Suitable digital elevation model


Proposed method for all-purpose high quality DEM modelling
We are going to put more energy to enhanced DEM modelling and then visually compare the results with previous interpolations. The main idea here is to produce as good as possible DEM that would be useful for most of applications. The main data source is still the same, contour lines, but the DEM is being enhanced with fusion of some other data sources, like local ones, lower quality DEMs, geodetic network points and others. One could even use datasets without a height attribute such as lines of the hydrological network, roads, railways, standing water polygons, etc.

A method of weighted sum of data with geomorphologic enhancement was developed. With this method, DEM is modelled through averaging and fusion of individual datasets considering their quality. Grid based datasets are thus overlaid as regards the weights of particular grid cells. After overlaying, geomorphologic enhancement is applied. At the beginning a unique grid size for all data sources is determined - the same as for the final DEM.

Furthermore, each particular data source should be precisely evaluated by a reference dataset (points) regarding the standard test areas delineated by standard regionalised layers. The result is a predicted quality for each grid cell denoted with a random error ( ). For the sake of simplicity we will continue with our discussion with only two data sources. Height of DEM (Hi+j) regarding weights wi and wj and variances and are then

Weighted sums of pairs of surfaces (i+j)k are calculated iteratively by adding independent datasets to previous ones (Fig 2). The random error of the computed DEM ( ) incrementally decreases with every iteration. For two datasets it is calculated with the differentiation of heights as

The best practical solution is to start DEM modelling with data sources of the lowest quality (lowest weights) and to finish with the best data.


Fig 2: DEM, interpolated as weighted sum of data sources

DEM, derived iteratively with weighted sums of data is smoother than the geomorphologically highest quality data source (Fig 3). This is usually a consequence of the nature of the weighted sum. Geomorphologic enhancements of such a derived DEM are therefore required. The best solution seems to be to apply the enhancements only when the DEM is already derived from all weighted data sources.


Fig 3: DEM, geomorphologically enhanced from weighted sum of data sources

The main step of geomorphologic enhancement is the generation of trend surfaces as low frequency functions - with generalising DEMs. Trends are produced with the same conditions for datasets of the statistically best DEM derived by weighting (i+j), and the DEM with appropriate geomorphology (j) (Fig 3). Relative elevations (?j) as a high frequency part are computed from j and then added to the trend surface i'+j' of the dataset i+j. In this way the final geomorphologically enhanced DEM is produced. Statistically it is slightly worse than the weighted one (i+j), but geomorphologically it is much better. The main problem of the described enhancement lies in finding a suitable filter to calculate the appropriate trend surfaces. The optimal solution is a compromise between geomorphologic improvements and retaining statistic quality.

Described method of DEM modelling was tested on the same study area as in the previous chapter. The modelled DEM looks visually geomorphologically high quality with clear and reasonable details (Fig 4). As it had been tested before, the method serves also DEM with high precision and accuracy. If we are going to produce geomorphologically and statistically highest quality DEM, we do not need to think much about required application.


Fig 4: DEM, generated with more advanced modelling using weighted sum of data with geomorphologic enhancement (area of 5000 by 5000 m around lake Bled).

Effective and suitable DEM modelling from variable datasets is complex, rather iterative process that cannot be achieved intuitively or via a single step. In this sense experience is connected to the execution of stacks of tests and analyses, as well as a better understanding of the nature (parameters) of data. The quality of the DEM is evaluated for every data element and the portion of every data source element used for DEM modelling is known. With purposed approach, we can have full control of the production and effectively inform the final user about the characteristics of the DEM.

Conclusions
Before to start modelling of our DEM we should ask ourselves: Do we need to produce all-purpose high quality DEM? Or: Do we need to produce DEM just for our application? It is known that high quality DEM could consumes even more than 100 times more time then production with using basic algorithms like IDW, or spline are. Furthermore we need advanced software, higher quality of hardware, experienced team and advanced know-how. For our decision is important to have a review over existent DEMs which can be used unchanged for our applications or they are just sources within more advanced DEM production.

Specialisation in the information society is currently so high that we can not master all the processes on enough high level, so it is necessary to trust to the particular specialists and organise them to a reasonable team. It is nice to hear that quantity of digital spatial data is increasing, but unfortunately quality of data doesn't follow the quantity. Many of the producers do not test produced data sources or models enough carefully. The result of such work is data of unpredictable quality. Similarly, the software always offers more than hardware can manage.

After such experiences we propose some kind instructions that should come together with interpolation algorithms and that suggest the most important steps of DEM production for required application. The instructions should be prepared on basic and on higher level and may include following steps: preparation for DEM production, pre-processing of data sources, processing DEM from sources and managing the DEM data. Furthermore we suggest that user's manuals of the DEM interpolation algorithms should propose more tips and tricks for the common users. Most often they include only general information as description of the algorithm with parameters, common purpose of use, and some simple examples. We suggest at least hints regarding appropriate algorithm and parameters implementation if data sources are differently distributed or different type. For example contour lines interpolation algorithms are different to the algorithms for scattered points. The tip that suggests which parameters might be used for production of high quality DEM from particular datasets might be also important.

Significant aim of the DEM's nature is to find a balance between users' demands and capability of the developed realisation process. High quality DEM production using advanced methods could be very expensive. However, users always demand higher quality then it is offered, but this is not always reasonable. We should stress that even if we produce more sophisticated DEM and if more experienced producers are to be employed in the job, we would get different models. The solution proposed in this paper was confirmed through applied experimentation that enables cost-effective, high quality production and assumes higher collaboration between producers and users. Better DEM we can produce or choose regarding higher knowledge of the terrain characteristics and if we are aware of the application for that DEM is being used. Nevertheless the model should look reasonable!

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