Hypsometric Curve Integral Calculator
Free Hypsometric curve integral Calculator for geomorphology & mapping. Enter variables to compute results with formulas and detailed steps.
Formula
HI = (H_mean - H_min) / (H_max - H_min)
Where HI is the hypsometric integral. Values > 0.6 = young, 0.35-0.6 = mature, < 0.35 = old.
Worked Examples
Example 1: Young Tectonically Active Basin
Problem: Max elev 3500 m, min 600 m, mean 2200 m, area 350 km2, area above mean 160 km2.
Solution: Total Relief = 2900 m\nHI = (2200-600)/(3500-600) = 0.5517\nStage: Mature
Result: HI: 0.5517 | Stage: Mature | Relief: 2,900 m
Example 2: Old Peneplain Basin
Problem: Max 280 m, min 50 m, mean 105 m, area 800 km2, area above mean 250 km2.
Solution: Total Relief = 230 m\nHI = (105-50)/(280-50) = 0.2391\nStage: Old
Result: HI: 0.2391 | Stage: Old (Peneplain) | Relief: 230 m
Frequently Asked Questions
What is a hypsometric curve?
A hypsometric curve is a graphical representation showing the proportion of a drainage basin area at or above a given elevation. The horizontal axis represents relative area from 0 to 1, and the vertical axis shows relative height. Convex curves indicate youthful landscapes where most of the original surface remains intact, while concave curves characterize deeply eroded old-age landscapes. S-shaped curves represent mature equilibrium landscapes with balanced erosion and deposition processes.
What is the hypsometric integral and how is it calculated?
The hypsometric integral is a single numerical value summarizing the hypsometric curve shape. The Pike and Wilson method calculates it as HI = (Hmean - Hmin) / (Hmax - Hmin). This dimensionless value ranges from 0 to 1, where higher values indicate more volume remaining above base level and younger geomorphic landscapes. The integral can also be computed by numerical integration of the full hypsometric curve using the trapezoidal rule applied to area-elevation data from a digital elevation model.
How does the hypsometric integral relate to erosion stage?
The hypsometric integral provides a quantitative measure of erosional development stage. Values greater than 0.6 indicate youthful landscapes with deep incision and significant remaining upland surface. Values between 0.35 and 0.6 represent mature landscapes where erosion and deposition are roughly balanced. Values below 0.35 indicate old-age landscapes extensively eroded to near base level. These classifications help geomorphologists compare relative tectonic and erosional activity across different regions.
What factors influence the hypsometric curve shape?
The curve shape is controlled by tectonic uplift, lithological resistance, climate-driven erosion, and time since the last major tectonic event. Active uplift maintains convex curves because material is added faster than erosion removes it. Lithological variations create stepped curves where resistant rock layers preserve flat surfaces. Glaciated landscapes show distinctive curves with concavities at cirque elevations. Climate influences the dominant erosion mechanism, with fluvial, glacial, and arid weathering each producing characteristic morphologies.
How is the curve generated from a DEM?
Generating a hypsometric curve from a DEM involves extracting elevation distribution within a drainage basin boundary. The basin is delineated using flow direction and accumulation algorithms. Elevation values of all grid cells are sorted and cumulative area at or above each elevation is calculated. Values are normalized by dividing each elevation by total relief and each cumulative area by total basin area. GIS packages like ArcGIS, QGIS, and GRASS GIS have built-in tools for automated hypsometric analysis.
What is the difference between HI and the full curve?
The curve is the full graphical representation of area-elevation distribution, while the integral is a single scalar summarizing the area beneath it. The curve contains more information because basins with different shapes can have identical HI values. A basin with a convex upper portion and concave lower portion might have the same HI as one with a linear curve. Therefore, comprehensive geomorphometric analysis should examine both the full curve shape and the integral value to avoid losing important information about elevation distribution.