**-s**- Check the spatial topology of temporally related maps and process only spatially related maps
**-n**- Register Null maps
**-g**- Use granularity sampling instead of the temporal topology approach
**-d**- Perform a dry run, compute all dependencies and module calls but don't run them
**--help**- Print usage summary
**--verbose**- Verbose module output
**--quiet**- Quiet module output
**--ui**- Force launching GUI dialog

**expression**=*string***[required]**- r.mapcalc expression for temporal and spatial analysis of space time raster datasets
**basename**=*string***[required]**- Basename of the new generated output maps
- A numerical suffix separated by an underscore will be attached to create a unique identifier
**nprocs**=*integer*- Number of r.mapcalc processes to run in parallel
- Default:
*1*

** "result = expression" **

The statement structure is similar to r.mapcalc, see r.mapcalc.
Where **result** represents the name of a space time raster dataset (STRDS)that will
contain the result of the calculation that is given as **expression**
on the right side of the equality sign.
These expression can be any valid or nested combination of temporal
operations and spatial overlay or buffer functions that are provided by the temporal algebra.

The temporal raster algebra works with space time raster datasets only (STRDS).
The algebra provides methods for map selection from STRDS based on their temporal relations.
It is also possible to temporally shift maps, to create temporal buffer and to snap time
instances to create a valid temporal topology. Furthermore expressions can be nested and
evaluated in conditional statements (if, else statements). Within if-statements the algebra
provides temporal variables like start time, end time, day of year, time differences or
number of maps per time interval to build up conditions.

In addition the algebra provides
a subset of the spatial operations from r.mapcalc.
All these operations can be assigned to STRDS or to the resulting map lists of operations between STRDS.

As default, topological relationships between space time datasets will be
evaluated only temporal. Use the **s** flag to activate the
additionally evaluate the spatial topology based on the spatial extents of maps.

The expression option must be passed as **quoted**
expression, for example:

t.rast.algebra expression="C = A + B" basename=result

The map basename for the result STRDS must always be specified.

equals A ------ B ------ during A ---- B ------ contains A ------ B ---- starts A ---- B ------ started A ------ B ---- finishs A ---- B ------ finished A ------ B ---- precedes A ---- B ---- follows A ---- B ---- overlapped A ------ B ------ overlaps A ------ B ------ over booth overlaps and overlapped

Topological relations must be specified in {} parentheses.

LEFT REFERENCE l Use the time stamp of the left space time dataset INTERSECTION i Intersection DISJOINT UNION d Disjoint union UNION u Union RIGHT REFERENCE r Use the time stamp of the right space time dataset

C = A : B

In addition the inverse selection operator **!:** is defined as the complement of
the selection operator, hence the following expression

C = A !: B

To select parts of a STDS by different topological relations to other STDS,
the temporal topology selection operator can be used. The operator consists of
the temporal selection operator, the topological relations, that must be separated
by the logical OR operator **|** and the temporal extent operator.
All three parts are separated by comma and surrounded by curly braces:
{"temporal selection operator", "topological relations", "temporal operator"}

**Examples:**

C = A {:, equals} B C = A {!:, equals} B

C = A {:,equals|during|overlaps} B

In addition we can define the temporal extent of the result STDS by adding the temporal operator.

C = A {:, during,r} B

The selection operator is implicitly contained in the temporal topology selection operator, so that the following statements are exactly the same:

C = A : B C = A {:} B C = A {:,equal} B C = A {:,equal,l} B

C = A !: B C = A {!:} B C = A {!:,equal} B C = A {!:,equal,l} B

Note A and B can either be space time datasets or expressions. The temporal relationship between the conditions and the conclusions can be defined at the beginning of the if statement. The relationship between then and else conclusion must be always equal. if statement decision option temporal relations if(if, then, else) if(conditions, A) A if conditions are True; temporal topological relation between if and then is equal. if(conditions, A, B) A if conditions are True, B otherwise; temporal topological relation between if, then and else is equal. if(topologies, conditions, A) A if conditions are True; temporal topological relation between if and then is explicit specified by topologies. if(topologies, conditions, A, B) A if conditions are True, B otherwise; temporal topological relation between if, then and else is explicit specified by topologies.

