Web Scraper cannot handle drop down menus but usually there is a solution for those that involves creating range start urls. If you look at the sites url you can see that year and month are simply numeric values and by changing them you can load another year/month. When specifying the start url for a sitemap you can specify a numeric range in it like this - [1-12]. In these cases Web Scraper will start with 12 urls. Here is a sitemap that scrapes year 2010. If you want to add more years then add more start urls for each year (only one range is allowed in the url).
Also the site could be scraped using element click selector that would click the "next month" button but the range url solution is much better.
{"_id":"climate-weather-gc-ca","startUrl":"
http://climate.weather.gc.ca/climateData/dailydata_e.html?timeframe=2&Prov=AB&StationID=1865&dlyRange=1959-05-01%7C2012-04-11&cmdB1=Go&Year=2010&Month=[1-12]&cmdB1=Go#","selectors":[{"parentSelectors":["_root"],"type":"SelectorElement","multiple":true,"id":"table-row","selector":"table.wet-boew-zebra tr:nth-of-type(n+2):not(:has(th))","delay":""},{"parentSelectors":["table-row"],"type":"SelectorText","multiple":false,"id":"day","selector":"td:nth-of-type(1)","regex":"","delay":""},{"parentSelectors":["table-row"],"type":"SelectorText","multiple":false,"id":"temp-max","selector":"td:nth-of-type(2)","regex":"","delay":""},{"parentSelectors":["table-row"],"type":"SelectorText","multiple":false,"id":"temp-min","selector":"td:nth-of-type(3)","regex":"","delay":""},{"parentSelectors":["table-row"],"type":"SelectorText","multiple":false,"id":"temp-mean","selector":"td:nth-of-type(4)","regex":"","delay":""},{"parentSelectors":["_root"],"type":"SelectorText","multiple":false,"id":"year","selector":"form#frmDateNav1 select.display-inline.align-center option:selected","regex":"\\d+","delay":""},{"parentSelectors":["_root"],"type":"SelectorText","multiple":false,"id":"month","selector":"select#Month1.display-inline option:selected","regex":"","delay":""}]}