Theapplication is an explorer for the Agrometeorological indicators from 1979 to present derived from reanalysis (AgERA5) dataset with a facility to download data for a selectable point location. The easy-to-use interface provides access to a wealth of data that could be used as input for most agriculture and agro-ecological models.
The AgERA5 dataset is based on bias-adjusted ERA5 data. It includes daily aggregates of agronomic relevant elements, tuned to local day definitions and adapted to the finer topography, finer land use pattern and finer land-sea delineation of the ECMWF HRES operational model. The elements cover temperature, precipitation, snow depth, humidity, cloud cover and radiation. These variables match the input needs of most agriculture and agro-ecological models.
The interactive map displays global maps with a layer for each selected variable and optional layers for cities, lakes, state/province borders and country borders to assist in navigation. Users can also use the snapshot tool to take an image of the visible area of the map.
Clicking at any location on the map with visible data or searching a city in the search bar will produce a time-series for the selected variables. The time-series data can be downloaded in comma separated variables (.csv) format if the user agrees to the Copernicus licence. The resolution of the point selection is set to 0.1 which matches the spatial resolution of the underlying data. In the case of city selection, the 0.1 grid cell closest to the city coooridinates is extracted.
GMDE is a program, available on the desktop for Apple Macintosh, Microsoft Windows, and Linux platforms and in a mobile version for iOS, that enables geologists to extract quantitative structural information from geologic maps and satellite images. The program facilitates the digitizing of strikes and dips or calculating them from three-point problems, calculation of stratigraphic map thickness, determination of piercing points on faults, and the construction of down-plunge projections and vertical cross sections with projected apparent dips, contacts, and cylindrical folds. The program also enables the automatic plotting of planar contacts across topography based on orientation calculated from three clicked points, which can be carried out in the field for immediate hypothesis testing. Error propagation is built into many of the calculations. Maps and satellite images require no projection or datum information, just four points with known latitude and longitude information. Alternatively, the user can enter the map or image in MBTiles format. Users can easily extract X-Y-Z data for any clicked or calculated point or polygon, enabling them to make their own calculations.
Geologic maps are seen in some quarters as arcane graphical devices that are rapidly losing their significance in a world awash with digital data, easily accessible online with the click of a mouse. This impression is inadvertently reinforced in the typical undergraduate structural geology laboratory where students are taught a variety of seemingly unconnected graphical constructions. We now have the tools to do twenty-first century map interpretation. All of the calculations typically taught in structural geology and performed by professional geologists can be carried out precisely and accurately with simple vector calculations and matrix transformations from linear algebra. In the past, however, it was so tedious to extract X-Y-Z data from paper copies of geologic maps that few people took advantage of the quantitative information contained in these maps. Those data can be extracted from full-fledged GIS programs, but the learning curve of those programs is typically steep and the cost high. While many of those systems can be scripted to carry out specialized structural geology calculations, the functions required are seldom built in.
Three trends now make it feasible to extract information from a geologic map quickly and easily: (1) the widespread availability of free raster images of geologic maps from national and state geological surveys such as the U.S. Geological Survey (USGS) and the Geological Survey of Canada (GSC); (2) the ability to access the elevation of most points on Earth with a simple query over the internet or from free digital elevation models (DEMs); and (3) easy access to high-resolution satellite imagery from Google and other providers.
GMDE can use base maps in two general formats. The desktop version can read single raster images at full scale and then display them at different zoom percentages. It can also read maps in MBTiles format (Fischer et al., 2018). The mobile version can only ready MBTiles format because of the small amounts of random-access memory (RAM) in most mobile devices.
Most elevations, either retrieved from an internet elevation server or in downloaded DEMs (next section), are referenced to the World Geodetic System 1984 (WGS84) geodetic datum (although some older DEMs in the United States are referenced to the North American Datum of 1927 [NAD27]). To use elevations in calculations, the difference between the datum used by an elevation server and that of the image can be critical. If the datum of the image is known, then the user can select it from a drop-down menu. GMDE then calculates the difference using the multiple linear regression equations (National Geospatial-Intelligence Agency, 2014). This is a critical step because the difference can be significant. For example, in the part of southeastern Idaho (USA) used in some examples below, the difference between the North American Datum of 1983 (NAD83) and NAD27 is >60 m (Fig. 2).
If the absolute location of points on the map is not of concern, the user can bypass the process of georeferencing because the program also keeps track of the local X-Y values based on pixels in the image, which have their origin at the lower left corner of the image. These are the numbers that appear in the datum information area (Fig. 1, upper right corner) for east and north coordinates, rather than the longer and more cumbersome UTM coordinates. In such cases, the scale can be set by dragging a line along the scale bar of the map, or between any two points of known distance, and then entering the distance and the units. This works well if the user is entering elevations by reading topographic contours on a scanned map.
Internet satellite images use a pseudo-Mercator (i.e., Spherical Mercator) projection where, for reasons of calculation speed, the Earth is assumed to be perfectly spherical rather than ellipsoidal, resulting in a 0.33% scale distortion in the north direction (Schwartz, 2018).
Many mapping systems provide X and Y coordinates, but to calculate things of interest to the geologist, one also needs Z, the elevation. GMDE desktop can retrieve point and profile elevations from internet elevation servers in real time, or read DEMs downloaded from the internet, which is necessary for offline use and for a few intensive calculations.
It is instructive for the user to see the variation in elevation values returned by different servers. The given elevation at a single point can vary by >10 m depending on the server (or topographic contours) used. This uncertainty can be important when estimating errors in elevation.
Digital elevation models come in a bewildering array of formats; GMDE accepts only a single but widely popular format: binary GridFloat and its text equivalent, ASCII Grid. This type of DEM is one of those offered by the USGS and other government agencies for direct download and can be written by most popular GIS programs such as ArcGIS and Global Mapper. A GridFloat DEM consists of three files: (1) a small header file (.hdr) that has information about the number of rows and columns in the DEM, the grid spacing, and other file attribute data; (2) a datum and projection file (.prj); and (3) a large binary file (.flt) containing the actual elevation data. The grid comes in two basic flavors: (1) a grid spacing and bottom left corner specified in decimal degrees, or (2) a grid spacing and bottom left corner specified in meters. GMDE can read both formats, although for the latter type, the grid must use a standard UTM central meridian. Finally, DEMs can be produced using a variety of map datums. GMDE can recognize several different types of map datums specified in the .prj file and accounts for the difference with the base-map datum. If the application does not recognize the datum, it will default to WGS84, which might not be correct.
Many basic structural geology calculations can be carried out computationally (Allmendinger et al., 2012) by converting orientations to direction cosines in a Cartesian north-east-down (NED) coordinate system and then using vector operations such as dot, cross, and dyad products (Table 1). Map data are usually referenced to an east-north-up coordinate system. Several calculations involve the transformation into a coordinate system fixed to the structure, as described below. In these cases, the transformation matrix is composed of the direction cosines of the new coordinate axes in the old coordinate system.
The orientation of a plane crossing topography (or pierced in multiple boreholes) can be determined from three non-collinear points on the plane. The pole to a plane can be calculated using a vector cross product (Allmendinger et al., 2012) or with the approach outlined in the next section. Calculation has the advantage that the errors can be propagated (Allmendinger and Judge, 2013), which is especially useful for identifying degenerate cases where the points are nearly collinear.
Fault slip is generally determined from the offset of a linear feature displaced across a fault. The intersection of that linear feature with the planar fault surface results in two piercing points. This problem is geometrically identical to the question of an exploration geologist who wants to drill a hole into an inclined plane, e.g., a mineralized fault zone, at depth.
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