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U.S. DEPARTMENT OF THE INTERIOR
U.S. GEOLOGICAL  SURVEY 




Shaded-Relief Map of the San 
Francisco Bay Region,
California


By SCOTT E. GRAHAM and RICHARD J. PIKE1




The most detailed and accurate portrayal of the
region's topography to date was created
from 35,000,000 digital elevations
spaced 30 meters apart




OPEN-FILE REPORT 97-745 B

1997





This report is preliminary and has not been reviewed for conformity with U.S. Geological Survey editorial standards 
or with the North American Stratigraphic Code.  Any use of trade, product, or firm names is for descriptive purposes 
only and does not imply endorsement by the U.S. Government.

This database, identified as "Shaded Relief Map of the San Francisco Bay Region, California," has been approved for 
release and publication by the Director of the USGS.  Although this database has been subjected to rigorous review 
and is substantially complete, the USGS reserves the right to revise the data pursuant to further analysis and review.  
Furthermore, it is released on condition that neither the USGS nor the United States Government may be held liable for 
any damages resulting from its authorized or unauthorized use.

1MENLO PARK, CA  94025
Shaded-Relief Map of the San Francisco Bay Region, California

by
Scott E. Graham and Richard J. Pike


Summary

Topography, the configuration of the land surface, plays a major role in the 
initiation of one type of landslide common to the San Francisco Bay region, the 
debris flow (Ellen and others, 1997), and in the recognition of such other modes of 
slope failure as slumping, translational sliding, and earthflow (Wentworth and 
others, 1997).  Accordingly, a topographic portrayal at both local and regional scales is 
helpful in assessing the likelihood of slope failure and mapping the extent of its past 
activity.  This report, one of six separate but related documents (San Francisco Bay 
Landslide Mapping Team, 1997), provides digital data and plottable map files that 
depict Bay region topography in detail by analytical hill-shading, a old technique at 
last made practicable by the digital computer.

Hill shading, or chiaroscuro, portrays the three-dimensional shape of the land in 
two dimensions by intensity of the Sun's shadows.  At least as old as Leonardo da 
Vinci's 1502-3 sketches of the Tuscan landscape (Horn, 1981), manual (artistic) 
executions of the technique can economically show only small areas accurately and 
in detail.  However, Lehmann (1799) and later Wiechel (1878) developed analytical 
treatments that would eventually lead to automation.  Thus quantified, the 
technique was finally adapted to the computer by Yoeli (1967).  Analytical hill-
shading in its current, digital, form has unique advantages for the portrayal and 
analysis of surface features:

 it combines fine detail with large-area coverage;
 it shows terrain accurately and in its true complexity, two properties 
often lost in sketches and diagrams of large areas;
 the view is continuouslimited only by size of the digital data set
unlike relief models, aerial photos, and radar images;
 the map is free of distortion and the vegetation and cultural features that 
mask topographic form on satellite images;
 positions of Sun and viewer can be varied to obtain a different 
perspective on a landform or to enhance certain terrain features.

Most of these advantages are evident in the 11 digital shaded-relief images presented 
here, at 1:125,000 (county maps) and 275,000 (regional map) scale, the most detailed 
and accurate physiographic views to date of San Francisco Bay region and its ten 
constituent counties.  Containing a vast amount of information, these computer 
portraits faithfully reflects the cumulative work of tectonism, fluvial activity, 
marine erosion and deposition, and other geologic events and processes shaping the 
region's landscape (for example, Brown, 1990).

The 11 maps are numbered here, and in the other reports bearing the Open-file 
number 97-745, as follows:


 1. San Francisco Bay Region
 2. Alameda County
 3. Contra Costa County
 4. Marin County
 5. Napa County
 6. Santa Clara County
 7. Santa Cruz County
 8. San Francisco County
 9. San Mateo County
10. Solano County
11. Sonoma County


The new maps supersede earlier mechanized portrayals of the region.  Included are 
those parts of the California (Edwards and Batson, 1990) and U.S. (Thelin and Pike, 
1991) shaded-relief maps covering the Bay area.  A 1:125,000-scale slope map of the 
ten-county region (U.S. Geological Survey, 1972), derived photomechanically from a 
contour map (U.S. Geological Survey, 1970), had previously been the only medium-
scale relief portrayal of Bay region topography.  Prior to this report, a satisfactory 
shaded-relief map had been prepared only for San Mateo county (Mark and Aitken, 
1990).  

