Generation of a critical weather year for hygrothermal simulations using partial weather data sets

Building and Environment 76 (2014) 54e61

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Building and Environment journal homepage: www.elsevier.com/locate/buildenv

Generation of a critical weather year for hygrothermal simulations using partial weather data sets
*
ra, Robert Cerný Jan Ko
cí, Ji
rí Made Department of Materials Engineering and Chemistry, Faculty of Civil Engineering, Czech Technical University in Prague, Thákurova 7, 166 29 Prague 6, Czech Republic

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 January 2014 Received in revised form 4 March 2014 Accepted 5 March 2014

This paper offers a novel approach for selecting a critical weather year for hygrothermal simulations. The method is suitable, in particular, for the countries where a typical damage caused by the external environment is due to the freeze/thaw cycles in the external surface layers of building structures. The main advantage of the proposed treatment consists in its applicability for such locations where the longterm history of hourly weather data is not available. The lack of data is solved by the creation of an artificial weather history using the reference years from several different places having similar climate to the investigated locality. Then, the severity of each reference year is ranked by the newly formulated damage function, denoted as the Winter Index, and an inverse analysis is applied. After that, the mathematical relations between the weather data and the level of its severity to an investigated structure are found. Finally, the derived mathematical formulas are used to select the critical weather year using the monthly averages of partial weather data for the given location. The practical application of the method is demonstrated on the example of the Czech Republic. Similarly it can be used, e.g., for some other countries in the Central and Eastern Europe. However, the main ideas of the new approach can also be applied for many other geographical areas if the Winter Index is replaced by different damage functions characteristic for the particular territories. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Critical weather year Hygrothermal simulations Freeze/thaw cycles Partial weather data Inverse modeling

1. Introduction Contemporary construction technologies applied for both new and refurbished buildings are characterized by an increasing use of sophisticated multi-layered systems of different types of materials. The growing complexity is, logically, reflected in the increasing demands on the design process and the demands for closer-tooptimal solutions. A thorough stress and strain analysis is still its most essential part but the hygrothermal considerations are gaining more and more importance. The simplified steady-state methods, such as the Glaser method [1] or the Dew-Point method [2], are often insufficient for a reliable prediction of the hygrothermal performance of complex construction systems [3e5] as they are not able to describe their dynamic response. Therefore, the hygrothermal design of both building envelopes and

* Corresponding author. Tel.: þ420 22435 5044; fax: þ420 22435 7131.
ra), E-mail addresses: [email protected] (J. Ko
cí), [email protected] (J. Made
[email protected] (R. Cerný). http://dx.doi.org/10.1016/j.buildenv.2014.03.006 0360-1323/Ó 2014 Elsevier Ltd. All rights reserved.

construction details [6e8] is frequently performed using advanced computer simulation tools. Climatic data including temperature, relative humidity, wind speed and velocity, rainfall and solar radiation have become an integral part of current hygrothermal simulation models. They are implemented mostly in the form of Test Reference Years (TRY) [9e11] or Typical Meteorological Years (TMY) [12e14] for the chosen localities. The data in TRY and TMYare averaged, thus both the more severe years and more favorable years that occurred in the applied time period are hidden. The averaging makes the TRY and TMY very convenient for the long-term simulations of energy performance or studies of hygrothermal performance. However, moisture-induced damage is often caused either by sudden or rapid changes in the weather conditions or by a specific combination of several changes in weather conditions occurring at the same time. Such peak changes or specific sequence of changes in the weather conditions appear in TRY or TMY highly unlikely. Therefore, in some cases it is advantageous to use the critical-year data, i.e., the weather conditions for the most severe year in a given locality, with respect to the investigated damage. The current methods for generation of a critical weather year for hygrothermal simulations can be divided into two main categories:

