In a Sobol type sensitivity analysis we ci sider a function $y=f(x)$. As long as the with $x=(x_1,x_2,..,x_q)$. As long as the components of $x$ are probabilistically independent then $f$ has the unique ANOVA decomposition. To perform the SA I need a probability distribution over $X$, I.e. I need to formulate my uncertainty in $X$. The uncertainty in $X$ induces uncertainty in $Y$, SA tells me how uncertainty in model inputs influences uncertainty in model outputs. The entire sensitivity analysis depends on this distribution so please make sure it is sensible prior to proceeding.

$$ f(x) = f_0 + \sum_i f_i (x_i) + \sum_{i<j} f_{ij}(x_{ij}) + \ldots + f_{12 \ldots , q } (x)$$

$f_0$ is the mean value of the fucntion, the $f_i$ are the main effects, $f_{ij}$ are the second order interactions and so on.

Then let $V = var(Y)$ and $V_J = Var_{X_J}( E(f(x) | X_{-J} ) )$ for any set $ J \subseteq \{ 1, 2 , \ldots , q \}$. In general $S_J = V_J / V$.

Then $S_i = V_i / V$ is the proportion of uncertainty in $Y$ attributed to the main effect of variable $i$. Some authors (e.g. Tony O'Hagan) believe that this is the single most important variable.

Other authors prefer to measure the most important variable by

$$S_{T_i} = \sum_{J \supseteq i } (V_J / V) = \sum_{J \supseteq i} S_J $$

This quantity represents the total uncertainty induced by variable $i$. E.g. for a three parameter input we have

$$ S_{T_1} = S_1 + S_{12} + S_{13} + S_{123}. $$

So from your analysis $10/%$ of output uncertainty is due to the main effect of the first variable; it is however related to $60\%$ of total output uncertainty due to how it interacts with the other variables.

In a Sobol type sensitivity analysis we consider a function $y=f(x)$ where $x=(x_1,x_2,..,x_q)$. As long as the components of $x$ are probabilistically independent then $f$ has the unique ANOVA decomposition. To perform the SA I need a probability distribution over $X$, I.e. I need to formulate my uncertainty in $X$. The uncertainty in $X$ induces uncertainty in $Y$, SA tells me how uncertainty in model inputs influences uncertainty in model outputs. The entire sensitivity analysis depends on this distribution so please make sure it is sensible prior to proceeding.

$$ f(x) = f_0 + \sum_i f_i (x_i) + \sum_{i<j} f_{ij}(x_{ij}) + \ldots + f_{12 \ldots , q } (x)$$

$f_0$ is the mean value of the function, the $f_i$ are the main effects, $f_{ij}$ are the second order interactions and so on.

Then let $V = var(Y)$ and $V_J = Var_{X_J}( E(f(x) | X_{-J} ) )$ for any set $ J \subseteq \{ 1, 2 , \ldots , q \}$. In general $S_J = V_J / V$.

Then $S_i = V_i / V$ is the proportion of uncertainty in $Y$ attributed to the main effect of variable $i$. Some authors (e.g. Tony O'Hagan) believe that this is the single most important variable.

Other authors prefer to measure the most important variable by

$$S_{T_i} = \sum_{J \supseteq i } (V_J / V) = \sum_{J \supseteq i} S_J $$

This quantity represents the total uncertainty induced by variable $i$. E.g. for a three parameter input we have

$$ S_{T_1} = S_1 + S_{12} + S_{13} + S_{123}. $$

So from your analysis $10\%$ of output uncertainty is due to the main effect of the first variable; it is however related to $60\%$ of total output uncertainty due to how it interacts with the other variables.