Physically based hydrological modelling


Spatial Modelling in GIS
The lumped hydrological model was required to run on a spatial platform to estimate the river flow status. In selecting the modelling functionality in SPANS GIS, the main criterion was the capability of direct spatial data processing in the modelling exercise. Map modelling allows to use spatially distributed and tabulated data through various mathematical processes to derive associated data and information. It was noted that the accuracy of model representation was dependent on the quad resolution of the data and data analysis process. Hence, the selection of the best quad level was made carefully after considering the accuracy of data representations, storage requirements, and computational efficiency. The quad level 11 was rated as the best in terms of these variables.

Table 1. Statistical Summary of Spatiotemporal Modelling Results

Sub Staistical Parametres Catchments

Talawakele Kotmale Peradeniya Victoria Randenigala
Mean (mm) Measured 105.12 148.14 163.11 89.51 119.8
Runoff Simulated 96.94 137.39 156.62 84.82 102.48
STD (mm) Measured 68.8 141.82 111.72 83.34 116.42
Runoff Simulated 88.69 129.18 131.88 83.62 119.59
Coefficient of Determination 0.84 0.92 0.83 0.90 0.96
Cross Correlation Coefficient 0.71 0.84 0.69 0.81 0.92
Lag 01 Correction 0.49 0.23 0.22 0.33 0.46
Coefficient of Efficiency 0.15 0.69 0.22 0.62 0.82
Residual Mass Curve Cof. -0.40 -1.20 0.21 0.32 0.35



Figure 1 Generic Structure of the Hydrological Model


Several interpolation methods were attempted to represent spatial distribution of rainfall in GIS. Thiessen polygon method was adopted due to its computational efficiency with the time invariant spatial boundary demarcation.

Saptial Model Structure
A series of equations were formulated using map modelling language codes of SPANS GIS. Each sub model of the UMCA hydrological model was represented in a set of equations and additional equations were required to increment the file pointer along the columns of the data tables for daily rainfall.

In the case of Thiessen polygons, representative areas for each gauging station are directly identified from the morton numbers of the gauging locations. Morton numbers are hexa-decimal numbers used for spatial referencing in SPANS GIS. For a particular day, the hydrological model reads the relevant column of the rainfall data tables and calculate the fog interception according to the season. The total precipitation is then assigned to the corresponding Thiessen polygons. Based on sub models, it calculates the spatial distribution of interception and evaporation losses according to the hydrological parameters assigned for each land use. It also takes into account the spatial variation of antecedent moisture and the soil moisture stress. Finally, the model calculates the daily runoff and changes in soil moisture regime through the water balance equations. It then updates spatial coverage for cumulative runoff, soil moisture, cumulative interception and evaporation, stored in thematic maps. The updated map of soil moisture provides antecedent moisture status for the water balance calculations of the following day. The entire model structure was set-up to run on actual numerical values of each quad cell of thematic coverage.

Data Output Formats
The distributed modelling approach adopted for the study was capable of estimating daily upstream flow at any desired point of the drainage network. However, the model calibration required flow to be predicted at the flow gauging locations in order to make comparison with the historical flow records. Further, provisions were made in the model to estimate composite flow values at the identified 32 sub catchments in UMCA. In addition to the real time series of flow data generated from the model, it provided the display facilities representing the spatial distribution of runoff on thematic maps at any desired time period of interest.

Spatiotemporality in GIS
SPANS GIS menu driven functions can be run using equivalent command mode codes. The advantage is that a series of SPANS functions can be programmed into a batch file recognised as an audit file and run on the command mode. In order to include the temporal dimension into hydrological modelling, command mode functions were used extensively. The entire methodology depends on the format and thematic details of the input data and map files. Having prepared daily rainfall data in monthly tables with a column of data series for each day, it was possible to use only one set of equations for a month, incrementing the file pointer to read the data in different columns. One equation file was designed for each year incorporating a series of monthly equations. In addition to the equation files, command files were required to call the relevant equations for map modelling. The command filing system was organised in such a way that each file contains executable files for each month. The REXX procedures, the available programming language in OS/2 were set up so that they could produce monthly values of weighted average of spatial distribution of runoff at each subcatchment. They also created maps showing spatial distribution of monthly runoff on the thematic scale according to the user-defined classification scheme. Cumulative monthly totals of the other hydrological parameters such as evaporation, interception and soil moisture were also calculated whenever required.

Discussions
Limitations for Spatiotemporal Modelling in GIS Hydrological modelling efforts in GIS are generally hampered by the limitations of time representation in spatial data structures. As such, it is not possible to readily model the evolution through time of spatial variations in a phenomenon with GIS and such variations are often needed in hydrology.

However, the continuous development of the conceptual framework for spatiotemporal modelling confirms that the goal of fully functional temporal GIS is close to realisation. Nevertheless, it was found that provisions are made within the existing software architecture for the time varying modelling at discrete temporal resolutions through iterative procedures. This study shows how time dimension could be implicitly incorporated into the existing GIS modelling algorithms in order to employ time variant modelling while maintaining the integrated spatial dimension.

Model Performance
A comprehensive statistical evaluation was made to compare the observed flow data with the simulated flow series of the modelling exercise. The statistical summary of the modelling results is listed in Table 01. It is apparent that there is a great deal of agreement between the measured and simulated flow time series. In addition, the sensitivity of the model for the defined hydrological parameters, spatial resolution and land use changes were also assessed. The model is obviously sensitive to land use changes in the catchment and it shows 15 – 35% increase of annual runoff when forests are converted to grasslands.

Page 2 of 2
| Previous |