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construction dependent and construction independent approaches. Construction dependent methods require some form of hygrothermal simulation and knowledge of the envelope characteristics. They are used for detailed studies under a particular climate. Construction independent methods require weather data analysis only. They are designed for large-scale parametric studies combining many climates. One of the simplest approaches was developed by Rode [15]. He proposed to calculate the annual amount of accumulated moisture in the investigated construction for as many weather years as available. The accumulated moisture content was calculated using hourly weather data for several wall types with different orientations and then the weather years were ranked according to the severity. The highest amount of accumulated moisture represented the worst moisture conditions in the construction related to the most severe year from the weather history. Geving [16] examined the applicability of the Rode’s method [15] for different types of construction and orientation, different climate zones, indoor conditions and initial moisture content in the construction. For each type of investigated construction the results of year-long simulations were analyzed and subsequently the maximum and average moisture content in the construction was determined. From the normal distribution function the 10% level (90th percentile) moisture content was determined for both maximum- and average moisture content criteria and the mean and standard deviation was calculated. The p-factor method was formulated within the frame of IEA Annex 24 [17]. The p-factor uses the drying potential of a wall by defining the mean value of the difference between the absolute humidity per unit volume at saturation (water vapor density) at the outside wall surface and the absolute humidity per volume in the external air. In the case of low drying potential of the wall, the pfactor is low. The worst year according to this method would be the year with the smallest value of the p-factor. Cornick et al. [18] presented the Moisture Index method, which was developed within the MEWS project (Moisture management of Exterior Wall Systems) [20,21]. This method has been developed for a wide range of climate zones across North America as a parametric study with four main types of parameters (climate, wall constructions, construction materials and amount of accidental water entered to the stud cavity). The Moisture Index can be considered to be a moisture budget that consists of wetting and drying functions. The wetting function described the source part of the budget (e.g., rainfall), the drying function a sink part of that budget (e.g., evaporation, soil retention, or run-off). The Moisture Index approach was based on selecting a 3-year weather data period, where each year could be classified as wet (high Moisture Index), dry (low Moisture Index), or average. Wet and dry years were defined as those years that differed by more than one standard deviation from the mean Moisture Index value of the sample set for a given location. Salonvaara et al. [19] reviewed some of the existing methods for selecting a critical weather year for hygrothermal simulations. They found out that none of the existing methods were deemed satisfactory, as consistent predictions were not achieved. Therefore, they suggested a new approach. At first, they carried out a series of longterm simulations for each of the available weather data. The simulations were performed with different wall constructions and orientations. The simulation performance data were analyzed using a damage function and the service life of the particular structures was quantified. After that, Salonvaara et al. [19] introduced a simple approximation to select the weather years for hygrothermal design. Although the method was developed using simulation results for an individual construction, the authors concluded that the selected years seemed to be the most severe for many types of constructions.

55

The methods for selection of critical weather years for hygrothermal simulations which were described above require longterm hourly weather data for the investigated location, spanning optimally 30 or more years. Such data sets are available in the USA or in several European countries (e.g., Germany). For example, the weather data in the USA are provided by NOAA-NCDC data sets (1961e1990) and the NCDC update (1985e2005) for many locations across the USA. The data includes outdoor temperature and relative humidity, wind speed and wind direction, sky radiation, and precipitation. However, in many countries such weather data sets are not available which makes the mentioned approaches inapplicable. A solution to the problem of complete data sets unavailability may be found by involving a specific damage function that requires partial weather data only, e.g., temperature and relative humidity in a form of monthly values. Damage functions are used to estimate different kind of damages to the materials involved in building envelopes. Construction materials are exposed to a range of physical, chemical and mechanical stresses during their service life. The ability of construction materials to transfer loads depends on the magnitude of the applied stresses, moisture contents, and temperatures. The particular damage function should be chosen with respect to the investigated material, type of damage and, of course, the ambient environment in order to obtain credible results. The damage mode can vary in different climates, for example in cold climate serious damage can be caused by freeze/thaw cycles or winter condensation, whereas in hot climates, UV-radiation is more dangerous to the structures. Although the material type and composition is essential for a proper choice of damage function, geographical location of the investigated structure should be taken into account as well. Time-of-Wetness (TOW) is one of the standard damage functions that have been widely used in the past [22e24]. Generally, in civil engineering TOW is applied for various building materials such as bricks, wooden construction, stone, or renders in order to describe atmospheric corrosion. As it was described by McCabe et al. [25], although TOW has proved conceptually useful, it has been used in different ways by different groups to mean very different things. For example, Salonvaara et al. [19] calculated TOW as the time in hours during a year when both the temperature and relative humidity were above the prescribed critical levels. The reference values were 80% for relative humidity and 0  C for temperature. The TOW ranged between 0 and 8760. Mukhopadhyaya et al. [26,27] used the RHT-Index. It was similar to TOW, but instead of only calculating the hours when the prescribed conditions were met, the method placed emphasis also on the rate of exceeding the prescribed values. The RHT-Index was calculated only if T > TL and RH > RHL. The limits TL and RHL were set to 0  C for temperature and 80% for relative humidity, which presents favorable conditions for mold growth. The RHT-index was calculated as

