SQL rownumber by columngroup, Sql Server

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create table [Data] (
    [Date] date
  , Initials varchar(10)
  , Activity varchar(255)
  , ActivityType varchar(255)
);

insert into [dbo].[Data] ([Date],[Initials],[Activity],[ActivityType]) values 
 ('2016-12-05','PersonA','Work','Work')
,('2016-12-06','PersonA','Work','Work')
,('2016-12-07','PersonA','AbsenceActivity','Absence')
,('2016-12-08','PersonA','AbsenceActivity','Absence')
,('2016-12-09','PersonA','AbsenceActivity','Absence')
,('2016-12-10',null,null,'NoShift')
,('2016-12-11',null,null,'NoShift')
,('2016-12-12','PersonA','AbsenceActivity','Absence')
,('2016-12-13','PersonA','Work','Work')
,('2016-12-14','PersonA','AbsenceActivity','Absence')
,('2016-12-15','PersonA','AbsenceActivity','Absence')
/* -- added test data
,('2016-12-16','PersonA','Work','Work')
,('2016-12-17','PersonA','Work','Work')
,('2016-12-18','PersonA','AbsenceActivity','Absence')
,('2016-12-19','PersonA','Work','Work')
,('2016-12-20','PersonA','AbsenceActivity','Absence')
--*/
;

with cte as (
  select  
        [Date]
      , Initials
      , activity
      , ActivityType
      , irn=row_number() over (
          partition by Initials 
          order by [date]
          )
      , atrn=row_number() over (
          partition by Initials, activitytype 
          order by [date]
          )
    from    [data] d
    group by [Date], Initials, Activity, ActivityType
    )

select 
      [date] = convert(varchar(10),[Date],120) 
        /* convert to override rextester date format */
    , Initials
    , activity
    , ActivityType
    , ActivityGroup = case 
        when ActivityType='Work' 
          then 0 
        else dense_rank() over (
            partition by Initials, ActivityType 
            order by irn-atrn
            )
        end
  from cte
order by [date]

/* desired results */
/*
select [date]='2016-12-05',Initials='PersonA',Activity='Work',ActivityType='Work',identifier='0'union all
select '2016-12-06','PersonA','Work','Work','0'  union all
select '2016-12-07','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-08','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-09','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-12','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-13','PersonA','Work','Work','0'  union all
select '2016-12-14','PersonA','AbsenceActivity','Absence','2'  union all
select '2016-12-15','PersonA','AbsenceActivity','Absence','2'  
--*/
/* alt 1 */
/*
select [Date]='2016-12-05' ,Initials='PersonA',Activity='Work',ActivityType='Work',identifier='0'union all
select '2016-12-06','PersonA','Work','Work','0'  union all
select '2016-12-07','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-08','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-09','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-10',null,'Weekend','noShift',null  union all
select '2016-12-11',null,'Weekend','noShift',null  union all
select '2016-12-12','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-13','PersonA','Work','Work','0'  union all
select '2016-12-14','PersonA','AbsenceActivity','Absence','2'  union all
select '2016-12-15','PersonA','AbsenceActivity','Absence','2'  
--*/
/* alt 2 */
/*
select [Date]='2016-12-07',Initials='PersonA',Activity='AbsenceActivity',ActivityType='Absence',identifier='1'union all
select '2016-12-08','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-09','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-10',null,'Weekend','noShift',null  union all
select '2016-12-11',null,'Weekend','noShift',null  union all
select '2016-12-12','PersonA','AbsenceActivity','Absence','1'  union all
select '2016-12-14','PersonA','AbsenceActivity','Absence','2'  union all
select '2016-12-15','PersonA','AbsenceActivity','Absence','2'  
--*/

​x
select [Date]='2016-12-07',Initials='PersonA',Activity='AbsenceActivity',ActivityType='Absence',identifier='1'union all
 
create table [Data] (
    [Date] date
  , Initials varchar(10)
  , Activity varchar(255)
  , ActivityType varchar(255)
);
​
insert into [dbo].[Data] ([Date],[Initials],[Activity],[ActivityType]) values 
 ('2016-12-05','PersonA','Work','Work')
,('2016-12-06','PersonA','Work','Work')
,('2016-12-07','PersonA','AbsenceActivity','Absence')
,('2016-12-08','PersonA','AbsenceActivity','Absence')
,('2016-12-09','PersonA','AbsenceActivity','Absence')
,('2016-12-10',null,null,'NoShift')
,('2016-12-11',null,null,'NoShift')
,('2016-12-12','PersonA','AbsenceActivity','Absence')
,('2016-12-13','PersonA','Work','Work')
,('2016-12-14','PersonA','AbsenceActivity','Absence')
,('2016-12-15','PersonA','AbsenceActivity','Absence')
/* -- added test data
,('2016-12-16','PersonA','Work','Work')
,('2016-12-17','PersonA','Work','Work')
,('2016-12-18','PersonA','AbsenceActivity','Absence')
,('2016-12-19','PersonA','Work','Work')
,('2016-12-20','PersonA','AbsenceActivity','Absence')
--*/
;
​
with cte as (
  select  
        [Date]
      , Initials
      , activity
      , ActivityType
      , irn=row_number() over (
          partition by Initials 
          order by [date]

View schema
Execution time: 0,02 sec, rows selected: 11, rows affected: 11, absolute service time: 0,17 sec