Texas wildflowers

The weather has been awesome around here lately (yes, in Houston!, the weather!, awesome!), and otherwise uninteresting roadside places are starting to be flooded with colors. Here are a few shots; more over at Smugmug.



This one is actually from 2008:



One of the issues with photographing flowers is that parts of the pictures are often out of focus, as it is obvious in this shot:

 

And a way to deal with that is to take a number of pictures that are focused at different distances and then merge them in Photoshop (as described in this video). This image was put together from four different photographs, and is a somewhat better version of the previous scene (the fact that the wind was pretty strong didn't help):

 

Three photos from California Academy of Sciences, San Francisco

This is a fantastic place! Clearly worth a visit if you have a few hours to spend in San Francisco.

More photographs here.

Madagascar giant day gecko

Coral reef from the Philippines

Jellyfish

Lunar Crater volcanic field, Nevada

I was on my way to San Francisco / AGU last week when I saw these volcanoes and shot these pictures through the airplane window. It turns out that this is the Lunar Crater volcanic field in Nevada, named after the largest crater that is more than 1000 meters across and about 130 m deep. There are 95 vents that are 4.2 million to 15,000 years old. Lunar Crater is the largest feature in the image below; it is a maar; most of the other vents formed cinder cones.




Here is a map showing the Houston - San Francisco flight track and the location of the volcanic field:


View Lunar Crater volcanic field in a larger map

Three photos from Kauai

The rest are here.

Colors in Alakai swamp

Green turtle at Tunnels Beach

Na Pali Coast

Hillslope diffusion

Modeling erosion and deposition of sediment using the diffusion equation is among the important subjects that are usually omitted from sedimentary geology textbooks. Part of the reason for this is that ‘conventional’ sedimentary geology tended to only pay lip service to earth surface processes and was more interested in describing the stratigraphic record than figuring how it relates to geomorphology. Nowadays, a good discussion of stratigraphy and sedimentology cannot ignore anymore what geomorphologists have learned about landscape evolution. (One textbook that clearly recognizes this is this one.)

But let's get back to the subject of this post. Hillslope evolution can be modeled with the diffusion equation, one of the most common differential equations in science, applied for example to describe how differences in temperature are eliminated through heat conduction. In the case of heat, the heat flux is proportional to the rate of spatial temperature change; on hillslopes, the sediment flux is proportional to the spatial rate of change in elevation. This last quantity of course is the slope itself. In other words,

q = -k*dh/dx,
or

q = -k*slope,
where q is the volumetric sediment flux per unit length, k is a constant called diffusivity, h is the elevation, and x is the horizontal coordinate.

We also know that sediment does not disappear into thin air: considering a small area of the hillslope, the amount of sediment entering and leaving this area will determine how large the change in elevation will be:


dh/dt = -dq/dx,
in other words, deposition or erosion at any location is determined by the change in sediment flux.

Combining this equation with the previous one, we arrive to the diffusion equation:

dh/dt = k*d²h/dx².
Note that the quantity on the right side is the second derivative (or curvature) of the slope profile. Large negative curvatures result in rapid erosion; places with large positive curvature have high rates of deposition. Through time, the bumps and troughs of the hillslope are smoothed out through erosion and deposition.

The simplest possible case is the diffusion of a fault scarp. The movie below illustrates how a 1 m high fault scarp gets smoothed out through time; the evolution of slope and curvature are also shown. The dashed line indicates the original topography, at time 0. [The plots were generated using Ramon Arrowsmith's Matlab code; right-click the flash animation for playback controls].



More complicated slope profiles can be modeled as well; here is an example with two fault scarps:



Note how both erosion and deposition get much slower as the gradients become more uniform.

The simplicity of the diffusion equation makes it an attractive tool in modeling landscape evolution. In addition to hillslopes and fault scarps, it has been successfully applied in modeling - for example - river terraces, deltaic clinoforms, cinder cones, fluvial systems, and foreland basin stratigraphy. However, it is important to know when and where the assumptions behind it become invalid. For example, steep slopes often have a non-linear relationship between sediment flux and slope as mass movements dramatically increase sediment flux above a critical slope value. Also, the models shown here would fail to reproduce the topography of a system where not all sediment is deposited at the toe of the steeper slope, but a significant part is carried away by a river. And that brings us closer to advection; a subject that I might take notes about at another time.

Further reading: 1) The book "Quantitative Modeling of Earth Surface Processes" by Jon Pelletier has a chapter with lots of details about the diffusion equation. 2) Analog and numerical modeling of hillslope diffusion - a nice lab exercise.