Moisture sources and pathways associated with the spatial variability of seasonal extreme precipitation over Canada

Abstract

Nine regions with spatially coherent seasonal 3-day total precipitation extremes across Canada were identified using a clustering method that is compliant to the extreme value theory. Using storm back-trajectory analyses, we then identified possible moisture sources and pathways that are conducive to occurrences of seasonal extreme precipitation events in four seasons for the nine regions identified. Moisture pathways for all extreme precipitation events were clustered to nine dominant moisture pathway patterns using the self-organizing map method. Results show that horizontal moisture pathway patterns and their occurrences were not evidently different between seasons. However, warm (summer and fall) and cold (winter and spring) seasons show considerable differences in the spreading of moisture sources in all nine regions, even though many sources do not frequently contribute to extreme precipitation events. In all four seasons, terrestrial evapotranspiration had provided major moisture sources to many extreme precipitation events occurred in inland regions. Central Canada had received more widespread moisture sources over surrounding oceans of North America than western and eastern Canada, because of more diverse moisture pathway patterns for central Canada that transport moisture from all surrounding oceans to central Canada. Extreme precipitation in southwestern Canada mainly resulted from atmospheric rivers over the North Pacific Ocean. For northwestern Canada, moisture pathway patterns were from the northern Pacific, Arctic and northern Atlantic oceans, even though more than 78% of trajectories for northwestern Canada were from the North Pacific. Westerlies from the North Pacific Ocean and northern polar jet streams controlled dominant pathways to central and eastern Canada. More extreme precipitation events over Canada were fed by the Arctic Ocean in warm than in cold seasons.

Appendix: F-madogram

Given N samples of bivariate extremal data ${(M_i^n,M_j^n)^N}$ from two locations i and j, the non-parametric estimator for the F-madogram is (Bernard et al. 2013),

$${\widehat d_{ij}} = \frac{1}{{2N}}\sum\limits_{n = 1}^N {\left| {{{\widehat F}_i}\left( {M_i^n} \right) - {{\widehat F}_j}\left( {M_j^n} \right)} \right|} ,$$

(1)

where

$${\widehat F_i}\left( u \right) = \frac{1}{N}\sum\limits_{n = 1}^N {{1_{\left\{ {M_i^n \leqslant u} \right\}}}} ,$$

(2)

where ${1_{\{ M_i^n \leqslant u\} }}$ is the indicator function for the event $\left\{ {M_i^n \leqslant u} \right\}$ which returns 1 if the statement if true or 0 otherwise. The entire function returns a proportion of the number of data points that are less than or equal to a given value u (the empirical cumulative distribution function). The F-madogram does not depend on the magnitude of extreme events and provides a dimensionless metric that compares the shape of the extreme value distributions between two stations. Coupled with the PAM algorithm, the F-madogram provides an efficient and theoretically sound method for clustering extremal data.

To avoid misclassifying stations from geographically disparate and remote regions into the same clusters, Bracken et al. (2015) proposed an extension to the F-madogram-based PAM algorithm that also incorporates physical proximity of stations. The extension involves computing a modified version of the F-madogram

$${\widehat {\widehat d}_{ij}} = {\widehat d_{ij}} + {p_{ij}},$$

(3)

where

$${p_{ij}} = \frac{{{q_{ij}}}}{{\sum\nolimits_{n = 1}^N {{q_{ij}}} }}\mathop {\max }\limits_{ij} {\widehat d_{ij}}\quad {\text{and}}\quad {q_{ij}} = \sqrt {{{\left( {{x_i} - {x_j}} \right)}^2} + {{\left( {{y_i} - {y_j}} \right)}^2}} .$$

(4)

The computation of p _ij is simply the scaled Euclidian distance between locations of stations such that they will never exceed the largest value of the original F-madogram. The Euclidian distance formula, q _ij in which x and y are the geographic coordinates for two locations, may be replaced with the Haversine distance formula if the original data are not projected.