The cross sections applied in this model are from two sources: a few of them downstream are taken from the measurements, and the remaining ones are extracted from the DEM. The overland flow appears after the net rainfall rate exceeds the infiltration capacity of the soil; water then ponds on the ground surface. The main parameter to calculate this flow is the Stickler roughness coefficient M. DHI suggested three methods for describing the flow in this zone: Richards' equation, gravity flow and two-layer UZ. However, the application demonstrates that the various approaches do not provide very different results.

For the current application, the simple two-layer water balance method is chosen to reduce the computational time. The physical property of each soil type is presented via the water content at saturation, water content at field capacity, water content at wilting point, and saturated hydraulic conductivity.

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The characteristic of the aquifer is mainly presented by horizontal hydraulic and vertical hydraulic conductivities. In addition, the sensitivity analysis quantifies the dependent rate of runoff on the change of these parameters. As a result, these rates make the calibration easier and allow acceptable values to be more quickly obtained. It is seen to be a prior step to the calibration process. For the model applied to the Vu Gia Thu Bon catchment, the sensitivity of each parameter is analyzed based on the response of discharge in the Nong Son and Thanh My stations.

In such a complex system as hydrology, the implication of the change in magnitude of several model parameters due to other parameters is undeniable Sivapalan et al. It is clear that the sensitivity analysis will be better when accounting for the interactions between model parameters Mishra However, with a model containing many parameters such as the MIKE SHE model applied to a large catchment, the evaluation of the interaction between model parameters during the sensitivity analysis is complicated and requires many simulations.

In this analysis, the sensitivity analysis was done manually by varying the values of the parameters individually, one by one. This method has been applied by many authors Refsgaard ; Andersen et al. The parameter sensitivity is demonstrated via the variation tendency of the base flow and peak flow at the Vu Gia Thu Bon river system. Subsequently, the result of this process is expected to provide valuable information for the calibration process.

The available data over the Vu Gia Thu Bon cover the — period. The chosen strategy for calibration and validation has to be implemented within this period. The first period of 11 years from to is used for calibration. Over these 11 years, the recorded climate situations include two major flood events — and — with a return period of years ICEM and severe drought events in — and Vu et al.

For the validation phase, the 11 year period from to also includes two major flood events — , with a return period of years; , with a return period of 20 years Chau et al. The two periods allow analysis of the hydrological dynamic at the catchment scale and ensure representative results. Obviously, the availability of data — lack of measurements — is a serious constraint, but the proposed approach tries to overcome the difficulty by maximizing information production from the available data.

In order to stabilize the model and establish proper initial conditions, the first year of each period is used for warming up the model. Hence, in this analysis, only 10 years of daily data are taken to calibrate and validate the model. The calibration is done manually. This process, of course, is based on the results of the sensitivity analysis. Only a few sensible model parameters are used for the calibration process. The Vu Gia Thu Bon catchment has a complicated river system.

Although the length of the two main rivers reaches km, there is only one flow measuring station in the middle of each main river: Nong Son on the Thu Bon branch and Thanh My on the Vu Gia branch. This situation creates several difficulties for comparison of the results between simulations and observations. Especially, this is not only an inconvenience for predicting flood risk in the downstream region, but it is also a factor that produces uncertainty when assessing the impact of climate change on runoff.

The lack of observation data for comparing with simulation results degrades the performance of the distributed model. Many hydrologists have suggested realizing calibration by multi-site, with not only the discharges but also the water levels Wang et al. The smaller the RMSE value is, the higher the model performance will reach.

The optimal values of these two factors are all 1 Safari et al. The results demonstrate the effects of the parameters on the simulated stream flows.

### International Journal of Hydrology Science and Technology

These effects are not similar for all parameters. The results show that the difference is not only about the quantity but also about the timing of the peaks. Parameters for the precipitation-dependent time step control are put forward to reduce the numerical instabilities DHI b. These parameters define the maximum rainfall value per time step and they are expected to have a great impact on river flows, at least on peak flows. Accordingly, if the Max precipitation depth per time step P Max depth increases, the peak flow will reduce.

This tendency happens similarly with Input precipitation rate requiring its own time step P Input rate. However, the impact of P Input rate on runoff is not as high as the P Max depth. The increase of this factor from 0. An important aspect for this factor is related to simulation time. The smaller P Input rate is, the longer the model is running.

Regarding the correlation between the Nong Son and Thanh My stations in connection with precipitation parameters, the results show that change at the Nong Son station is generally two times higher compared to the Thanh My station. This difference might be related to the characteristics of the catchment. Overland flow simulates the movement of ponded surface water across the topography. It can be used for calculating flow on a flood plain or runoff to streams DHI b.

In this case, the finite difference method is selected to solve the overland flow for the Vu Gia Thu Bon catchment. The Manning number M , which is equivalent to the Stickler roughness coefficient, is estimated as the basic factor of the Overland flow module. Therefore, this part considers mostly the effects of the Manning number on runoff.