The data from which the new maps were computed consist of a digital elevation 
model (DEM), an (X,Y) array of terrain heights spaced 30 m apart.  The data set was 
assembled from 204 separate DEM's derived from topographic maps in the USGS 
7.5' series (see the quadrangle index map in Pike, 1997).  Because all constituent 
DEM's were created by the recent and higher-accuracy "Level II" procedures that 
interpret elevations from digital line graphs of the map contours (U.S. Geological 
Survey, 1993), these maps are free from the striped artifacts that mar shaded-relief 
portrayals computed from older 7.5' DEM's.

At 1:275,000 scale, the full Bay Region map comprises some 35,000,000 rectangular 
picture elements (pixels), each about 0.11 mm across.  The array measures 7743 cells 
in the east-west direction and 7423 cells in the north-south direction.  Pixels of the 
ten 1:125,000-scale county maps, at about 0.24 mm across, are below the size at which 
the human eye begins to resolve individual elements.

On all 11 maps the gray tone of each pixel is a brightness value computed from a 
mathematical relation between ground-surface slope and azimuth and elevation of 
the observer and a simulated Sun (see, for example, Yoeli, 1967; Thelin and Pike, 
1991).  All images are illuminated from the north-northwest, halfway between the 
zenith and the horizon.  Light and dark tones show steep areas, facing the Sun and 
in shadow, respectively; intermediate tones are gentle terrain.  To enhance fine 
detail in low-relief terrain, we applied a modest vertical exaggeration.  As a result, 
ridges appear about twice as high as they actually are, and valleys twice as deep.  
Details on the processing follow below.  For references to the vast literature on relief 
shading see Horn (1981) and Thelin and Pike (1991).

Drainage lines and nearshore bathymetry from an existing digital base (Aitken, 1997) 
enhance the relief-shaded portrayal on all 11 maps.  To facilitate rapid location of 
specific areas of interest, particularly for emergency-response applications, the ten 
1:125,000-scale county maps carry a detailed road network and major place names 
(Aitken, 1997).  Similarly, we added a two-km buffer zone, mapped by a white-
bounded black line, around each county to provide context for any slope failures and 
response activities near the county limits.


Data Processing

The digital compilation was performed in ARC/INFO, a commercial Geographic 
Information System (Environmental Research Institute [ESRI], Redlands, 
California).  The database for shaded-relief maps consists of ARC/INFO GRID 
coverages for the region as a whole and for each of the ten counties (two versions of 
each set, the light-toned edition to be used as a base map for plotting other data), 
postscript map-image files for each of those 11 areas, and a postscript version of this 
text.  See San Francisco Bay Landslide Mapping Team (1997) for information about 
filenames and how to obtain the data and plotfiles.

The 7.5-minute DEM's were compiled into a single data set by the LATTICEMERGE 
command in ARC/INFO.  Inconsistencies and edge-match problems between 
adjacent quadrangles were resolved using the FOCALMEAN function in 
ARC/INFO GRID.  The hillshade grid (sfbr-sr) was prepared by the HILLSHADE 
command in ARC/INFO, using a Sun azimuth of 315 degrees, a Sun-elevation 
angle of 45 degrees, and a z-factor (vertical exaggeration) of 2.0. 

The light-toned hillshade grid was prepared by the HILLSHADE command in 
ARC/INFO, again using a Sun azimuth of 315 degrees and a Sun angle of 45 degrees, 
but a z-factor (vertical exaggeration) of 1.0.  This grid was then recalculated from 255 
brightness values to 100 values using the SLICE function in ARC/INFO GRID.  The 
resulting grid was run through two additional grid algorithms (see below), which 
moved the hillshading towards the lighter end of the gray-scale spectrum yet still 
preserved the details of topographic features.

Step 1:
       temp_grid = (ltgrid - [value GRD$MEAN]) * 15 / [value GRD$STDV] + 90

           where ltgrid is the grid produced by the SLICE function

Step 2:
       sfbr-srlt = con(isnull(temp_grid), 99, temp_grid <= 60, 60,temp_grid <= 99,
            int(temp_grid),99)

          where temp_grid is the grid produced by Step 1

Hillshade grids for the ten counties were prepared with the LATTICECLIP command 
in ARC/INFO, using a buffered county boundary-line (2 Km buffer) as the clip 
cover.


