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PolyGeo
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With the back-and-forth comments, I am honestly not entirely clear as to what you are after here. In a quantitative sense there are metrics that provide an interaction of slope and aspect, that forest road engineers have commonly used.

One transformation is the Stage (1976) enter image description here where; alpha=rad(aspect) and theta=percent(slope) which is an a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum. An resulting value for 50% slope example aspects of 0(N) would be 0.50 at 60E=0.25 at 180S=-0.500 and at 270W=0. The metric ranges from [-1 - 1].

Another slope/aspect interaction is the Balice et al., (2000) site exposure index (SEI) enter image description here where; alpha=rad(aspect) and theta=deg(slope), which rescales aspect to a north/south axis and weights it by steepness of the slope. The metric represents relative exposure ranging from -100 to 100.

You could also linearize aspect and multiply it by slope. Metrics such as Roberts and Cooper (1989) Topographic Radiation Index (TRASP) enter image description here not only linearize aspect but recenter it around an expected. In the case of TRASP, aspect is re-centered around a north-northeast azimuth and has a range of [0-1].

These functions are all available in the ArcGIS Desktop/ArcProPro Gradient Metrics Toolbox.

With the back-and-forth comments, I am honestly not entirely clear as to what you are after here. In a quantitative sense there are metrics that provide an interaction of slope and aspect, that forest road engineers have commonly used.

One transformation is the Stage (1976) enter image description here where; alpha=rad(aspect) and theta=percent(slope) which is an a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum. An resulting value for 50% slope example aspects of 0(N) would be 0.50 at 60E=0.25 at 180S=-0.500 and at 270W=0. The metric ranges from [-1 - 1].

Another slope/aspect interaction is the Balice et al., (2000) site exposure index (SEI) enter image description here where; alpha=rad(aspect) and theta=deg(slope), which rescales aspect to a north/south axis and weights it by steepness of the slope. The metric represents relative exposure ranging from -100 to 100.

You could also linearize aspect and multiply it by slope. Metrics such as Roberts and Cooper (1989) Topographic Radiation Index (TRASP) enter image description here not only linearize aspect but recenter it around an expected. In the case of TRASP, aspect is re-centered around a north-northeast azimuth and has a range of [0-1].

These functions are all available in the ArcGIS/ArcPro Gradient Metrics Toolbox.

With the back-and-forth comments, I am honestly not entirely clear as to what you are after here. In a quantitative sense there are metrics that provide an interaction of slope and aspect, that forest road engineers have commonly used.

One transformation is the Stage (1976) enter image description here where; alpha=rad(aspect) and theta=percent(slope) which is an a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum. An resulting value for 50% slope example aspects of 0(N) would be 0.50 at 60E=0.25 at 180S=-0.500 and at 270W=0. The metric ranges from [-1 - 1].

Another slope/aspect interaction is the Balice et al., (2000) site exposure index (SEI) enter image description here where; alpha=rad(aspect) and theta=deg(slope), which rescales aspect to a north/south axis and weights it by steepness of the slope. The metric represents relative exposure ranging from -100 to 100.

You could also linearize aspect and multiply it by slope. Metrics such as Roberts and Cooper (1989) Topographic Radiation Index (TRASP) enter image description here not only linearize aspect but recenter it around an expected. In the case of TRASP, aspect is re-centered around a north-northeast azimuth and has a range of [0-1].

These functions are all available in the ArcGIS Desktop/Pro Gradient Metrics Toolbox.

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Jeffrey Evans
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With the back-and-forth comments, I am honestly not entirely clear as to what you are after here. In a quantitative sense there are metrics that provide an interaction of slope and aspect, that forest road engineers have commonly used.

One transformation is the Stage (1976) enter image description here where; alpha=rad(aspect) and theta=percent(slope) which is an a priori assumption of a maximum in the NW quadrant (45 azimuth) and a minimum in the SW quadrant can be replaced by an empirically determined location of the optimum. An resulting value for 50% slope example aspects of 0(N) would be 0.50 at 60E=0.25 at 180S=-0.500 and at 270W=0. The metric ranges from [-1 - 1].

Another slope/aspect interaction is the Balice et al., (2000) site exposure index (SEI) enter image description here where; alpha=rad(aspect) and theta=deg(slope), which rescales aspect to a north/south axis and weights it by steepness of the slope. The metric represents relative exposure ranging from -100 to 100.

You could also linearize aspect and multiply it by slope. Metrics such as Roberts and Cooper (1989) Topographic Radiation Index (TRASP) enter image description here not only linearize aspect but recenter it around an expected. In the case of TRASP, aspect is re-centered around a north-northeast azimuth and has a range of [0-1].

These functions are all available in the ArcGIS/ArcPro Gradient Metrics Toolbox.