RHT ¼

X ðT  TL Þ$ðRH  RHL Þ

(1)

Another mold growth damage functions were used by Johansson et al. [28] or Sedlbauer [29]. In this paper, we present a new approach which needs for the generation of a critical weather year for hygrothermal simulations only partial weather data. The lack of data is solved by the creation of an artificial weather history. Ranking the severity of the artificial weather data by a chosen damage function and applying a subsequent inverse analysis, the critical weather year is generated on the basis of monthly averages of partial weather data for the given location. The method in the proposed form is suitable, in particular, for the countries where a typical damage caused by the external environment is due to the freeze/thaw cycles in the external surface

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layers of building structures. However, the main ideas of the new approach can also be applied for other geographical areas if a suitable damage function characteristic for the particular territory is defined. 2. Description of the new approach for selecting a critical weather year The proposed approach is targeted on the localities with incomplete weather data where the full long-term hourly data sets are not available. Therefore, it is based on the creation of an artificial weather history using the TRY from several different places having similar climate to the investigated locality. These artificial data sets are then utilized in an inverse analysis providing the mathematical relations between the selected weather data and the level of their severity which can be applied for the selection of a critical weather year using only partial weather data. The critical weather year for the hygrothermal analyses is then found using the following consecutive steps: 1. Substitution of missing weather data 2. Definition of the investigated wall systems and computer simulations of their hygrothermal performance 3. Analysis of the simulation outputs and ranking the weather years using the damage function 4. Inverse analysis of the damage-function values 5. Selection of the critical weather year. The scheme of the selection process is shown in Fig. 1. Its application is demonstrated on the practical example below. 3. Application for the climatic conditions in the Czech Republic 3.1. Definition of the damage function Prior to the application of the method described in Section 2, a damage function must be specified. Generally, the method can work with many existing damage functions or newly developed ones. In this paper, we will concentrate on the geographical areas which are characterized by an alternation of the freezing and

thawing periods. In such climatic conditions, a typical damage caused by the external environment which we will focus on is due to the freeze/thaw cycles in the external surface layers of building structures. Therefore, we introduce a new damage function denoted as the Winter Index which ranks the weather years based on the induced frost in the building enclosures. The definition of the Winter Index (WI) is similar to the RHTindex proposed by Mukhopadhyaya et al. [26,27],

WI ¼

X

ðT  T0 Þ$ðRH  RH0 Þ;

(2)

but both its limits, T0 and RH0, and the interpretation of its values is completely different. The limiting temperature, T0, is set equal to an equilibrium temperature of the watereice phase change. The limiting relative humidity, RH0, is defined as the RH value corresponding to the maximum hygroscopic moisture content of a porous building material. For RH > RH0, the overhygroscopic moisture, i.e., the water in the liquid state, which is available for freezing, is present in the pore system. As the damage is supposed to occur only in the case that water freezes in the pore system of a material involved in a building envelope, WI is calculated only if T < T0 and RH > RH0. The overall reasons why RH is used in the definition of WI are practical. Most current computer codes commonly applied for hygrothermal simulations work with RH as the primary variable in the water mass balance equation. Another practical aspect of using RH instead of other possible quantities is a fact that only one limiting value of RH can be set, which does not depend on the investigated material or material composition. If a recalculation of generated RH data to the moisture content is necessary for further considerations, it can easily be done using the sorption isotherm and water retention which are included in a general moisture accumulation function. In the practical settings of the limiting temperature, T0, and limiting relative humidity, RH0, one should take into account the safety factors, i.e., the settings are supposed to guarantee that for a wide class of materials and their multi-layered systems the absolute value of WI is not lower than in the reality. Therefore, for common building materials T0 ¼ 0  C can be considered a wise choice although in specific conditions (e.g., highly salted materials of some historical buildings without a horizontal waterproof

Fig. 1. Scheme of the process of selecting a critical weather year.

