Explicame con mayor detalle la formula para calcular los indicadores en el siguiente texto. El texto es el siguiente: "\section{Metrics with environmental implications}
 This section delves into various metrics employed to assess the environmental implications of computational processes \cite{oyedeji2018catalogue, Calero2021, noman2022exploratory, calero2013systematic}. From the fundamental measure of runtime to more nuanced evaluations such as CPU/GPU or TPU hours and RAM energy consumption, each metric provides unique insights into the interplay between computational efficiency and environmental sustainability \cite{tornede2023towards, heguerte2023estimate, lannelongue2021green, strubell2019energy, patel2015green}.


\subsection{Runtime}
Runtime is a fundamental measure assessing the total duration a program needs for execution. While not perfect for evaluating program efficiency, it is significantly correlated with the energy consumption associated with the corresponding experiment. Despite not providing a precise estimate of energy efficiency, measuring runtime serves as a valuable indicator. Using runtime as a metric allows for estimating the total carbon footprint of the experiment, contingent upon additional information such as the specific power consumption of the hardware and the composition of the power mix. Despite these additional considerations, runtime stands out for its ease of measurement, making it a practical and widely used tool for evaluating program performance across various environments and platforms compared to other metrics.

\subsection{CPU/GPU/TPU Hours}
Measuring CPU/GPU/TPU hours represents a practical and simple approach to quantifying environmental impact. However, this metric can be ambiguous, as its calculation can be based on both the actual clock time and the actual activity time, which can lead to different interpretations of the environmental impact.

Despite its usefulness, counting usage hours presents itself as a suboptimal indicator of efficiency, largely due to its dependence on specific hardware. Even so, this metric remains one of the most practical thanks to its ease of measurement and its relatively simple ability to estimate the carbon footprint. This, of course, assumes that the devices consume a constant amount of energy and that the composition of the energy combination used is known.

The calculation of the total power consumption of all active devices, denoted as \(E_{TotalPU}\) (Equation \ref{eq:EnergyTOTAL}), is done by the product of the power consumption of the devices and their charging time. The power calculation for all CPU devices is denoted by \(E_{CPU}\) (Equation \ref{eq:EnergyCPU}):
    \begin{align}
    \label{eq:EnergyCPU}
     E_ {CPU} = TDP \int_{0}^{n} W_{CPU}(t) dt 
    \end{align}
here, \(TDP\) represents the specific power consumption of the equivalent CPU model under long-term load, and \(W_{CPU}\) is the total load of all processors expressed as a fraction. Analogously, the total power consumption of all active GPUs, denoted as \(E_{GPU}\), is calculated using a similar formula (Equation \ref{eq:EnergyGPU}): 
    \begin{align}
    \label{eq:EnergyGPU}
     E_{GPU} = TDP_{GPU} \int_{ 0}^{n} W_{GPU}(t) dt 
    \end{align}    
where \(TDP_{GPU}\) is the specific power consumption of the equivalent GPU model under long-term load and \(W_{ GPU}\) is the total load of all graphics processing units expressed as a fraction. Analogously, the total power consumption of all active TPUs, denoted as \(E_{TPU}\), is calculated using a the mathematical expression to determine the energy consumption of one or more TPUs would be the sum of the products of the voltage and current of each TPU, multiplied by the time of use, plus the sum of the energy consumption of each TPU in case of operating sequentially. This could be represented as follows (Equation \ref{eq:EnergyTPU}): 

    \begin{align}
    \label{eq:EnergyTPU}
     E_{TPU} = \sum _{i=1}^{n}(V_{i} \cdot C_{i} \cdot T_{usage}) + \sum _{i=1} ^{n}(TPUec _{i})
    \end{align}    

The equation \(E_{TPU}\) calculates total power of active TPUs. It sums the product of each TPU’s \(V_{i}\), \(C_{i}\), and usage \(T\), and its sequential energy consumption \(TPUec_{i}\).

