The Mahoney method is a four-step bioclimatic analysis tool that translates meteorological data into architectural recommendations for optimizing thermal comfort. Used primarily for arid and tropical climates, it guides the design of the building envelope, openings, and site layout. Based on basic climate data, it enables the identification of a site’s constraints and potential and the formulation of bioclimatic design recommendations to ensure the thermal comfort of occupants.

Diagnostic Tables

Diagnostic tables are used to collect and organize essential monthly climate data for the regions under study. They lay the groundwork for comfort analysis and subsequent recommendations.

Figure 1. Flowchart of the method for designing housing recommendation maps based on the Mahoney Table.

The meteorological data used are based on the centroid of each region (see Figure 1Figure 1):Monthly average maximum and minimum temperatures. This data is crucial for understanding daily and annual temperature variations. Maximum temperatures indicate the level of daytime heat to which the building will be exposed, influencing solar shading and ventilation strategies. Minimum nighttime temperatures are important for assessing the potential for passive cooling and the risk of cold-related discomfort [4][5].Monthly average precipitation is critical for water management and protection against moisture. High precipitation levels require effective drainage systems, roofs with adequate slopes, and protective measures for openings and walls. The seasonal pattern of rainfall also influences landscape design and the choice of materials [6][7].The average monthly relative humidity has a significant impact on the perception of thermal comfort. High humidity intensifies the sensation of heat by limiting the evaporation of sweat. It also promotes mold growth. Effective ventilation strategies are crucial in humid climates to remove moisture-laden air [8][9].The prevailing wind direction and average monthly wind speed, which are essential for optimizing natural ventilation. The prevailing wind direction helps determine the building’s orientation and the placement of openings to promote air circulation within the spaces. Wind speed influences the efficiency of ventilation [10][11].

For illustrative purposes, consider the example of Alaotra Mangoro region, which falls within climate zone B (very humid, influenced by moderate trade winds, with an average annual temperature of 18˚C to 22˚C and annual precipitation of 1350 to 2500 mm (see Figure 2Figure 2).

Table 1 of meteorological data for Alaotra Mangoro region is as follows:

Table 1. Table of meteorological data for Alaotra Mangoro region.

Comfort Table [12][13]

This table is used to determine the thermal comfort limits for the site under study based on the Annual Mean Temperature (TMA) and the humidity group.

The average temperature in Alaotra Mangoro region is 20.1˚C (See Table 2).

Table 2. Moisture group table.

Using the TMA and the humidity group table, we can define the daytime and nighttime comfort zones. These limits are not universal but are tailored to populations acclimated to specific conditions (see Table 3). They take into account the fact that people living in hot climates can tolerate higher temperatures.

To fill out this comfort table for each month, let’s take January as an example; first, fill in the humidity group using Table 2. Next, enter the maximum temperature value. Next, find the maximum and minimum TMA values for the day corresponding to the month’s humidity group to fill in the maximum and minimum daytime comfort levels; the same principle applies to filling in the maximum and minimum nighttime comfort levels, but using the TMA for the night. Finally, to fill in the daytime (nighttime) thermal stress, compare the average maximum (minimum) temperature value to the maximum and minimum daytime (nighttime) comfort levels; if the average maximum (minimum) temperature falls between the maximum and minimum daytime (nighttime) comfort levels, we have “comfort ©”; if it is lower, the sensation is “too cold (TF)”; otherwise, the sensation is “too hot (TC)”.

Table 3. Comfort table for Alaotra Mangoro region.

Tables of indicators [14]-[18]

The first indicator table is used to populate the second indicator table. Recall the following definitions of the Koenigsberger indicators:

H1 (Essential ventilation): Daytime temperature ≥ 32˚C for 4 or more months, consecutive or otherwise.H2 (Ventilation desirable): Daytime temperature 29˚C - 32˚C for 4 months or more.H3 (Rain protection): Annual rainfall ≥ 1000 mm with a dry season < 3 months.A1 (Thermal inertia desirable): Annual temperature range (Tmax warmest month – Tmin coldest month) ≥ 10˚C.A2 (Sleeping outdoors possible): Nighttime temperature ≥ 22˚C for 4 months or more.A3 (Cold season issue): Minimum temperature of the coldest month < 10˚C.W1 (Strong, disruptive wind (protection)): Wind > 4 m/s for 4 months or more, or gusts > 10 m/s.W2 (Wind useful for ventilation): Moderate wind (2 - 4 m/s) for 4 months or more.

