NAME
t.rast.algebra - Apply temporal and spatial operations on space time raster datasets using temporal raster algebra.
KEYWORDS
temporal,
algebra,
raster,
time
SYNOPSIS
t.rast.algebra
t.rast.algebra --help
t.rast.algebra [-sngd] expression=string basename=string [nprocs=integer] [--help] [--verbose] [--quiet] [--ui]
Flags:
- -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
Parameters:
- 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
t.rast.algebra performs temporal and spatial map algebra operations on
space time raster datasets (STRDS) by using the temporal raster algebra.
The module expects an
expression as input parameter in the following form:
"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.mapcalc2 expression="C = A + B" basename=result
Where
C is the new space time raster dataset that will contain maps
with the basename "result" that represent the sum of maps from STRDS
A and
equally temporal related maps from STRDS
B.
The map basename for the result STRDS must always be specified.
The temporal algebra provides a wide range of temporal operators and
functions that will be presented in the following section.
Several temporal topology relations between registered maps of space
time datasets are supported:
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
The relations must be read as: A is related to B, like - A equals B - A is
during B - A contains B
Topological relations must be specified in {} parentheses.
The temporal algebra defines temporal operators that can be combined with other
operators to perform spatio-temporal operations.
The temporal operators process the time instances and intervals of two temporal
related maps and calculate the result temporal extent by five different possibilities.
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
The temporal selection simply selects parts of a space time dataset without
processing raster or vector data.
The algebra provides a selection operator
: that selects parts
of a space time dataset that are temporally equal to parts of a second one
by default. The following expression
means: Select all parts of space time dataset A that are equal to B and store
it in space time dataset C. The parts are time stamped maps.
In addition the inverse selection operator !: is defined as the complement of
the selection operator, hence the following expression
means: select all parts of space time time dataset A that are not equal to B
and store it in space time dataset (STDS) C.
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
We can now define arbitrary topological relations using the OR operator "|"
to connect them:
C = A {:,equals|during|overlaps} B
Select all parts of A that are equal to B, during B or overlaps B.
In addition we can define the temporal extent of the result STDS by adding the
temporal operator.
Select all parts of A that are during B and use the temporal extents from B for
C.
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
Same for the complementary selection:
C = A !: B
C = A {!:} B
C = A {!:,equal} B
C = A {!:,equal,l} B
Selection operations can be evaluated within conditional statements.
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.
The conditions are comparison expressions that are used to evaluate
space time datasets. Specific values of temporal variables are
compared by logical operators and evaluated for each map of the STDS.
Important: The conditions are evaluated from left to right.
Logical operators
Symbol description
== equal
!= not equal
> greater than
>= greater than or equal
< less than
<= less than or equal
&& and
|| or
Temporal functions
The following temporal function are evaluated only for the STDS that must be given in parenthesis.
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]
Comparison operator
The conditions are comparison expressions that are used to evaluate
space time datasets. Specific values of temporal variables are
compared by logical operators and evaluated for each map of the STDS and
the related maps.
For complex relations the comparison operator can be used to combine conditions:
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:
Examples:
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
Hash operator
Additionally the number of maps in intervals can be computed and used in
conditional statements with the hash (#) operator.
This expression computes the number of maps from space
time dataset B which are during the time intervals of maps from
space time dataset A.
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)
This expression selects all maps from A that temporally contains at least 2
maps from B and stores them in space time dataset C. The leading equal statement
in the if condition specifies the temporal relation between the if and then part
of the if expression. This is very important, so we do not need to specify a
global time reference (a space time dataset) for temporal processing.
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
Single map with temporal extent
The temporal algebra can also handle single maps with time stamps in the
tmap function.
For example:
C = A {:,during} tmap(event)
This statement select all maps from space time data set A that are during
the temporal extent of single map 'event'
The module supports the following raster operations:
Symbol description precedence
% modulus 1
/ division 1
* multiplication 1
+ addition 2
- subtraction 2
And raster functions:
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
Single raster map
The temporal raster algebra feature also a function to integrate single raster
maps without time stamps into the expressions.
For example:
C = A * map(constant_value)
This statement multiply all raster maps from space time raster data set A
with the raster map 'constant_value'
We combine the temporal topology relations, the temporal operators and the
spatial/select operators to create spatio-temporal operators:
{"spatial or select operator", "list of temporal relations", "temporal operator"}
For multiple topological relations or several related maps the spatio-temporal
operators feature implicit aggregation.
The algebra evaluates the stated STDS by their temporal topologies and apply
the given spatio temporal operators in a aggregated form.
If we have two STDS A and B, B has three maps: b1, b2, b3 that are all during
the temporal extent of the single map a1 of A, then the following arithmetic
calculations would implicitly aggregate all maps of B into one result map for
a1 of A:
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
The neighbourhood modifier of r.mapcalc is extended for the temporal
raster algebra by the temporal dimension. The format is strds[t,r,c],
where t is the temporal offset, r is the row offset and c is the column
offset.
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.
Sum maps from space time dataset A with maps from space time dataset
B which have equal time stamps and are temporary before Jan. 1. 2005 and
store them in space time dataset D.
D = if(start_date(A) < "2005-01-01", A + B)
Create the sum of all maps from STRDS A and B that have equal time stamps
and store the new maps in STRDS C:
Same expression with explicit definition of the temporal topology relation
and temporal operators:
Select all cells from STRDS B with equal temporal relations to STRDS A, if the
cells of A are in the range of [100.0, 1600] of time intervals that have more
then 30 days (Jan, Mar, Mai, Jul, Aug, Oct, Dec):
C = if(A > 100 && A < 1600 && td(A) > 30, B)
Same expression with explicit definition of the temporal topology relation
and temporal operators:
C = if({equal}, A > 100 && A < 1600 {&&,equal} td(A) > 30, B)
Compute the recharge in meter per second for all cells of precipitation
STRDS "Prec" if the mean temperature specified in STRDS "Temp" is higher
than 10 degrees. Computation is performed if STRDS "Prec" and "Temp" have
equal time stamps. The number of days or fraction of days per interval is
computed using the td() function that has as argument the STRDS "Prec":
C = if(Temp > 10.0, Prec / 3600.0 /24.0 / td(Prec))
Same expression with explicit definition of the temporal topology relation
and temporal operators:
C = if({equal}, Temp > 10.0, Prec / 3600.0 / 24.0 {/,equal,l} td(Prec))
Compute the mean value of all maps from STRDS A that are located during time
intervals of STRDS B if more than one map of A is contained in an interval
of B, use A otherwise, the resulting time intervals are either from B or A:
C = if(B {#,contain} A > 1, (B {+,contain,l} A - B) / (B {#,contain} A), A)
Same expression with explicit definition of the temporal topology relation
and temporal operators:
C = if({equal}, B {#,contain} A > 1, (B {+,contain,l} A {-,equal,l} B) {equal,=/} (B {#,contain} A), A)
r.mapcalc
t.vect.algebra
t.rast3d.algebra
t.select
t.rast3d.mapcalc
t.rast.mapcalc
Temporal data processing Wiki
PLY(Python-Lex-Yacc)
Thomas Leppelt, Sören Gebbert, Thünen Institute of Climate-Smart Agriculture
Last changed: $Date: 2016-11-14 00:09:36 +0100 (Mon, 14 Nov 2016) $
SOURCE CODE
Available at: t.rast.algebra source code (history)
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