prasinos' work memo



DEM to watershed algorithm - Jenson and Domingue 1988

The algorithm to extract watershed from a DEM, described in Jenson and Domingue 1988. 続きを読む


何だってアフィン変換を高次多項式に拡張したものを地理業界では curvilinear transformation というのだろう。原典をあたったわけでないが、URL から察するにこれは NCGIA に含まれているのだろう。

数学では curvilinear coordinates とは曲線座標のことである。局所直交とは限らない。

ま、たしかに高次多項式を使えば大抵のことはできるだろうが、だからといって曲線座標全般というのはやや言いすぎではなかろうか。Polynomial という言葉もあるわけだし。


なお、本当にどうでもいい話だが、Curvilinear という内装業者がイギリスにあるらしい。

scale dependency

The professor said that the wetness index is defined by w = ln(a/tanβ), where a is upstream drainage area divided by contour length and β is downward slope angle. I felt very unconfortable with this equation, since area divided by length is given to log. Nonsense!

I asked "Is it scale dependent?" The reply was no. If we calculate the equation on 100x100m grid and 10x10m grid, both of the UDA area and contour lengths per pixel will be 10:1.

His idea seems to be to express water influx divided by width of outlet (i.e. proportional to some dimensional value such as depth of water), so it makes sense.

So why did I feel so unconfortable? The answer is it is still scale dependent with respect to units of measurement. If we calculate the equation in meters and feet, we will have different answer. Unfortunately (or fortunately), the factor (such as meter/feet) is converted to "plus constant" term by logarithm function, so the effect is not so significant in this case.

This indicates the difference of culture or discipline between geography and physical sciences.