₁₉ /0 5 0 :0₀ 12/2 4/0_{5 0} :0₀ Time, h RH, % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Kitchen

(b)

Figure 11 – Comparison of the predictions of the four models with measured data over time for house number 3 in Inuvik NT; a) bathroom, b) kitchen.

0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % Pr e d ic te d R H , % Bathroom Kitchen Class Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % P re d ic te d RH, % Bathroom Kitchen ASHRAE Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % Pr e d ic te d R H , % Bathroom Kitchen BRE Model 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 Observed RH, % Pr e d ic te d R H , % Bathroom Kitchen

ASHRAE Simple Model

Figure 12 – Predicted versus measured data for each of the four models for both rooms of house 3 in Inuvik NT.

Ottawa ON

The Ottawa climate is cold and humid. The air change rate (ACH) calculated for the CCHT reference house was 0.204 ACH. This ventilation rate includes the operation of a heat recovery ventilator. At CCHT there is a simulated occupancy. No persons live in the house. The moisture generation is greater than zero due to the automatic operation of showers, taps, and appliances, but less than would occur with single person occupancy. The moisture generation rate was conservatively assumed to be 3 Kg/day or one person. Of the 4 models tested the ASHRAE intermediate model showed the best concurrence generally showing the lowest MBE. The Class model also showed good concurrence but overestimated the relative humidity in the space. The ASHRAE simple model showed a large error from the measured results and overestimated the RH. The BRE model also overestimated the relative humidity in the space and showed a large error performing worst of the four. The same results are obtained from examining the MAE, the ASHRAE intermediate model giving the lowest MAE overall, the Class model the next best result with the BRE and ASHRAE simple models showing large errors. Large RSME errors indicate considerable variability in the predicted results from the measured for the BRE and ASHRAE simple models. The best RMSE results were obtained from using the ASHRAE intermediate model, followed by the Class model. The ASHRAE simple and BRE models showed large systematic errors when compared to the noise in the model while the other models exhibited about the same or less amount of systematic error than the noise in the model. There was little effect from switching from locally measured weather data to the airport or meteorological station weather data. The results are shown in Figure 15 and Figure 16. The error data are presented in the Appendix (See Table A 4).

Carmacks YT; House 5 0 10 20 30 40 50 60 70 80 90 100 1/13/ 06 0: 00 1/ 18/₀₆ 0 :0₀ 1/23 /06 0 :0₀ 1/₂₈ /06 0 :00 2/2/ 06 0: 00 2/7/₀₆ 0_:0 0 2/12 /0_{6 0} :00 2/ 17/ 06 0: 00 2/22/ 06 0: 00 2/27 /06 0: 00 Time, h RH , % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Living Room

(a) Carmacks YT; House 5

0 10 20 30 40 50 60 70 80 90 100 1/13 /06 0 :0 0 1/ 18/₀₆ 0_:0 0 1/₂₃ /06 0_:0 0 1/ 28/ 06 0 :0 0 2/_2/ 06 0: 00 2/_7/ 06 0: 00 2/ 12/ 06 0 :0 0 2/₁₇ /06 0_:0 0 2/22 /06 0 :0 0 2/27 /06 0 :0 0 Time, h RH , % Observed Class model ASHRAE Model BRE Model ASHRAE Simple Model

Kitchen

(b)

Figure 13– Comparison of the predictions of the four models with measured data over time for house number 5 in Carmacks YT; a) living room, b) kitchen.