mongodb - datetime で日付を取得、操作、保存する

Question

注：投稿を小さくても直感的に保つために、出力にいくつかのドキュメントのみを提供しました

ソース コレクション:

{
        "_id" : {
                "SpId" : 840,
                "Scheduler_Id" : 1,
                "Channel_Id" : 2,
                "TweetId" : 15
        },
        "PostDate" : ISODate("2013-10-31T18:30:00Z")
}
{
        "_id" : {
                "SpId" : 840,
                "Scheduler_Id" : 1,
                "Channel_Id" : 2,
                "TweetId" : 16
        },
        "PostDate" : ISODate("2013-10-31T18:30:00Z")
}
{
        "_id" : {
                "SpId" : 840,
                "Scheduler_Id" : 1,
                "Channel_Id" : 2,
                "TweetId" : 17
        },
        "PostDate" : ISODate("2013-10-30T18:30:00Z")
}

Step-1 : PostDate によるグループ化

クエリ:

db.Twitter_Processed.aggregate({$match : { "_id.SpId" : 840, "_id.Scheduler_Id" : 1 }},{$project:{SpId : "$_id.SpId",Scheduler_Id : "$_id.Scheduler_Id",day:{$dayOfMonth:'$PostDate'},month:{$month:'$PostDate'},year:{$year:'$PostDate'}, senti : "$Sentiment"}}, {$group : {_id : {SpId : "$SpId", Scheduler_Id : "$Scheduler_Id",day:'$day',month:'$month',year:'$year'}, sentiment : { $sum : "$senti"}}}, {$group : {_id : "$_id" , avgSentiment : {$avg : "$sentiment"}}})

出力:

{
        "result" : [
                {
                        "_id" : {
                                "SpId" : 840,
                                "Scheduler_Id" : 1,
                                "day" : 31,
                                "month" : 10,
                                "year" : 2013
                        },
                        "avgSentiment" : 2.2700000000000005
                },
                {
                        "_id" : {
                                "SpId" : 840,
                                "Scheduler_Id" : 1,
                                "day" : 30,
                                "month" : 10,
                                "year" : 2013
                        },
                        "avgSentiment" : 4.96
                }
}

ステップ-2:これを達成しようとしています:

{
        "result" : [
                {
                        "_id" : {
                                "SpId" : 840,
                                "Scheduler_Id" : 1,
                 "Date" : ISODate("2013-10-31T18:30:00Z")
                        },
                        "avgSentiment" : 2.2700000000000005
                },
                {
                        "_id" : {
                                "SpId" : 840,
                                "Scheduler_Id" : 1,
                "Date" : ISODate("2013-10-31T18:30:00Z")
                        },
                        "avgSentiment" : 4.96
                }
}

私が試みたクエリ：

db.Twitter_Processed.aggregate({$match : { "_id.SpId" : 840, "_id.Scheduler_Id" : 1 }},{$project:{SpId : "$_id.SpId",Scheduler_Id : "$_id.Scheduler_Id",day:{$dayOfMonth:'$PostDate'},month:{$month:'$PostDate'},year:{$year:'$PostDate'}, senti : "$Sentiment"}}, {$group : {_id : {SpId : "$SpId", Scheduler_Id : "$Scheduler_Id",day:'$day',month:'$month',year:'$year'}, sentiment : { $sum : "$senti"}}}, {$group : {_id : "$_id" , avgSentiment : {$avg : "$sentiment"}}}, {$project : {_id : {SpId : "$_id.SpId",Scheduler_Id : "$_id.Scheduler_Id", date : new Date("$_id.year","$_id.month","$_id.day")}, avgSentiment : "$avgSentiment"}})

出力 (エラー) :

Error: Printing Stack Trace
    at printStackTrace (src/mongo/shell/utils.js:37:15)
    at DBCollection.aggregate (src/mongo/shell/collection.js:897:9)
    at (shell):1:22
Tue Dec 31 09:41:42.916 JavaScript execution failed: aggregate failed: {
        "errmsg" : "exception: disallowed field type Date in object expression (
at 'date')",
        "code" : 15992,
        "ok" : 0
} at src/mongo/shell/collection.js:L898

Step-2 を達成するにはどうすればよいですか?