Daily totals for sawtooth pattern local maxima - sql

Question

I have multiple monotonic counters that can be reset ad-hoc. These counters exhibit sawtooth behavior when graphed (however they are not strictly increasing). I want a monthly report showing daily sums of the maxima for each counter.
My strategy so far is to put a '1' on the rows where the counter is less than the previous sampling of the counter (also less than or equal to the next). Then calculate a running total on that column to identify series without resets.
Then I group over the daily intervals to calculate max-min for each series in the day, then sum those portions to get grand totals for the day.
What I have works, but it takes ~10s to run. The execution plan shows two big sorts: one in cteData and I think the other is in cteSeries. I feel like I should be able to eliminate one of them but I'm at a loss how to do it.
The result of this code is (which I can now see is actually skipping a sample across the interval boundary):
interval tagname total
2020-01-01 alpha 3
2020-01-01 bravo 4
2020-01-02 alpha 3
2020-01-02 bravo 4
IF OBJECT_ID('tempdb..#counter_data') IS NOT NULL
DROP TABLE #counter_data;
CREATE TABLE #counter_data(
t_stamp DATETIME NOT NULL
,tagname VARCHAR(32) NOT NULL
,val REAL NULL
PRIMARY KEY(t_stamp, tagname)
);
INSERT INTO #counter_data(t_stamp, tagname, val)
VALUES
('2020-01-01 04:00', 'alpha', 0)
,('2020-01-01 04:00', 'bravo', 0)
,('2020-01-01 08:00', 'alpha', 1)
,('2020-01-01 08:00', 'bravo', 1)
,('2020-01-01 12:00', 'alpha', 2)
,('2020-01-01 12:00', 'bravo', 2)
,('2020-01-01 16:00', 'alpha', 0)
,('2020-01-01 16:00', 'bravo', 3)
,('2020-01-01 20:00', 'alpha', 1)
,('2020-01-01 20:00', 'bravo', 4)
,('2020-01-02 04:00', 'alpha', 2)
,('2020-01-02 04:00', 'bravo', 5)
,('2020-01-02 08:00', 'alpha', 3)
,('2020-01-02 08:00', 'bravo', 6)
,('2020-01-02 12:00', 'alpha', 0)
,('2020-01-02 12:00', 'bravo', 7)
,('2020-01-02 16:00', 'alpha', 1)
,('2020-01-02 16:00', 'bravo', 8)
,('2020-01-02 20:00', 'alpha', 2)
,('2020-01-02 20:00', 'bravo', 9)
;
DECLARE #dateStart AS DATETIME = '2020-01-01';
DECLARE #dateEnd AS DATETIME = DATEADD(month, 2, #dateStart);
WITH cteData AS(
SELECT
t_stamp
,tagname
,val
,CASE
WHEN val < LAG(val) OVER(PARTITION BY tagname ORDER BY t_stamp)
AND val <= LEAD(val) OVER(PARTITION BY tagname ORDER BY t_stamp)
THEN 1
ELSE 0
END AS rn
FROM #counter_data
WHERE
t_stamp >= #dateStart AND t_stamp < #dateEnd
AND tagname IN(
'alpha'
,'bravo'
)
)
,cteSeries AS(
SELECT
CAST(t_stamp AS DATE) AS interval
,tagname
,val
,SUM(rn) OVER(PARTITION BY tagname ORDER BY t_stamp) AS series
FROM cteData
)
,cteSubtotal AS(
SELECT
interval
,tagname
,MAX(val) - MIN(val) AS subtotal
FROM cteSeries
GROUP BY interval, tagname, series
)
,cteGrandTotal AS(
SELECT
interval
,tagname
,SUM(subtotal) AS total
FROM cteSubtotal
GROUP BY interval, tagname
)
SELECT *
FROM cteGrandTotal
ORDER BY interval, tagname

Answer 1

I would just calculate the increase of the counter in each row by comparing it to the previous row:
with cte
as
(
SELECT *,isnull(lag(val) over (partition by tagname order by t_stamp),0) as previousVal
FROM counter_data
)
SELECT cast(t_stamp as date),tagname, sum(case when val>previousVal then val-previousval else val end )
FROM cte
GROUP BY cast(t_stamp as date),tagname;

Answer 2

This looks like a gaps-and-islands problem. I think that you want lag() to get the "previous" value and a conditional sum to compute the daily count.
select
tag_name,
cast(t_stamp as date) t_date,
sum(case when val = lag_val + 1 the 1 else 0 end) total
from (
select
c.*,
lag(val) over(
partition by tagname, cast(t_stamp as date)
order by t_stamp
) lag_val
from #counter_data c
) c
group by tagname, cast(t_stamp as date)
order by t_date, tagname