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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 python-ply
       # Fedora
       sudo dnf install python-ply
       # MS-Windows (OSGeo4W: requires "python-pip" package to be installed)
       python-pip install ply

SEE ALSO

        v.overlay, v.buffer, v.patch, r.mapcalc

AUTHORS

       Thomas Leppelt, Sören Gebbert, Thünen Institute of Climate-Smart Agriculture

       Last changed: $Date: 2018-08-24 15:03:58 +0200 (Fri, 24 Aug 2018) $

SOURCE CODE

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

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       © 2003-2019 GRASS Development Team, GRASS GIS 7.6.1 Reference Manual