Provided by: grass-doc_7.8.2-1build3_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)
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© 2003-2019 GRASS Development Team, GRASS GIS 7.8.2 Reference Manual