# Dasymetric Mapping

National-level fertilizer and pesticide statistics can be represented in a GIS through the traditional approach of choroplethic mapping. This techqnique falsely assumes that values are even distributed across the entire polygon making it insufficient for making watershed-level estimates of fertilizer and pesticide consumption. Using a dasymetric mapping technique, we were able to use ancillary land cover data to better represent the true heterogeneous distribution of these phenomenon.

## Determining National Pesticide and Fertilizer Consumption

The FAO Stats database was used to extract 10 year averages (1993 through 2002) by nation for:

- Total Fertilizer Consumption (TFC)
- Total Pesticide Consumption (TPC)

It was important, since the FAO database did not seem to distinguish between null values and true zero values, to mark missing data as null where appropriate. In cases of missing data, some "10 year" averages were averaged over less than ten data points.

Of the 223 countries defined in our study, only 134 had valid fertilzer and pesticide averages. 45 countries had valid fertlizer data but no pesticide data. 44 countries lacked valid averages for either variable.

In cases where we had fertilzer data but lacked pesticide data, a linear relationship between the two variables allowed us to estimate poesticide usage. A linear regression was used to determine the relationship amongst the 134 countries with known values of both variables; The Adjusted R

^{2}was 0.7271 and the linear relationship between TFC and TPC was:

TPC = 4560 + 0.01651(TFC)

*Residual standard error: 23090 on 131 degrees of freedom*

Multiple R-Squared: 0.7292, Adjusted R-squared: 0.7271

F-statistic: 352.8 on 1 and 131 DF, p-value: < 2.2e-16

Multiple R-Squared: 0.7292, Adjusted R-squared: 0.7271

F-statistic: 352.8 on 1 and 131 DF, p-value: < 2.2e-16

For the remaining 44 countries lacking either variable, we used supplemental data from the CIA World Factbook. From the Gross Domestic Product (GDP) and the percent GDP per economic sector, we were able to determine the total GDP from Agriculture (GDPAG) for each country. GDPAG was shown to have a significant linear relationship with TPC and TFC (Adjusted R

^{2}of 0.57 and 0.82 respectively). The relationships were defined as follows:

TPC= 7338 + 0.0000004073(GDPAG)

*Residual standard error: 37420 on 172 degrees of freedom*

Multiple R-Squared: 0.5768, Adjusted R-squared: 0.5743

F-statistic: 234.4 on 1 and 172 DF, p-value: < 2.2e-16

Multiple R-Squared: 0.5768, Adjusted R-squared: 0.5743

F-statistic: 234.4 on 1 and 172 DF, p-value: < 2.2e-16

TFC = 97110 + 0.00002749(GDPAG)

*Residual standard error: 1400000 on 172 degrees of freedom*

Multiple R-Squared: 0.8161, Adjusted R-squared: 0.8151

F-statistic: 763.4 on 1 and 172 DF, p-value: < 2.2e-16

Multiple R-Squared: 0.8161, Adjusted R-squared: 0.8151

F-statistic: 763.4 on 1 and 172 DF, p-value: < 2.2e-16

## Dasymetric Mapping

*Explain Basics of Dasymetric Mapping*

Typically, statistics aggregated over a defined geographic region such as a country is represented as choroplethic map whereby the aggregate value is assumed to apply homogeneously across the region. This may lead map readers and spatial analysts to believe that we can determine the value for a small subset of the region based on the aggregate region statistics. This error in statistical interpretation is widely known as the ecological fallacy (Robinson, 1950).

Dasymetric mapping aims to correct for the ecological fallacy by using ancillary data to inform the spatial distribution of the phenomenon *within *the defined region. Rather than distribute the aggregate value homogeneously over the region, this technique allows heterogeneous distribution based on the geography within the region. Dasymetric mapping has historically been used for population mapping to help better visualize the population distribution. A common use case is using aggregate population values (ie total population by zip code) and using more spatially-detailed land cover data to inform where that population might be located within the region (ie population is higher in urbanized areas than forests).

*Weighting tables*. Define the percentage of the aggregate value which is assigned to each auxillary class. For example, this table could define that 80% of pesticide consumption occurs in agricultural land.*Attribute Lookup*: Aggregate values by regions (eg. pesticide and fertilizer use by country)*Auxillary Raster*: Raster dataset with cells defining discrete classes of the auxillary variable (eg land cover types)*Rasterized Spatial Units*: Raster with cells representing the region by unique identifier, which is used to relate it to the attribute lookup.

The rasterized spatial units are reclassified by the attribute lookup values yielding an attribute value raster; the raster equivalent of a choropleth map. This is combined with the auxillary raster to produce both a table and a raster representing each unique combination of the two input rasters. The weighting table is joined with the combination table and the value per pixel (VPP) is calculated based on:

VPP = AggregateValue * Weight/CellCount

The VPP table is used to reclassify the combined raster dataset, yielding a dataset with pixels in the real units of the variable of interest.

Validity testing confirmed that the dasymetric process conserved sum. Using zonal stats, the total values for each country were calculated from the dasymetric output and compared to the aggregate value; they were practically equal in every case.

The fertilizer and pesticide raster datasets that resulted from this process preserved overall sums, just as choroplethic mapping would have, but more realistically distributed the values heterogenously withing the region based on auxillary land cover information.

## Citations

Robinson, W.S. (1950). "Ecological Correlations and the Behavior of Individuals". American Sociological Review **15**: 351–357.

Holloway, Steven R., Schumacher, James, Redmond, Roland L. (1997). "Dasymetric Mapping Using Arc/Info". Cartographic Design Using ArcView and ARC/INFO. High Mountain Press, NM.

Hultgren, Torrin. "Raster Based Automated Dasymetric Mapping". ??

Mennis, Jeremey. (2003?) "Generating Surface Models of Population Using Dasymetric Mapping". The Professional Geographer. p 55(1).