The Digital Database

No paper maps accompany this document or the other five reports in the San 
Francisco Bay Region Landslide Folio.  Rather, the Folio is released as a digital 
database that can be obtained by either (1) connecting with a USGS Web page, (2) 
through anonymous ftp (file transfer protocol) over the Internet, or (3) sending a 
request, accompanied by a blank magnetic tape, to USGS.  Available in two data 
formats (ARC/INFO Export-compatible or PostScript), the map files described here 
can be plotted on the user's equipment or that of a commercial vendor.

The data files are as follows.  (See San Francisco Bay Landslide Mapping Team (1997) 
for information on how to obtain the data.)
	
	sfbr-sr-dbsesc.ps	-Postscript version of this text
            sfbr-sr.dbdesc.txt	-ASCII version of this text

    ARC/INFO GRIDS

	sfbr-sr.tar		-Tar file containing Bay Region hillshade grid
	al-sr.tar		-Tar file containing Alameda County hillshade grid
	cc-sr.tar		-Tar file containing Contra Costa County hillshade grid
	ma-sr.tar		-Tar file containing Marin County hillshade grid
	na-sr.tar		-Tar file containing Napa County hillshade grid
	scl-sr.tar		-Tar file containing Santa Clara County hillshade grid
	scr-sr.tar		-Tar file containing Santa Cruz County hillshade grid
	sf-sr.tar		-Tar file containing San Francisco County hillshade grid
	sm-sr.tar		-Tar file containing San Mateo County hillshade grid
	sol-sr.tar		-Tar file containing Solano County hillshade grid
	son-sr.tar		-Tar file containing Sonoma County hillshade grid

	sfbr-srlt.tar		-Tar file containing Bay Region light hillshade grid
	al-srlt.tar		-Tar file containing Alameda County light hillshade grid
	cc-srlt.tar		-Tar file containing Contra Costa County light hillshade grid
	ma-srlt.tar		-Tar file containing Marin County light hillshade grid
	na-srlt.tar		-Tar file containing Napa County light hillshade grid
	scl-srlt.tar		-Tar file containing Santa Clara County light hillshade grid
	scr-srlt.tar		-Tar file containing Santa Cruz County light hillshade grid
	sf-srlt.tar		-Tar file containing San Francisco County light hillshade grid
	sm-srlt.tar		-Tar file containing San Mateo County light hillshade grid
	sol-srlt.tar		-Tar file containing Solano County light hillshade grid
	son-srlt.tar		-Tar file containing Sonoma County light hillshade grid

    POSTSCRIPT MAP-IMAGE FILES

	sfbr-sr.ps		-Shaded relief map of the San Francisco Bay Region
	al-sr.ps		-Shaded relief map of Alameda County
	cc-sr.ps		-Contra Costa County
	ma-sr.ps		-Marin County
	na-sr.ps		-Napa County
	scl-sr.ps		-Santa Clara County
	scr-sr.ps		-Santa Cruz County
	sf-sr.ps		-San Francisco County
	sm-sr.ps		-San Mateo County
	sol-sr.ps		-Solano County
	son-sr.ps		-Sonoma County


The map database itself is rather simple, consisting of attributed GRID cells stored in 
Universal Transverse Mercator (UTM) projection (Table 1).

Table 1 - Map Projection

PROJECTION		UTM
UNITS			meters
ZONE			    10
DATUM			NAD27
PARAMETERS		none


Content of the map database can be described in terms of the grid cells comprising 
the map.  Descriptions of the database fields use the terms explained in Table 2.


Table 2 - Field Definition Terms

ITEM NAME	name of the database field (item)
WIDTH		maximum number of digits or characters stored
OUTPUT		output width
TYPE			B-binary integer, F-binary floating-point number,
				I-ASCII integer, C-ASCII character string
N.DEC		number of decimal places maintained for floating-
				point numbers


The gray-shaded picture elements (pixels) comprising the maps are rectangular cells 
shown on each map by a GRID coverage, consisting of 30-m cells derived from 
values of terrain steepness and azimuth as described briefly in the Introduction.

