pygmt.surface(data=None, x=None, y=None, z=None, outgrid=None, **kwargs)[source]

Grid table data using adjustable tension continuous curvature splines.

Surface reads randomly-spaced (x, y, z) triplets and produces gridded values z(x,y) by solving:

\[(1 - t)\nabla^2(z)+t\nabla(z) = 0\]

where \(t\) is a tension factor between 0 and 1, and \(\nabla\) indicates the Laplacian operator. Here, \(t = 0\) gives the “minimum curvature” solution. Minimum curvature can cause undesired oscillations and false local maxima or minima (see Smith and Wessel, 1990), and you may wish to use \(t > 0\) to suppress these effects. Experience suggests \(t \sim 0.25\) usually looks good for potential field data and t should be larger (\(t \sim 0.35\)) for steep topography data. \(t = 1\) gives a harmonic surface (no maxima or minima are possible except at control data points). It is recommended that the user preprocess the data with pygmt.blockmean, pygmt.blockmedian, or pygmt.blockmode to avoid spatial aliasing and eliminate redundant data. You may impose lower and/or upper bounds on the solution. These may be entered in the form of a fixed value, a grid with values, or simply be the minimum/maximum input data values. Natural boundary conditions are applied at the edges, except for geographic data with 360-degree range where we apply periodic boundary conditions in the longitude direction.

Takes a matrix, (x, y, z) triplets, or a file name as input.

Must provide either data or x, y, and z.

Full option list at


  • C = convergence

  • I = spacing

  • Ll = lower

  • Lu = upper

  • M = maxradius

  • R = region

  • T = tension

  • V = verbose

  • a = aspatial

  • b = binary

  • d = nodata

  • e = find

  • f = coltypes

  • h = header

  • i = incols

  • r = registration

  • w = wrap

  • data (str, numpy.ndarray, pandas.DataFrame, xarray.Dataset, or geopandas.GeoDataFrame) – Pass in (x, y, z) or (longitude, latitude, elevation) values by providing a file name to an ASCII data table, a 2-D numpy.ndarray, a pandas.DataFrame, an xarray.Dataset made up of 1-D xarray.DataArray data variables, or a geopandas.GeoDataFrame containing the tabular data.

  • x/y/z (1-D arrays) – Arrays of x and y coordinates and values z of the data points.

  • spacing (float, str, or list) –

    x_inc[+e|n][/y_inc[+e|n]]. x_inc [and optionally y_inc] is the grid spacing.

    • Geographical (degrees) coordinates: Optionally, append an increment unit. Choose among m to indicate arc-minutes or s to indicate arc-seconds. If one of the units e, f, k, M, n or u is appended instead, the increment is assumed to be given in meter, foot, km, mile, nautical mile or US survey foot, respectively, and will be converted to the equivalent degrees longitude at the middle latitude of the region (the conversion depends on PROJ_ELLIPSOID). If y_inc is given but set to 0 it will be reset equal to x_inc; otherwise it will be converted to degrees latitude.

    • All coordinates: If +e is appended then the corresponding max x (east) or y (north) may be slightly adjusted to fit exactly the given increment [by default the increment may be adjusted slightly to fit the given domain]. Finally, instead of giving an increment you may specify the number of nodes desired by appending +n to the supplied integer argument; the increment is then recalculated from the number of nodes, the registration, and the domain. The resulting increment value depends on whether you have selected a gridline-registered or pixel-registered grid; see GMT File Formats for details.

    Note: If region=grdfile is used then the grid spacing and the registration have already been initialized; use spacing and registration to override these values.

  • region (str or list) – xmin/xmax/ymin/ymax[+r][+uunit]. Specify the region of interest.

  • outgrid (str | None, default: None) – Name of the output netCDF grid file. If not specified, will return an xarray.DataArray object. For writing a specific grid file format or applying basic data operations to the output grid, see for the available modifiers.

  • convergence (float) – Optional. Convergence limit. Iteration is assumed to have converged when the maximum absolute change in any grid value is less than convergence. (Units same as data z units). Alternatively, give limit in percentage of root-mean-square (rms) deviation by appending %. [Default is scaled to \(10^{-4}\) of the rms deviation of the data from a best-fit (least-squares) plane.] This is the final convergence limit at the desired grid spacing; for intermediate (coarser) grids the effective convergence limit is divided by the grid spacing multiplier.

  • maxradius (float or str) – Optional. After solving for the surface, apply a mask so that nodes farther than maxradius away from a data constraint are set to NaN [Default is no masking]. Append a distance unit (see Units) if needed. One can also select the nodes to mask by using the n_cellsc form. Here n_cells means the number of cells around the node is controlled by a data point. As an example "0c" means that only the cell where the point lies is filled, "1c" keeps one cell beyond that (i.e. makes a 3x3 square neighborhood), and so on.

  • lower (float or str) – Optional. Impose limits on the output solution. Parameter lower sets the lower bound. lower can be the name of a grid file with lower bound values, a fixed value, d to set to minimum input value, or u for unconstrained [Default]. Grid files used to set the limits may contain NaNs. In the presence of NaNs, the limit of a node masked with NaN is unconstrained.

  • upper (float or str) – Optional. Impose limits on the output solution. Parameter upper sets the upper bound and can be the name of a grid file with upper bound values, a fixed value, d to set to maximum input value, or u for unconstrained [Default]. Grid files used to set the limits may contain NaNs. In the presence of NaNs, the limit of a node masked with NaN is unconstrained.