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insulation or materials with a very fine pore structure where the high capillary pressure can lead to a decrease of the freezing point) T0 can be obviously lower than 0  C. Similarly, setting RH0 ¼ 95% is a reasonable choice, taking into account that the RH values which are very close to the maximum hygroscopic moisture content are difficult to measure (most RH sensors have a lower accuracy in the range of very high RH), although for certain types of materials 95% can be distinctly lower than RH corresponding to the critical degree of saturation which is applied in common freeze/thaw models [30]. 3.2. Substitution of missing weather data In the Czech Republic, the weather data are provided by the Czech Hydrometeorological Institute which is the only reliable data source. Contrary to the USA or Germany, the ready-to-use data sets for hygrothermal simulations are not available. The hourly longterm climatic data for most localities are either not complete or have not been digitalized yet, due to the lack of the necessary financial resources. The winter conditions in the Czech Republic are characterized by the changing freezing and thawing periods which can potentially lead to the accumulation of damage in the building envelopes. Therefore, the approach for the determination of a critical weather year, which was described in the previous Section, is very suitable for this geographical area. In the process of selection of a critical weather year, a substitution of missing weather data was performed at first because the data availability for the Czech Republic was not sufficient. Twentyone Test Reference Years (TRY) for the locations with a similar climate were used for that purpose. The different parts of the Czech Republic experience either hot summers (in the region of South Moravia) or cold winters (in the mountain regions). Therefore, some of the chosen localities were in the regions with a hot summer (e.g., Nantes, Atlantic City) and others were characteristic by a

ov, Grossenzersdorf). During cold winter (e.g., Strbské Pleso, Churán the selection of the substituting weather years, similarities in terms of temperature, relative humidity and precipitation were sought, in particular. In this way, an artificial weather history of the Czech Republic was created. The overview of the applied TRY is presented in Table 1. All the climatic data were obtained by the Meteonorm software [31], which is a meteorological database and computer program for climatological calculations for the locations all over the world. 3.3. Definition of the investigated wall systems and computer simulations of their hygrothermal performance The proposed method for the selection of a critical weather year is construction-dependent. Therefore, it was applied for several different material compositions of building enclosures. The most common construction materials used in the Czech Republic either

Table 1 List of used Test Reference Years. Location

Country

Location

Country

1 Atlantic City, NJ 2 Bodo 3 Columbia, MO 4 Dublin 5 Lerwick 6 London 7 Nantes 8 Reykjavik 9 Hradec Kralové 10 Mannheim 11 Uccle

USA Norway USA Ireland Scotland England France Iceland Czech Republic Germany Germany

12 13 14 15 16 17 18 19 20 21

Poland Austria France Denmark Slovakia Czech Republic France Austria Germany Hungary

Warzsava Graz Nancy Kobenhavn
Strbské Pleso
ov Churán Bourges Grossenzersdorf Osnabrueck Budapest

57

presently or in the historical times were chosen as the load-bearing materials, namely ceramic brick, sandstone, argillite, autoclaved aerated concrete (AAC), and concrete. The contemporary building envelopes were provided with different types of thermal insulation layers, including polystyrene and mineral wool, the historical masonry was considered without any thermal insulation. The plasters were chosen with respect to the material composition of the envelopes. The detailed list of the studied building envelopes is presented in Table 2. For each building envelope listed in Table 2, computer year-long simulations of the hygrothermal performance were performed, using the climatic data for the twenty-one locations listed in Table 1. The computer simulation tool HEMOT (HEat and MOisture Transport) [32], which is based on the general finite element package SIFEL (SImple FInite Elements) [33] and uses an implementation of the Künzel’s mathematical model of coupled heat and moisture transport [34], was utilized in the calculations. HEMOT allows the simulation of transport phenomena in constructive building details for 1D and 2D problems, whereas the basic variables characterizing the hygrothermal state of building constructions (temperature, moisture content, relative humidity) can be obtained as functions of space and time. The HEMOT code allows an investigation of variants concerning different constructions, different materials, and different climatic loads. HEMOT uses a material database as data source, which simplifies computations and allows obtaining more complex results. HEMOT has been successfully validated in various engineering tasks [35e38]. In the calculations throughout this paper, the material properties necessary as input parameters were obtained from Refs. [39e46]. 3.4. Analysis of the simulation outputs and ranking the weather years using the damage function For evaluating the induced damage the Winter Index (WI) damage function was used. Eq. (2) shows that WI returns negative values. The lower value the damage functions returns, the more