The database format of the grid is described in Tables 3 and 4, which show the 
format of the GRID attribute and statistics tables.


Table 3 - Contents of GRID Value Attribute Table (<GRIDNAME>.VAT)

ITEM NAME	WIDTH	OUTPUT	TYPE		N.DEC

     AREA	      4		      10		    B		     --
     COUNT	      4		      10		    B		     --



Table 4 - Contents of GRID Statistics Table (<GRIDNAME>.STA)

                  ITEM NAME	WIDTH	OUTPUT	TYPE		N.DEC

                        MIN		      8		       15                 F                       3
                        MAX                    8		       15                 F                       3
                        MEAN                 8		       15                 F                       3
                        STDV                   8		       15                 F                       3



References cited
Aitken, D.S., 1997, Digital version of the 1970 Topographic Map of the San Francisco 
Bay Region: U.S. Geological Survey Open-file Report 97-500, three sheets, map 
scale 1:125,000.
Brown, R.D., Jr., 1990, Quaternary deformation, in Wallace, R.E., ed., The San 
Andreas Fault System: U.S. Geological Survey Professional Paper 1515, p. 83-113.
Edwards, Kathleen, and Batson, R.M., 1990, Experimental digital shaded-relief map 
of California: U.S. Geological Survey Miscellaneous Investigations map I-1848, 
scale 1:1,000,000.
Ellen, S.D., Mark, R.K., Wieczorek, G.F., Wentworth, C.M., Ramsey, D.W., and May, 
T.E., 1997, Map Showing  Principal debris-flow source areas in the San Francisco 
Bay Region, California: U.S. Geological Survey, Open-file Report 97-745 E, map 
scales 1:275,000 and 1:125,000.
Horn, B.K.P., 1981, Hill shading and the reflectance map: Proceedings of the Institute 
of Electrical and Electronics Engineers, v. 69, no. 1, p. 14-47.   [originally released 
1979, in Workshop on Image Understanding, Palo Alto, CA, April, Proceedings: p. 
79-120; reprinted 1982, in Geo-processing, v. 2, no. 1, p. 65-146.]
Lehmann, J.G., 1799, Darstellung einer neuen Theorie der Bezeichnung der schiefen 
Flchen im Grundriss oder der Situationzeichnung der Berge (in German): 
Leipzig, paging unknown.
Mark, R.K., and Aitken D.S., 1990, Shaded-relief topographic map of San Mateo 
County, California: U.S. Geological Survey Miscellaneous Investigations Map I-
1257-K, one sheet, scale 1:62,500.
Pike, R.J., 1997, Index to detailed maps of landslides in the San Francisco Bay Region, 
California: U.S. Geological Survey, Open-file Report 97-745 D.
San Francisco Bay Landslide Mapping Team, 1997, Introduction to the San Francisco 
Bay Region, California, Landslide Folio: U.S. Geological Survey Open-file Report 
97-745 A.
Thelin, G.P., and Pike, R.J., 1991, Landforms of the conterminous United StatesA 
digital shaded-relief portrayal: U.S. Geological Survey Miscellaneous 
Investigations Map, I-2206, scale l:3,500,000
U.S. Geological Survey, 1970, Topographic map of the San Francisco Bay region: 3 
sheets, scale 1:125,000.
U.S. Geological Survey, 1972, Slope map of the San Francisco Bay region: 3 sheets, 
scale 1:125,000.
U.S. Geological Survey, 1993, Digital elevation modelsdata users guide 5: Reston, 
Virginia, U.S. Geological Survey, National Mapping Division, 48 p.
Wentworth, C.M., Graham, S.E., Pike, R.J., Beukelman, G.S., Ramsey, D.W., and 
Barron, A.D., 1997, Summary distribution of slides and earth flows in the San 
Francisco Bay Region, California: U.S. Geological Survey, Open-file Report 97-745 
C, map scales 1:275,000 and 1:125,000.
Wiechel, H., 1878, Theorie und Darstellung der Beleuchtung von nicht gesetzmssig 
gebildeten Flchen mit Rcksicht auf die Bergzeichnung (in German): 
Civilingenieur, v. 24, p. 335-364.
Yoeli, Pinhas, 1967, The mechanisation of analytical hill shading: Cartographic 
Journal, v. 4, no. 2, p. 82-88.