Provided by: grass-doc_7.8.7-1_all 
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 [suffix=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
suffix=string
Suffix to add at basename: set ’gran’ for granularity, ’time’ for the full time format, ’num’ for
numerical suffix with a specific number of digits (default %05)
Default: num
nprocs=integer
Number of r.mapcalc processes to run in parallel
Default: 1
DESCRIPTION
t.rast.algebra performs temporal and spatial map algebra operations on space time raster datasets (STRDS)
using the temporal raster algebra.
PROGRAM USE
The module expects an expression as input parameter in the following form:
"result = expression"
The statement structure is similar to that of r.mapcalc. In this statement, result represents the name
of the 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 expressions 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 only with space time raster datasets (STRDS). The algebra provides
methods for map selection 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 map lists resulting of operations between STRDS.
By default, only temporal topological relations among space time datasets (STDS) are evaluated. The -s
flag can be used to additionally activate the evaluation of the spatial topology based on the spatial
extent of maps.
The expression option must be passed as quoted expression, for example:
t.rast.algebra expression="C = A + B" basename=result
Where C is the new space time raster dataset that will contain maps with the basename "result" and a
numerical suffix separated by an underscore that represent the sum of maps from the STRDS A and
temporally equal maps (i.e., maps with equal temporal topology relation) from the STRDS B.
The map basename for the result STRDS must always be specified.
TEMPORAL RASTER ALGEBRA
The temporal algebra provides a wide range of temporal operators and functions that will be presented in
the following section.
TEMPORAL RELATIONS
Several temporal topology relations are supported between maps registered in space time datasets:
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 both 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 with curly brackets {}.
TEMPORAL OPERATORS
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
temporally related maps and calculate the resulting temporal extent in five possible different ways.
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
TEMPORAL SELECTION
The temporal selection simply selects parts of a space time dataset without processing any raster or
vector data. The algebra provides a selection operator : that by default selects parts of a space time
dataset that are temporally equal to parts of a second space time dataset. The following expression
C = A : B
means: select all parts of space time dataset A that are equal to B and store them in space time dataset
C. These parts are time stamped maps.
In addition, the inverse selection operator !: is defined as the complement of the selection operator,
hence the following expression
C = A !: B
means: select all parts of space time time dataset A that are not equal to B and store them in space time
dataset C.
To select parts of a STRDS using different topological relations regarding to other STRDS, the temporal
topology selection operator can be used. This 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 brackets as follows: {"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 resulting STRDS by adding the temporal operator.
C = A {:,during,r} B
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
CONDITIONAL STATEMENTS
Selection operations can be evaluated within conditional statements as showed below. Note that A and B
can be either space time datasets or expressions. The temporal relationship between the conditions and
the conclusions can be defined at the beginning of the if statement (third and fourth examples below).
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 explicitly specified by topologies.
if(topologies, conditions, A, B) A if conditions are True, B otherwise; temporal topological relation between if, then and else is explicitly 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 STRDS.
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 functions 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
As mentioned above, 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 (optionally) related maps. For complex relations, the comparison operator can be
used to combine conditions.
The structure is similar to the select operator with the addition of an aggregation operator:
{"comparison operator", "topological relations", aggregation operator, "temporal operator"}
This aggregation operator (| or &) defines the behaviour when a map is related to more than one map, e.g.
for the topological relation ’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 &&). By default, the aggregation operator is related
to the comparison operator:
comparison operator -> aggregation operator:
|| -> | and && -> &
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.
A {#, contains} B
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 contain 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.
tmap()
For example:
C = A {:, during} tmap(event)
This statement selects all maps from space time data set A that are during the temporal extent of the
single map ’event’
Spatial raster operators
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 features also a function to integrate single raster maps without time stamps
into the expressions.
map()
For example:
C = A * map(constant_value)
This statement multiplies all raster maps from space time raster data set A with the raster map
’constant_value’
Combinations of temporal, raster and select operators
The user can combine the temporal topology relations, the temporal operators and the spatial/select
operators to create spatio-temporal operators as follows:
{"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
Important: the aggregation behaviour is not symmetric
C = B {+, during} A --> c1 = b1 + a1
c2 = b2 + a1
c3 = b3 + a1
Temporal neighbourhood modifier
The neighbourhood modifier of r.mapcalc is extended for the temporal raster algebra with 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.
EXAMPLES
Computation of NDVI
# Sentinel-2 bands are stored separately in two STDRS "S2_b4" and "S2_b8"
g.region raster=sentinel2_B04_10m -p
t.rast.list S2_b4
t.rast.list S2_b8
t.rast.algebra basename=ndvi expression="ndvi = float(S2_b8 - S2_b4) / ( S2_b8 + S2_b4 )"
t.rast.colors input=ndvi color=ndvi
Sum of space-time raster datasets
Sum maps from STRDS A with maps from STRDS B which have equal time stamps and are temporally before Jan.
1. 2005 and store them in STRDS 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:
C = A + B
Sum of space-time raster datasets with temporal topology relation
Same expression with explicit definition of the temporal topology relation and temporal operators:
C = A {+,equal,l} B
Selection of raster cells
Select all cells from STRDS B with equal temporal relations to STRDS A, if the cells of A are in the
range [100.0, 1600] of time intervals that have more than 30 days (Jan, Mar, May, Jul, Aug, Oct, Dec):
C = if(A > 100 && A < 1600 && td(A) > 30, B)
Selection of raster cells with temporal topology relation
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)
Conditional computation
Compute the recharge in meters 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))
Conditional computation with temporal topology relation
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))
Computation with time intervals
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)
Computation with time intervals with temporal topology relation
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)
SEE ALSO
r.mapcalc, t.vect.algebra, t.rast3d.algebra, t.select, t.rast3d.mapcalc, t.rast.mapcalc
Temporal data processing Wiki
REFERENCES
The use of this module requires the following software to be installed: PLY(Python-Lex-Yacc)
# Ubuntu/Debian
sudo apt-get install python3-ply
# Fedora
sudo dnf install python3-ply
# MS-Windows (OSGeo4W: requires "python3-pip" package to be installed)
python3-pip install ply
Related publications:
• Gebbert, S., Pebesma, E. 2014. TGRASS: A temporal GIS for field based environmental modeling.
Environmental Modelling & Software 53, 1-12 (DOI) - preprint PDF
• Gebbert, S., Pebesma, E. 2017. The GRASS GIS temporal framework. International Journal of
Geographical Information Science 31, 1273-1292 (DOI)
• Gebbert, S., Leppelt, T., Pebesma, E., 2019. A topology based spatio-temporal map algebra for big
data analysis. Data 4, 86. (DOI)
SEE ALSO
v.overlay, v.buffer, v.patch, r.mapcalc
AUTHORS
Thomas Leppelt, Sören Gebbert, Thünen Institute of Climate-Smart Agriculture
SOURCE CODE
Available at: t.rast.algebra source code (history)
Accessed: unknown
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© 2003-2022 GRASS Development Team, GRASS GIS 7.8.7 Reference Manual
GRASS 7.8.7 t.rast.algebra(1grass)