This document discusses using a modified bivariate frequency ratio method for spatial prediction in GIS and Excel. It involves calculating the spatial correlation between predictive factors and dependent factors, autocorrelation between predictive factors, and producing a susceptibility map in Excel and ArcMap. Validation is done using the area under the curve statistical method. The method calculates frequency, relative frequency, and predictor ratios to consider interrelationships among predictive factors and produce a susceptibility index map. Required data includes landcover, topographic, dependent event locations and predictive factors.

1. Spatial Prediction Using Modified
Bivariate Frequency Ratio
Using
Excel and ArcMap only !
Omar F. Althuwaynee, PhD
GIS and Geomatics Engineering

2. Spatial Prediction Using Modified Bivariate
Frequency Ratio
Omar F. Althuwaynee, PhD
GIS and Geomatics Engineering
In this session i will talk about
1. pairwise comparison of prediction rates.
2. producing Susceptibility index maps.
3. prediction accuracy assessment (validation) using AUC.
Let us begin..!

3. 1. Calculate the spatial correlation between;
prediction factors, and the dependent factor.
2. Calculate autocorrelations between; the prediction
factors, by considering their prediction importance
or contribution.
3. Produce susceptibility map using; Microsoft Excel
and ESRI ArcMap only.
4. Validate the prediction accuracy using; most
common statistical method of Area under the curve
(AUC).
LET US BEGIN..! 
End of this session, you will be able to

4. Susceptibility mapping methods with GIS
Bivariate-statistics-based Multivariate statistical
Easy to apply and update • More realistic, accurate and sensitive
to the independents
• optimistic by showing evidences if
further investigations needed to enhance
the precision
Not considering the mutual
interrelationships among the
independents
Considering the mutual interrelationships
among the independents
ex. Probability statistics, like, FR
(Frequency ratio)
ex. Machine learning , like, ANN (artificial
neural network)
Common regression methods, like, LR
(Logistic regression)

5. Model application
requirements ..!
Dependent factor: prediction target locations inventory
(Landslides, wells, minerals test porholes).
Independent factors: predisposing factors (predictors) As
conditioning factors, the parameters slope angle, soil types,
and land use.
1. Identification and mapping of a set of dependent (target)
and independents factors that are directly or indirectly
correlated.
2. Estimating the relative contribution of these independents
factors in predicting of dependent factor.

6. What is FR..!
A bivariate statistical analysis method, based on the spatial
distribution (Probability) of dependent factor (landslides, pollutants),
and such of the considered conditioning factors (slope, aspect,
temperature, rainfall..etc..).
Probabilistic analysis considers the statistical relationships
between historical target locations and its conditioning factors
Relative Frequency (RF) = relative density index (RDI) = Frequency
Ratio (FR)

7. 2001 El Salvador Landslide Located
Near San Salvador
Newark and Sherwood District Council
Natural hazards

8. Permit Times for Mining Exploration http://bit.ly/2keyuNP Gold mining: NYU Graduates Seeking $11
Billion of Gold in Ransacked Mine
http://bit.ly/2k2ZL6C
Minings and Groundwater
exploration
Groundwater: Agriculture Water Pump
http://bit.ly/2keDeHl

9. Calculating FR, RF, and PR
coefficients for each factor
Calculating Pairwise
comparison
Spatial validation using AUC
Producing Susceptibility
index map
Processing Steps..!

10. Calculations..!!
Where
FR : Frequency ratio
RF : Index of the spatial association (Relative frequency ) of spatial factors and
targets.
PR : Predictor rate.
FR =
% target occurrence in each subcategory
% category of an independent factor
=
(points in factor class total points)
(factor class area total area)
𝑅𝐹 =
𝑓𝑎𝑐𝑡𝑜𝑟 𝑐𝑙𝑎𝑠𝑠 𝐹𝑅
∑𝑓𝑎𝑐𝑡𝑜𝑟𝑐𝑙𝑎𝑠𝑠𝑒𝑠 𝐹𝑅
𝑃𝑅 = 𝑅𝐹 𝑀𝑎𝑥 − 𝑅𝐹 𝑀𝑖𝑛 𝑅𝐹 𝑀𝑎𝑥 − 𝑅𝐹 𝑀𝑖𝑛 Min
𝑆𝐼 =
∑ 𝑅𝐹 × 𝑃𝑅
𝑀𝑎𝑥 𝑅𝐹 × 𝑃𝑅
× 100
To consider the mutual
interrelationships
among the
independents.

11. Software's:
Microsoft Excel- Microsoft
ArcMap - ESRI
QGIS 2.18.0 - OpenSource
Data and Tools..!!
Data type Data structure Source
Landcover Raster European Environment Agency
[http://www.eea.europa.eu/data-and-
maps/data/clc-2000-raster-1
Topographic and NDVI Raster USGS
[https://earthexplorer.usgs.gov/]
Study area Vector DivaGIS
[diva-gis.org/gdata]
Training and testing
points
Vector Experimental data

12. • Althuwaynee, Omar F., et al. "A novel ensemble bivariate statistical
evidential belief function with knowledge-based analytical hierarchy
process and multivariate statistical logistic regression for landslide
susceptibility mapping." Catena 114 (2014): 21-36.
• Sabatakakis, N., et al. "Landslide susceptibility zonation in Greece." Natural
hazards 65.1 (2013): 523-543.
More literature..!!