Symbol description == equal != not equal > greater than >= greater than or equal < less than <= less than or equal && and || or

td(A) Returns a list of time intervals of STDS A start_time(A) Start time as HH::MM:SS start_date(A) Start date as yyyy-mm-DD start_datetime(A) Start datetime as yyyy-mm-DD HH:MM:SS end_time(A) End time as HH:MM:SS end_date(A) End date as yyyy-mm-DD end_datetime(A) End datetime as yyyy-mm-DD HH:MM start_doy(A) Day of year (doy) from the start time [1 - 366] start_dow(A) Day of week (dow) from the start time [1 - 7], the start of the week is Monday == 1 start_year(A) The year of the start time [0 - 9999] start_month(A) The month of the start time [1 - 12] start_week(A) Week of year of the start time [1 - 54] start_day(A) Day of month from the start time [1 - 31] start_hour(A) The hour of the start time [0 - 23] start_minute(A) The minute of the start time [0 - 59] start_second(A) The second of the start time [0 - 59] end_doy(A) Day of year (doy) from the end time [1 - 366] end_dow(A) Day of week (dow) from the end time [1 - 7], the start of the week is Monday == 1 end_year(A) The year of the end time [0 - 9999] end_month(A) The month of the end time [1 - 12] end_week(A) Week of year of the end time [1 - 54] end_day(A) Day of month from the start time [1 - 31] end_hour(A) The hour of the end time [0 - 23] end_minute(A) The minute of the end time [0 - 59] end_second(A) The second of the end time [0 - 59]

The structure is similar to the select operator with the extension of an aggregation operator: {"comparison operator", "topological relations", aggregation operator, "temporal operator"}

This aggregation operator (| or &) define the behaviour if a map is related the more than one map, e.g for the topological relations 'contains'. Should all (&) conditions for the related maps be true or is it sufficient to have any (|) condition that is true. The resulting boolean value is then compared to the first condition by the comparison operator (|| or &&). As default the aggregation operator is related to the comparison operator:

Comparison operator -> aggregation operator:

|| -> | and && -> &

Condition 1 {||, equal, r} Condition 2 Condition 1 {&&, equal|during, l} Condition 2 Condition 1 {&&, equal|contains, |, l} Condition 2 Condition 1 {&&, equal|during, l} Condition 2 && Condition 3 Condition 1 {&&, equal|during, l} Condition 2 {&&,contains, |, r} Condition 3

A{#, contains}B

A list of integers (scalars) corresponding to the maps of A that contain maps from B will be returned.

C = if({equal}, A {#, contains} B > 2, A {:, contains} B)

Furthermore the temporal algebra allows temporal buffering, shifting and snapping with the functions buff_t(), tshift() and tsnap() respectively.

buff_t(A, size) Buffer STDS A with granule ("1 month" or 5) tshift(A, size) Shift STDS A with granule ("1 month" or 5) tsnap(A) Snap time instances and intervals of STDS A

tmap()

C = A {:,during} tmap(event)

Symbol description precedence % modulus 1 / division 1 * multiplication 1 + addition 2 - subtraction 2

abs(x) return absolute value of x float(x) convert x to foating point int(x) convert x to integer [ truncates ] log(x) natural log of x sqrt(x) square root of x tan(x) tangent of x (x is in degrees) round(x) round x to nearest integer sin(x) sine of x (x is in degrees) isnull(x) check if x = NULL isntnull(x) check if x is not NULL null set null value exist(x) Check if x is in the current mapset

map()

C = A * map(constant_value)

{"spatial or select operator", "list of temporal relations", "temporal operator"}

C = A {+, contains} B --> c1 = a1 + b1 + b2 + b3

Keep attention that the aggregation behaviour is not symmetric:

C = B {+, during} A --> c1 = b1 + a1 c2 = b2 + a1 c3 = b3 + a1

strds[2]Refers to the second successor of the current map

strds[1,2]Refers to the cell one row below and two columns to the right of the current cell in the current map

strds[1,-2,-1]Refers to the cell two rows above and one column to the left of the current cell of the first successor map

strds[-2,0,1]Refers to the cell one column to the right of the current cell in the second predecessor map.

D = if(start_date(A) < "2005-01-01", A + B)

C = A + B

C = A {+,equal,l} B

C = if(A > 100 && A < 1600 && td(A) > 30, B)

C = if({equal}, A > 100 && A < 1600 {&&,equal} td(A) > 30, B)

C = if(Temp > 10.0, Prec / 3600.0 /24.0 / td(Prec))

C = if({equal}, Temp > 10.0, Prec / 3600.0 / 24.0 {/,equal,l} td(Prec))

C = if(B {#,contain} A > 1, (B {+,contain,l} A - B) / (B {#,contain} A), A)

C = if({equal}, B {#,contain} A > 1, (B {+,contain,l} A {-,equal,l} B) {equal,=/} (B {#,contain} A), A)

*Last changed: $Date: 2017-10-10 01:27:00 -0700 (Tue, 10 Oct 2017) $*

Available at: t.rast.algebra source code (history)

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