In order to preserve seasonal information, temperature ranges and precipitation were analyzed on a monthly rather than an annual basis. This approach is consistent with the principles of bioclimatic design, which require a detailed consideration of seasonal climate variations in order to adapt architectural strategies to local conditions [18]. Therefore, we use the monthly value instead of the annual value for A1 (Monthly Temperature Range or MTR) and H3 (Monthly Precipitation), because the annual range is a single value that smooths out seasonal variations.

The first indicator table becomes Table 4.

Table 4. First table of indicators.

The second table of indicators is Table 5.

Based on the assessment and indicators, the recommendation tables propose specific bioclimatic design strategies to address the identified thermal stresses and optimize comfort. Columns H1 through A3 indicate the combinations of indicators for which the recommendation in the row applies (See Table 6).

Table 5. Second set of indicators for Alaotra Mangoro region.

Recommendation Tables [19][20].

Table 6. Site plan.

The orientation and compactness of the layout depend primarily on the requirements for thermal mass (A1) and protection against the cold (A3).

The spacing is determined almost exclusively by H1 (essential ventilation) (See Table 7).

Table 7. Spacing between buildings.

The ventilation strategy depends on H1 and H2 (ventilation requirements) and A3 (cold weather may limit the opening) (See Table 8).

The size of the openings depends on A1 (inertia) and A3 (cold). The lower the inertia and the less cold there is, the larger the openings can be (See Table 9).

Table 8. Airflow.

Table 9. Opening dimensions.

The position of the openings is controlled by H1 and H2 (ventilation) and limited by A3 (cooling) (See Table 10).

Table 10. Position of the openings.

Two distinct needs: protection from the sun (if it’s not cold) or from the rain (if H3 is active) (See Table 11).

Table 11. Opening controls.

The thermal mass is directly determined by A1 (See Table 12).

Table 12. Walls and floors.

Roofs are either lightweight and insulated (for hot or humid climates) or heavy-duty (for dry climates with significant temperature fluctuations) (See Table 13).

Table 13. Roof.

Outdoor spaces must comply with A2 (nighttime use) and H3 (rainwater management) (See Tables 14-17).

Table 14. Outdoor spaces.

Table 15. Wind protection (W1: Strong, disruptive wind).

Table 16. Use of usable wind (W2: Usable wind for ventilation).

Table 17. Dual orientation based on wind direction and temperature.

Madagascar’s climate is primarily tropical, characterized by a dry season (southern winter, April through October) and a rainy season (southern summer, November through March). It varies significantly by region (indicated by the red dots), which has led the General Directorate of Meteorology to define 10 climate zones (Figure 2Figure 2).

Figure 2. Climate classification of Madagascar. Source: [21].

To simplify the representation of bioclimatic design at the regional level, a red centroid point was used for each region (Figure 2Figure 2 and Table 18). However, a single region may encompass multiple climate zones, whereas the centroid belongs to only one of them and therefore does not fully represent the region’s climatic diversity. The geographic coordinates (latitude and longitude) of the centroid were used to extract the meteorological data needed to develop the Mahoney table. This approach provides a simplified representation of each region. For a more accurate analysis, it is recommended to use the exact coordinates of the bioclimatic design site, which can be easily obtained using a GPS device.

Table 18.Geographic coordinates of meteorological data and climate zones for the 24 regions.

The period covered by the meteorological data spans 30 years (1991 to 2020). The parameters used in the Mahoney table are: daily precipitation data; maximum and minimum temperatures from DGM (4 km resolution, in collaboration with the International Research Institute for Climate and Society (IRI) at Columbia University); monthly humidity calculated using hourly air temperature and dew point temperature data at 2 m (Equation (3) [22]) and hourly wind data at 10 m from ERA5-Land (9 km resolution).

RH: Relative humidity (%);T: Air temperature (˚C);T_d: Dew point temperature (˚C).

