# Defining Common Terrain Derivatives

Last month I shared some ways to calculate terrain derivatives in SAGA, focusing on the Basic Terrain Analysis function. Today I’m going to give you a quick overview of what each derivative means and some of its potential uses.

Let’s start with the most intuitive ones. Slope is how fast elevation is changing. A higher slope is a steeper incline. To take that back to calculus, slope is the first derivative of elevation. The second derivative is curvature, which is a measure of how convex or concave a surface is (I’ll leave it there for now, but at some point I’ll compare and contrast different types of curatures and show you how to calculate them).

Analytical hillshade is a little more complicated. It’s a measure of how much light hits the surface of the ground, which is important for understanding photosynthesis potential or expected ground temperatures. Usually hillshade is calculated with light coming from the northwest at a 45 degree angle from the earth’s surface.

Aspect is also important to consider when looking at where light falls. Aspect is the azimuth you’d face if your back was to the hill you’re on (face downhill). Did you ever get the navigation advice that moss grows on the north side of trees? This comes from the fact that the north side gets less sun than the south side. Northern aspect slopes are generally cooler.

Many terrain derivatives are important when considering where water flows. Convergence index looks at whether water is moving towards that point (like a valley bottom) or away (like a ridge top). Closed depressions are ares that lack surface drainage– water can only be removed from here using subsurface drainage or evaporation. Flow accumulation basically counts how many cells would drain into each cell. Topographic wetness is a little more complicated. It takes the slope, the amount of area “upstream” that would drain into that cell, and the width of the upstream area.

LS Factor is kinda related to water, but it is more important for erosion measurements. It takes the length and steepness/slope of an area, which helps determine how much speed moving water or particles can accumulate.

Valley depth is the difference between the ridge level and the elevation at that point. Relative slope position ranks each cell compared to the highest and lowest point within a moving window.

The non-grid outputs of basic terrain analysis are channels and drainage basins. Channels are the paths water will take for surface drainage. A drainage basin is basically a watershed. Both can be easily saved as shapefiles.

I hope that was a helpful overview– message me or comment if you want more details about any of these outputs or their uses!