  • tension (float or str) – [b|i]. Optional. Tension factor[s]. These must be between 0 and 1. Tension may be used in the interior solution (above equation, where it suppresses spurious oscillations) and in the boundary conditions (where it tends to flatten the solution approaching the edges). Add itension to set interior tension, and btension to set boundary tension. If you do not prepend i or b, both will be set to the same value. [Default is 0 for both and gives minimum curvature solution.]

  • verbose (bool or str) –

    Select verbosity level [Default is w], which modulates the messages written to stderr. Choose among 7 levels of verbosity:

    • q - Quiet, not even fatal error messages are produced

    • e - Error messages only

    • w - Warnings [Default]

    • t - Timings (report runtimes for time-intensive algorithms)

    • i - Informational messages (same as verbose=True)

    • c - Compatibility warnings

    • d - Debugging messages

  • aspatial (bool or str) – [col=]name[,…]. Control how aspatial data are handled during input and output. Full documentation is at

  • binary (bool or str) –

    i|o[ncols][type][w][+l|b]. Select native binary input (using binary="i") or output (using binary="o"), where ncols is the number of data columns of type, which must be one of:

    • c - int8_t (1-byte signed char)

    • u - uint8_t (1-byte unsigned char)

    • h - int16_t (2-byte signed int)

    • H - uint16_t (2-byte unsigned int)

    • i - int32_t (4-byte signed int)

    • I - uint32_t (4-byte unsigned int)

    • l - int64_t (8-byte signed int)

    • L - uint64_t (8-byte unsigned int)

    • f - 4-byte single-precision float

    • d - 8-byte double-precision float

    • x - use to skip ncols anywhere in the record

    For records with mixed types, append additional comma-separated combinations of ncols type (no space). The following modifiers are supported:

    • w after any item to force byte-swapping.

    • +l|b to indicate that the entire data file should be read as little- or big-endian, respectively.

    Full documentation is at

  • nodata (str) – i|onodata. Substitute specific values with NaN (for tabular data). For example, nodata="-9999" will replace all values equal to -9999 with NaN during input and all NaN values with -9999 during output. Prepend i to the nodata value for input columns only. Prepend o to the nodata value for output columns only.

  • find (str) – [~]“pattern” | [~]/regexp/[i]. Only pass records that match the given pattern or regular expressions [Default processes all records]. Prepend ~ to the pattern or regexp to instead only pass data expressions that do not match the pattern. Append i for case insensitive matching. This does not apply to headers or segment headers.

  • coltypes (str) – [i|o]colinfo. Specify data types of input and/or output columns (time or geographical data). Full documentation is at

  • header (str) –

    [i|o][n][+c][+d][+msegheader][+rremark][+ttitle]. Specify that input and/or output file(s) have n header records [Default is 0]. Prepend i if only the primary input should have header records. Prepend o to control the writing of header records, with the following modifiers supported:

    • +d to remove existing header records.

    • +c to add a header comment with column names to the output [Default is no column names].

    • +m to add a segment header segheader to the output after the header block [Default is no segment header].

    • +r to add a remark comment to the output [Default is no comment]. The remark string may contain \n to indicate line-breaks.

    • +t to add a title comment to the output [Default is no title]. The title string may contain \n to indicate line-breaks.

    Blank lines and lines starting with # are always skipped.

  • incols (str or 1-D array) –

    Specify data columns for primary input in arbitrary order. Columns can be repeated and columns not listed will be skipped [Default reads all columns in order, starting with the first (i.e., column 0)].

    • For 1-D array: specify individual columns in input order (e.g., incols=[1,0] for the 2nd column followed by the 1st column).

    • For str: specify individual columns or column ranges in the format start[:inc]:stop, where inc defaults to 1 if not specified, with columns and/or column ranges separated by commas (e.g., incols="0:2,4+l" to input the first three columns followed by the log-transformed 5th column). To read from a given column until the end of the record, leave off stop when specifying the column range. To read trailing text, add the column t. Append the word number to t to ingest only a single word from the trailing text. Instead of specifying columns, use incols="n" to simply read numerical input and skip trailing text. Optionally, append one of the following modifiers to any column or column range to transform the input columns:

      • +l to take the log10 of the input values.

      • +d to divide the input values by the factor divisor [Default is 1].

      • +s to multiple the input values by the factor scale [Default is 1].

      • +o to add the given offset to the input values [Default is 0].

  • registration (str) – g|p. Force gridline (g) or pixel (p) node registration [Default is g(ridline)].

  • wrap (str) –

    y|a|w|d|h|m|s|cperiod[/phase][+ccol]. Convert the input x-coordinate to a cyclical coordinate, or a different column if selected via +ccol. The following cyclical coordinate transformations are supported:

    • y - yearly cycle (normalized)

    • a - annual cycle (monthly)

    • w - weekly cycle (day)

    • d - daily cycle (hour)

    • h - hourly cycle (minute)

    • m - minute cycle (second)

    • s - second cycle (second)

    • c - custom cycle (normalized)

    Full documentation is at


ret (xarray.DataArray or None) – Return type depends on whether the outgrid parameter is set:

  • xarray.DataArray: if outgrid is not set

  • None if outgrid is set (grid output will be stored in file set by outgrid)


>>> import pygmt
>>> # Load a sample table of topography
>>> topography = pygmt.datasets.load_sample_data(name="notre_dame_topography")
>>> # Perform gridding of topography data
>>> grid = pygmt.surface(data=topography, spacing=1, region=[0, 4, 0, 8])