The datasets we used underwent prior quality control. According to the WMO Guidelines on the Calculation of Climate Normals (WMO-No. 1203, 2017) [23], climate normals are calculated from monthly values, which are themselves derived from daily or hourly observations. They correspond to the average of monthly values over a 30-year period, in this case from 1991 to 2020. For parameters such as temperature, humidity, or wind speed, a month is included only if no more than 10 days are missing and if there are no 5 consecutive missing days. For precipitation, the month must be complete. Months that do not meet these criteria were excluded from the calculations (See Table 19).

Table 19. Method for calculating climatological norms [23].

The vector components are calculated according to [23]:

V: wind speed;θ: meteorological wind direction (the direction from which the wind is coming).

Most regions are oriented east-west to minimize solar exposure, with the exception of the ANDROY region (semi-humid and windy, influenced by trade winds), which features a compact layout with interior courtyards to minimize heat loss (Figure 3Figure 3).

Regions requiring specific air circulation (Figure 4Figure 4):

Dual orientation with adjustable openings (shutters, tilt-and-turn windows) to limit the entry of cold air: BONGOLAVA, ITASY, VAKINAKARATRA, AMORIN’I MANIA, MATSIATRA AMBONY, and IHOROMBE have humid climates moderated by the terrain; ALAOTRA MANGORO (very humid, with the influence of trade winds mitigated); ANALANJIROFO and AMBATOSOA (very humid year-round, directly exposed to trade winds).Dual orientation (intermittent airflow, opposing windows for cross-ventilation): SOFIA (very humid, trade wind influences mitigated), BOENY (humid with heavy rainfall, directly exposed to the monsoon in summer), BETSIBOKA (humid with heavy rainfall, directly exposed to the monsoon in summer), ANALAMANGA (humid, climate moderated by the terrain), and ANDROY (semi-humid and windy, influenced by trade winds).

Figure 3. Site planning recommendation.

Figure 4. Dual orientation according to wind and heat/cold.

The compact layout is recommended for ANDROY region (semi-humid, windy) where ventilation is not a priority. For other regions, use medium spacing with protection against hot/cold winds (Figure 5Figure 5).

Figure 5. Spacing recommendation.

Most buildings have moderate openings (25% - 40% of wall area), except in hot/dry regions: BOENY (humid with high rainfall, directly exposed to the monsoon regime in summer), SOFIA (very humid, with limited influence from trade winds), DIANA (humid with high rainfall, directly exposed to the monsoon regime in summer) and MELAKY (humid with low precipitation, dry winter), which have intermediate openings (20% - 35% of the walls). Note that a 30% opening on a 10 m² wall represents 3 m² of windows or doors (Figure 6Figure 6).

Protection from rain (awnings, overhanging roofs, waterproof shutters) is necessary in central and eastern Madagascar (humid and very humid zones). Protection from direct sunlight, such as exterior blinds, horizontal sunshades, and verandas, is essential in the following regions: BOENY (humid zone with high rainfall), DIANA (humid zone with high rainfall), MELAKY (humid zone with low rainfall and a dry winter), and SOFIA (very humid zone) (Figure 7Figure 7).

Figure 6. Opening size recommendation.

Figure 7. Opening protection recommendation.

Solid construction, such as 40 cm thick stone walls or compressed earth bricks (thermal lag > 8 hours), is essential in regions with large daily temperature ranges, such as ALAOTRA MANGORO (daily temperature range > 12˚C), ANALAMANGA (temperature range between 8˚C and 10˚C), and ANDROY (temperature range > 15˚C). Lightweight construction, such as wood-frame structures with plant fiber panels (low thermal mass) and/or wood/straw sandwich panels, or wooden houses with a ventilated air gap under the roof, is recommended in the hot/humid areas of AMBATOSOA (average temperature > 23.6˚C and humidity > 85%), ATSIMO ATSINANANA (average temperature > 21˚C and humidity between 75% and 85%), ATSINANANA (average temperature > 23.6˚C and humidity > 85%), FITOVINANY (average temperature > 23.6˚C and humidity > 85%) and SAVA (average temperature > 23.6˚C and humidity > 85%) (Figure 8Figure 8).

Figure 8. Walls and floors recommendation.