Table 2 List of studied building envelopes. Building envelope

Load-bearing material

Thermal insulation

Plaster

1 2

Ceramic brick Ceramic brick

Baumit MVR Uni Baumit MVR Uni

3

Ceramic brick

4

Ceramic brick

5 6

Sandstone Sandstone

N/A Mineral wool, hydrophobic Mineral wool, hydrophilic Expanded polystyrene N/A N/A

7 8

Argillite Argillite

N/A N/A

9 10

Concrete Concrete

11

Concrete

12

Concrete

13 14

AAC AAC

15

AAC

16

AAC

N/A Expanded polystyrene Mineral wool, hydrophobic Mineral wool, hydrophilic N/A Expanded polystyrene Mineral wool, hydrophobic Mineral wool, hydrophilic

Baumit MVR Uni Baumit MVR Uni N/A Renovation plaster for historical masonry N/A Renovation plaster for historical masonry Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni Baumit MVR Uni

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58

severe conditions in the construction occurred. If WI is equal to zero, the construction is void of any freezing stresses. In the case of the building envelopes studied in this paper (Table 2), WI was calculated mostly for the external plaster as it was the part of the envelope most susceptible to the freeze/thaw damage. If the external plaster was missing (envelopes 5 and 7, see Table 2), the index was determined for the position 10 mm under the exterior surface. As all involved TRY’s locations are on the northern hemisphere, the orientation of the investigated envelopes was set to the north. The used TRY contained all necessary weather data, including solar radiation, precipitation and wind factors, in order to guarantee as much realistic outputs as possible. For each building envelope listed in Table 2 the localities with the lowest (most severe) and highest (most favorable) values of WI were identified. The summary is presented in Table 3. 3.5. Inverse analysis of the damage-function values The process of identifying the relations between the damagefunction values and the weather years that induced the damage was started with the assignment of totally 21 values of the Winter Index corresponding to the locations listed in Table 1 to each of the building envelopes listed in Table 2. In the Czech Republic, the only well available weather data sets provided by the Czech Hydrometeorological Institute are the monthly averages of temperature, relative humidity and precipitation. Therefore, the hourly data of each substituting weather year were recalculated into the monthly averages and these averages were used as the input data for the inverse analysis. The inverse relation was optimized in the following form:

Ypred ¼ c0 þ c1 $ðTw $RHw Þ þ c2 $ðTw $RRw Þ þ c3 $ðTs $RHs Þ þ c4 $ðTs $RRs Þ;

(3)

where Ypred is the predicted value of the Winter Index, c0ec4 are the optimized coefficients, Tw is the average temperature in the winter period (NovembereMarch), Ts the average temperature in the summer period (AprileOctober), RHw the average relative humidity in the winter period, RHs the average relative humidity in the summer period, RRw the average monthly precipitation in the winter period, RRs the average monthly precipitation in the summer period. The average values of temperature, relative humidity and precipitation for the winter and summer periods of the applied weather data are summarized in Table 4.

Table 3 Weather year severity ranking. Building envelope (Table 2)

Worst year

Winter Index

Best year

Winter Index

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Reykjavik
ov Churán Bodo Warzsava Columbia, MO
ov Churán Warzsava
ov Churán
Strbské Pleso
ov Churán Nancy Reykjavik Reykjavik
ov Churán
ov Churán Nantes

2921.0 100,745.1 4465.8 76,153.7 1307.5 156.1 92,707.8 4411.4 1101.4 95,194.4 29,507.1 6582.0 6809.7 100,235.5 108,522.2 7350.2

Dublin Grossenzersdorf Dublin Columbia, MO Dublin Nancy Dublin Atlantic City, NJ Dublin Dublin Grossenzersdorf Graz Budapest Dublin Columbia, MO Bourges

159.9 1188.2 601.1 3525.1 18.5 4.0 929.4 114.0 30.1 2379.8 644.2 252.5 881.3 2591.2 2423.1 1126.2

