## 3 Results
### Monte Carlo Method  
From the data obtained during 3 years it was concluded that there are important differences respect the calculated energy demand. Regarding the causes of this deviation, the occupation of the building and environmental variables such as outdoor temperature, climatology, etc. were analyzed. In this sense, the present study aims to analyze the outdoor temperature effect over standards indications by means the Monte Carlo method. This iterative methodology will allow us to analyze the impact of multiple variables on the energy efficiency of the building and will let us show the better retrofit option to reach the energetic optimization.  
It starts from the modeling of the energy certification method by spreadsheets and into comparing it with the results obtained by the CE3X software, observing that the deviations between the two are minimal, as it was shown in previous sections. After this, the application of the Monte Carlo method over this standard will let us to obtain thousands of energy certifications and the obtained bell of Gauss will let us define a mathematical model that relates main retrofit parameters with the cost of the actions and the energy consumption.  
In this sense, the building objective of this study is located in the province of La Coruna, with the environmental data (maximum temperature (T\({}_{\text{max}}\)), minimum temperature (T\({}_{\text{min}}\)), dry bulb temperature (T\({}_{\text{dry bulb}}\)), relative humidity (RH)) obtained from DB-HE1 standard showed in Table 3.  
As we can see in Table 3, outdoor temperature data can oscillate between the minimum and maximum-recorded value. With the aim to obtain the probability distribution of the energy consumption for each different retrofitting option, in accordance with the Monte Carlo method indications, the calculation of building energy consumption was modified from this monthly average value to a random one. Because of this random process, a bell of Gauss of the energy consumption for each different possible modification was obtained. In particular, after a minimum of 200 iterations, defined this number in accordance with previous research work results [31; 32; 33], it can be carried out an energetic analysis of the energy consumption distribution, respect the value proposed by CE3X software for constant outdoor temperature, reflected in Figure 10.  
On one hand, at the time to prepare the energy certification of this building a static value of dry temperatures defined by the Spanish technical building code (Table 3), 0.67 ach and category 2 window permeability (27 m\({}^{3}\)/h m\({}^{2}\)) was selected and gave us a base value 56.520 kWh/m\({}^{2}\). On the other hand, if a random outdoor dry bulb temperature is employed, the distribution of frequencies describes a bell of Gauss centered in 63.480 kWh/m\({}^{2}\). This difference shows the need of an analysis of deviation causes as it will be done in the discussion section.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Primary Energy Consumption** & **Initial Certification** & \
\begin{tabular}{c} **Certification** \\ **(after Retrofitting)** \\ \end{tabular} &
\begin{tabular}{c} **Real Sampled Data** \\ **(after Retrofitting)** \\ \end{tabular} \\ \hline Heating & 173,410 & 140,690 & 37,247 \\ DHW & 51,040 & 19,820 & 7,783 \\ Total & 224,500 & 160,510 & 45,948 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Future energy consumption.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & **Jan** & **Feb** & **Mar** & **Apr** & **May** & **Jun** & **Jul** & **Ago** & **Sep** & **Oct** & **Nov** & **Dec** \\ \hline \(\text{T}_{\text{dry bulb}}\) (°C) & 8.1 & 9.3 & 10.8 & 12.3 & 15.6 & 16.0 & 19.2 & 19.2 & 17.1 & 16.0 & 11.3 & 8.8 \\
**RH (\%)** & 74.7 & 64.6 & 60.2 & 57.4 & 57.3 & 47.0 & 40.2 & 42.1 & 49.7 & 62.7 & 70