The total power consumption of the system, denoted as \(E_{TCGT}\), is obtained by adding the total power consumption of the CPUs, GPUs and TPUs (Equation \ref{eq:EnergyTOTAL}): 
    \begin{align}
    \label{eq:EnergyTOTAL}
     E_{TCGT} = E_{CPU} + E_{GPU} + E_{TPU} 
    \end{align}
This formula provides a complete view of the environmental impact of the units processors, taking into account the contribution of both processing sources \cite{maevsky2017evaluating, eco2AI}. 

\subsection{RAM Energy Consumption}
RAM significantly contributes to energy consumption in modern computing, particularly with data-intensive tasks. Accounting for RAM energy poses challenges due to its dependency on data activities. The power consumption, \(E_{RAM}\), is calculated as (Equation \ref{eq:EnergyRAM}): 
    \begin{align}
    \label{eq:EnergyRAM}
    E_{RAM} = 0.375\int_{0}^{n} M_{RAM_{i}}(t) dt 
    \end{align}
where \(M_{RAM_{i}}\) is allocated memory (GB). It has been discussed how to calculate the energy consumption for processing units (CPU, GPU, and TPU) and RAM. Now, to get a comprehensive view of the system's environmental impact, it's important to consider all these energy consumption sources together. Therefore, we propose a new metric, \(E_{Total}\), which sums up the energy consumption of the processing units and the RAM. The modified formula is as follows (Equation \ref{eq:EnergyTOTALRAM}):

\begin{align}
\label{eq:EnergyTOTALRAM}
E_{Total} = E_{TCGT} + E_{RAM}
\end{align}

This metric provides a more comprehensive view of the system's environmental impact, taking into account both processing sources and memory. By including RAM in our metric, we can more accurately capture energy consumption in data-intensive tasks, enhancing our understanding of environmental impact \cite{maevsky2017evaluating, eco2AI}.


\subsection{Assessing the Carbon Footprint and CO\textsubscript{2}e}
Understanding the environmental impact of AutoML experiments requires a multi-faceted approach, considering both energy consumption and its broader implications. While directly measuring energy expenditure doesn't provide a perfect evaluation of specific algorithms, it serves as a valuable indicator for the overall environmental footprint. Quantifying energy consumption, despite its limitations in assessing internal efficiency, provides a commendable starting point for understanding the experiment-specific environmental impact. Hardware efficiency plays a crucial role in this assessment, as it significantly influences how much energy AutoML algorithms consume during execution. 

Accurately quantifying the Carbon Footprint ($CF$) associated with AI practices presents additional challenges beyond merely measuring energy consumption. Factors such as geographical location, execution duration, and various other parameters contribute to the complexity of this metric. However, despite these inherent difficulties, measuring CO\textsubscript{2}e remains essential for gaining a comprehensive understanding of the environmental impact of AI operations. This comprehensive approach to calculating the carbon footprint involves considering energy consumption alongside other critical factors such as emission intensity ($\gamma$) and Power Usage Effectiveness ($PUE$). Employing this comprehensive methodology, as outlined in Equation (\ref{eq:EnergyCF}), fosters a deeper understanding of the sustainability and eco-friendliness of AI practices.


\begin{align}
\label{eq:EnergyCF}
CF = \gamma \cdot PUE \cdot E_{Total}
\end{align}


By precisely measuring energy use and considering hardware efficiency and execution conditions, we can confidently approximate CO\textsubscript{2}e emissions generated during AutoML processes, thus offering a more comprehensive assessment of AutoML's environmental implications. This comprehensive approach considers not only the total energy consumption but also the key parameters mentioned above. Including these factors with the total energy consumption of the AI components, the equivalent CO\textsubscript{2}e rate is obtained in Equation (\ref{eq:EnergyCO2eq}), 

\begin{align}
\label{eq:EnergyCO2eq}
CO\textsubscript{2}e = \gamma \cdot PUE \cdot E_{Total}
\end{align}

providing a measure of the carbon emissions associated with the AI operation, enabling a deeper understanding of their sustainability and eco-friendliness.