The aim of the optimization was to find such combination of c0e c4 coefficients that produced the minimal difference x between the real and predicted values of the Winter Index, WI and Ypred, respectively, for a given construction, according to

x ¼ min

!  21  X   WIn  Ypred;n ðc0 ; c1 ; c2 ; c3 ; c4 Þ ;

(4)

n¼1

where n is the number of the particular test reference year (TRY, see Table 1), WIn is the value of the Winter Index for the TRY number n, Ypred,n is the estimated performance of the particular building envelope as a function of the c0ec4 coefficients. The optimization was performed using the genetic algorithm described in Ref. [47]. For each building envelope’s material composition, 16 weather years were used as the input data for the applied genetic algorithm to optimize the mathematical function (3). The remaining 5 weather years were used for the prediction within this optimization. In this way, the optimization process could be verified. The results of the inverse analysis are shown in Fig. 2, the summary of the optimized coefficients c0ec4 for each building envelope is presented in Table 5. 3.6. Selection of the critical weather year The optimized inverse relation (3) was applied for the selection of the critical weather year for the Czech Republic. The average monthly weather data for the city of Prague from the time period of 1982 to 2011, which were obtained from the Czech Hydrometeorological Institute, were recalculated into the summer and winter period averages to comply with Eq. (3). For each building envelope listed in Table 2 three and five worst weather years were selected. Based on that ranking, the worst years from the weather data history were chosen. The results of the application of Eq. (3) are shown in Table 6 where five worst years for each type of building envelope are listed as the main output of the construction dependent method. A summarization of results presented in Fig. 3 shows that the years 1996 and 1985 were among the worst for most investigated building envelopes.

Table 4 Summary of weather data applied in Eq. (3). Location (Table 1)

Ts [ C]

Tw [ C]

RHs [%]

RHw [%]

RRs [mm]

RRw [mm]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

18.33 9.19 19.34 12.23 9.61 13.94 15.30 8.10 14.69 13.93 15.96 13.70 13.50 14.26 13.93 12.44 9.14 9.84 16.14 15.56 16.34

4.08 0.04 2.96 6.20 4.76 6.08 6.66 0.98 0.62 0.42 4.54 4.16 0.24 0.26 3.12 1.78 3.00 1.74 5.78 2.34 2.06

70.94 73.40 69.86 81.13 84.81 75.19 76.59 77.47 51.20 75.69 71.53 78.79 73.73 74.66 75.00 75.49 76.47 77.44 69.50 65.20 63.99

66.78 74.16 69.84 85.70 82.14 83.56 84.14 77.96 80.48 85.40 81.62 84.76 84.52 85.64 82.24 83.80 79.42 82.76 82.88 76.40 79.58

100.14 75.57 101.86 54.00 62.57 49.14 55.86 59.86 27.29 58.43 52.71 67.57 53.29 90.00 63.71 55.00 79.14 68.00 64.00 58.00 47.43

73.60 94.80 76.40 51.60 104.00 57.20 79.40 76.40 47.00 33.60 34.40 69.60 28.40 41.60 63.00 42.40 63.20 64.60 59.60 34.40 36.80

J. Ko
cí et al. / Building and Environment 76 (2014) 54e61 Table 6 Ranking of the worst years for each building envelope.

-100000 Winter index [-]

59

-80000

Building envelope (Table 2)

Worst years 1st

2nd

3rd

4th

5th

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

2009 1982 1996 1996 1995 1996 1996 1996 1995 1987 2009 1996 1987 1996 1996 1996

1995 1996 1985 1985 2003 1985 1985 1985 2009 1996 1995 1985 2010 1987 1987 1985

1989 1985 1991 1982 1996 1987 1991 1987 2010 1985 1989 1982 1996 1985 1985 1987

2010 1987 2003 1987 2009 1982 2003 1982 1987 2010 2010 1987 1986 2010 1986 1982

1994 1986 1987 1986 1985 1986 1995 1986 1985 1995 1993 1986 1985 1995 1982 1984

-60000 -40000 -20000 0 0

-20000

-40000

-60000

-80000

-100000

Ypred [-] OpƟmizaƟon

PredicƟon

Fig. 2. Comparison of optimization results (Ypred) and damage-function values (WI).