In the Vu Gia Thu Bon catchment, there are many kinds of land use and soil.

### International Journal of Hydrology Science and Technology

These lead to there being many corresponding Manning values. The effect of different Manning parameters corresponding to different land use types regarding river runoff is expected not to be equal. The disparity is due to the diversity in Manning values and distribution of land use. Nevertheless, there is one common point, that the change in Manning value greatly affects the peak flow, but mostly does not affect the base one. The river flow seems quite sensitive to the change in the bed resistance. It is expected to be the key factor in the calibration process.

The unsaturated zone is usually heterogeneous and characterized by cyclic fluctuations in the soil moisture as water is replenished by rainfall and removed by evapotranspiration and recharge to the groundwater table. Hence, this process plays a significant role in river runoff. Correspondingly, the variation of parameters in the unsaturated zone will deeply impact the runoff factor, on both base flow and peak flow. In this model, the physical characteristics of each soil are supplied, such as water content at saturation, at field capacity, at wilting point, and saturated hydraulic conductivity, yet only saturated hydraulic conductivity K uz has a huge impact on the flow.

According to this table, the peak flow goes down quite quickly when increasing the typical infiltration parameter. Furthermore, the reduction of K uz also makes the base flow decrease. The groundwater plays a crucial role in the behavior of hydrological processes within the catchment.

Thus, the variation of this component will significantly influence the river flow, especially the base flow when the discharge from groundwater is seen as its principal source. The groundwater is present in the saturated zone. The flow in the saturated zone is characterized by aquifer properties, of which horizontal saturated hydraulic conductivity K h proves the most influential on saturated flow.

For this reason, in the model only this factor is considered. The peak flow tends to reduce quickly when increasing K h. In spite of the insignificant variation, it is quite important for adjusting the base flow. Observed and simulated daily and monthly discharges are compared. These numbers demonstrate the accuracy of the model and its efficiency for describing the hydrological processes of the Vu Gia Thu Bon catchment.

In the validation period, these factors slightly decrease. R and E coefficients at Nong Son station are 0. Over the 10 year period, the RMSE of simulation is only The value at Nong Son is Due to these big differences between maximum and minimum values of observed data, the values of the normalized root mean square error at these stations are quite small, with a value below 0. The difference of peak flow empirical extreme value distributions between calibration and observation at Thanh My a and Nong Son b. The difference in low flow empirical extreme value distributions between calibration and observation at Thanh My a and Nong Son b.

However, the accuracy of simulated water levels is not as good as for discharges. The relation coefficient in all stations is around 0. Despite the fact that statistical coefficients for water levels are still low, calibrating the model relying on these factors probably adds a certain value to show the correlative level of model results with real data.

Therefore, this model is able to be applied to a flood event or the variability of stream flow under the impact of climate change. Moreover, these results also demonstrate the performance of deterministic distributed models in simulating the hydrological process, especially with a large catchment. Although trying to reflect most truthfully the hydrological dynamic in the catchment, the model has not yet gained the optimal results when inaccuracies still remain.

These coefficients could not get maximum values for many reasons. The model has many potential uncertainties for simulating hydrological processes.

## Distributed Hydrologic Modeling Using GIS (Water Science and Technology Library)

The advantage of the distributed hydrological model is that it represents hydrological characteristics of the catchment cell by cell. However, the resolution used in the model is still coarse due to the limitation of topographic data and computation time. The 90 m topographic grid data used may not describe precisely enough the surface of the catchment. Thus, it derives some differences in surface flows between reality and the model. The land uses, the soil properties, or the roughness coefficients, which are simplified in order to optimize the calibration are the major causes of underestimation or overestimation for the model.

Another issue significantly influencing the model uncertainty is the rainfall, which is a key factor in the hydrological dynamic. Rainfall spatial variation heavily affects both runoff generation and the hydrologic process in a catchment Moon et al. The spatial variability in rainfall may introduce a significant uncertainty in model parameters during the calibration process Chaubey et al. The quality of spatial rainfall distribution usually depends on the characteristics of the study area and other factors, in particular, the rain gauge density.

The network of rain gauge stations in Vu Gia Thu Bon is sparse, with, on average, one station for an area of km 2. In the constructed model, the rainfall inputs are re-interpolated and could be considered as a great source of uncertainty. As well as the spatial distribution, the time factor is also a great potential source of uncertainty Dendy , especially within the Vu Gia Thu Bon catchment where the concentration time is short due to the steep topography. Using daily rainfall in this simulation probably affects the rising limb and the peak flow appearance. However, these data are the unique complete rainfall data set available for long-term simulations for the Vu Gia Thu Bon catchment.

The analysis regarding the rainfall distribution in space and in time demonstrates again the impact of lack of data on simulation uncertainty. The groundwater is an unignorable component when simulating hydrological processes Winter In terms of input data, the insufficiency of ground water data is seen as a major source of uncertainty for simulating hydrological processes.