4. Discussion The selection of the critical weather year presented in Section 4 was based on the assumption that only the temperature-, relative humidity- and precipitation data were available. The other standard TRY parameters, such as the wind speed, wind direction, solar and sky radiation, were not taken into account because of the lack of necessary data. On one hand, the application of limited weather data sets makes possible to simplify greatly the selection process and to determine the critical weather year also for the localities where the availability of weather data is poor. Temperature, relative humidity and precipitation belong to the group of data that are measured quite commonly. Therefore, obtaining this data is easy in most cases, in particular if only monthly averages instead of hourly values are required. On the other hand, neglecting some weather data during the inverse analysis, especially solar radiation, may bring some uncertainties to the optimization results. The solar radiation warms up the building construction and contributes to the water evaporation from the surface layers of a construction. Therefore, the predicted damage function values may be lower (worse) than in the real life, in some cases. The rate of water evaporation from the surface can be affected by wind speed and wind direction as well, with similar consequences for the predicted damage function. These aspects provide a higher level of safety to the calculations. However, some other aspects may decrease the safety level. For

Table 5 Optimized coefficients in Eq. (3). Building envelope (Table 2)

Optimized coefficients c0

c1

c2

c3

c4

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

3580.5 46,249.0 5971.7 26,498.0 238.9 100.5 18,601.0 2179.1 1267.1 2285.8 6449.7 28,695.0 8374.3 60,841.0 6352.2 39,187.0

1.219 39.994 1.176 119.870 0.861 0.140 147.170 6.444 0.215 28.5460 8.7472 142.4300 6.6181 127.7000 9.3879 122.9600

0.921 20.134 4.359 4.761 0.353 0.135 2.401 0.336 0.626 1.5173 9.6591 12.8780 9.6166 22.8960 14.7860 16.9280

2.428 16.322 5.070 61.107 0.426 0.072 51.822 2.322 1.355 31.7770 1.2960 68.8200 3.7821 39.9710 1.3242 56.7840

0.488 4.957 1.833 34.094 0.850 0.025 0.042 1.903 0.548 9.7397 2.4764 42.0990 1.6992 35.6420 2.2364 35.1980

example, the precipitation in a combination with wind, known as “driving rain”, may worsen the hygric environment inside an envelope. The predicted damage function value may then be higher (better) than under the real-life conditions. Nevertheless, if the above described effects are not on extreme levels, they should not affect the selection process critically. 5. Conclusions The approach for the selection of a critical weather year for hygrothermal simulations presented in this paper can be characterized by two main features: (i) it was derived for the geographical areas with an alternation of the freezing and thawing periods, and (ii) it is targeted on the localities with incomplete weather data where the full long-term hourly data sets are not available. The method was developed as construction-dependent. As a typical damage caused by the external environment was assumed to be due to the freeze/thaw cycles in the surface layers of building structures, a new damage function denoted as the Winter Index was introduced which ranked the weather years based on the induced frost in the building enclosures. The substitution of missing weather data was a fundamental task in the development of the new method. It was solved by replacing the unknown 30-year hourly weather data history in the investigated locality by the TRY weather data from different locations with similar climatic conditions. In this way, an artificial weather history for the given locality was created. Having the defined damage function and the necessary weather data, the selection process continued then by ranking each chosen TRY by the Winter-Index damage function. After that, an inverse relation between the damage function values and the selected principal parameters of the particular weather years was derived for each type of building envelope. In this way, the mathematical relations between the weather data and the level of its severity to a particular structure were found. As a final step, the derived mathematical formulas were used to select the critical weather year using the monthly averages of partial weather data for the given location. The practical applicability of the proposed approach was demonstrated on the example of the climatic conditions in the Czech Republic. Similarly, it can be applied for many countries in the Central and Eastern Europe where a long-term history of hourly weather data in most locations may not be available and an alternation of the freezing and thawing periods occurs during the

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16

Number of top rankings

14 12 10 8 6 4 2

1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

0

Year TOP 3

TOP 5

Fig. 3. Total numbers of top positions of each weather year.

winter period. This can facilitate the hygrothermal simulations aimed at the service life estimates of building structures in these countries. The main advantage of the new method is that, contrary to most previous treatments, it does not need the long-term hourly weather data sets for the investigated location. This makes possible its extension to many other geographical areas just by replacing the Winter Index by different damage functions characteristic for the particular territories.

Acknowledgment This research has been supported by the Czech Science Foundation, under project No P105/12/G059.

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