The quality of the groundwater data of the Vu Gia Thu Bon catchment is not very good, and the collected data do not present the groundwater properties concretely. For the whole catchment, the model integrates a unique geological layer. Regarding the modeling methods implemented in MIKE SHE, the selection of one or another method can potentially generate several sources of uncertainty. For example, there are three functions to select for unsaturated flow: Richards' equation, gravity flow, or the two-layer UZ.

The Richards' equation is supposed to be the best method for simulating unsaturated flow. However, in the current application, the two-layer UZ was chosen due to the limited available data sets and the short processing time. Lab Exercise. Cartographic modeling of small town. Land classification.

Capability assessment. Determine grazing capacity on Southwest rangeland using erosion tolerance, vegetation characteristics. Interpolation techniques; inverse distance weighting, spline, Thiessen. Derive rainfall surface from historical gauge data on a Southwest rangeland watershed. Radars, an alternative in hydrological modeling.

Lumped model. San Pablo , Col. Reynosa Tamaulipas, Azcapotzalco D. Corresponding author: E. Received January 11, ; Accepted September 13, The use of meteorological radars in hydrological modeling is a tool that is becoming more important each day throughout the world.

The use of weather radars is shown to be an alternative in the generation of hydrological models. The occurrence of intense rains over an area causes an increase in runoff. This may generate floods that eventually reach into considerable dimensions. In some cases, floods are caused by the overflowing of rivers that result in material damages, and sometimes loss of human lives.

The application of measures of prevention or of mitigation of the effects caused by flooding requires data to predict the magnitude, evolution through time and probability of occurrence, for which reason the use of a hydrological model is recommended. This depends on the spatial discretization scheme used to describe the characteristics of the watersheds, as they are based in physical or conceptual principles depending on the degree of mathematical analogy used in the analysis Mendoza et al.

In order to understand the causal relationship between rainfall and runoff, mathematical models have been developed that make it possible to obtain the response of a catchment, in terms of streamflow, to the stimulus of an input such as rainfall. The watershed has an area of The annual average rainfall in this area is mm Fig.

Urban growth also affects the potential infiltration of the soil and the hydrological response of the watershed. The first model input average rainfall data were obtained from pluviographs, and was estimated following Thiessen's polygon method. The second model input average rainfall data were estimated from radar data. On the other hand, a lumped parameter model was used to evaluate the goodness of the meteorological radar in hydrological modeling. Until recent years, lumped models have been the most commonly used models for hydrological processing in watersheds, particularly because of the practical impossibility of obtaining spatially distributed information of the characteristics of a catchment and of precipitation.

The variables and parameters used in this kind of model represent average values for each of the properties of the watershed, for example: area, slope, types of soil and cover, among others, without considering the topology of the basin and its stream network.

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A lumped model represents the watershed as a unit characterized by a reduced number of variables and parameters with averages that can be determined empirically or physically Maidment, The basic unit of a lumped model is the watershed, for which a unitary response is considered in a way that all its attributes are averaged DeVantier, Lumped parameter models do not explicitly take into consideration the spatial variability of the inputs, outputs and characteristics of the catchment.

They are generally structured to use average values of the characteristics of the basins, and this affects the estimation of the streamflow volume. Thus, averaging parameter values clearly imply that the processes represented by those parameters are also averaged Vieux, Four storms of the year were analyzed for this study Table II.

The Mixcoac hydrometric station is located at the watershed outlet, 35 km away from the radar Fig. These four storms caused considerable expense and flooding problems in the watershed. The time interval At used by the radar to record data was of 15 minutes, as was the time used to obtain rainfall from the rain gauges and the observed runoff. The spatial resolution of the radar images was l x l km. The six pluviographs in the area of influence of the basin that were used for the analysis are separated one from the other by an average distance of 7.

One of the most important parameters in lumped hydrological models is the losses, as it is through the estimation of these that the surface streamflow or runoff is inferred. With respect to the mechanisms that generate runoff in a basin, the most used and simplest traditional models consider that the water that falls directly as rain is immediately converted into surface runoff following one of these reasons: the amount of rain exceeds the infiltration capacity, called Hortonian runoff, or the soil is saturated, known as Dunne's runoff or saturation runoff Aparicio, Hortonian runoff is present only in areas where the hydraulic conductivity of the soil is very low or where exceptionally intense rainfall occurs.

## Teaching Spatial Analysis for Hydrology and Watershed Management

One of the simplest methods to estimate infiltration is the criterion of the runoff coefficient R c. This criterion establishes that the losses are proportional to the intensity of the rain, that is:. If the value of R c is known for a watershed, the outlet volume for a storm is obtained with the equation:. Another frequently used criterion is the criterion of the average infiltration capacity or its index. This last method was used in the analysis of the study case presented here.

As the remote sensing instruments, such as weather radar, do not measure but only estimate the rainfall using empirical relationships, it is necessary to validate the rain estimation Rosengaus, The calibration criterion used the equation. In this criterion, the coordinate of the matrix center is the same that the rain gauges Fig.

Then, the calibration equation was estimated from pairs Ultimately, the equation obtained was.