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The spatially distributed hydrologic model WetSpa that works on daily, hourly, and minutely timescales is used to predict the flood hydrographs and spatial distribution of the hydrologic characteristics in a river basin by combining elevation, soil and land-use data within Geographical Information System. This model was applied in Ziarat river basin (95.15 km
^{2}) located in Golestan Province of Iran. Hourly hydro-meteorological data from 2008 to 2010 consist of precipitation data of two stations, temperature data of one station and evaporation data measured at one station, which were used as input data of the model. Three base maps namely DEM, land-use and soil types were produced in GIS form using 30 × 30 m cell size. Results of the simulations revealed a good agreement between calculated and measured hydrographs at the outlet of the river basin. The model predicted the hourly hydrographs with a good accuracy between 62% - 74% according to the Nash-Sutcliff criteria. To evaluate the model performance during the calibration and validation periods an Aggregated Measure (AM) was introduced that measures different aspects of the simulated hydrograph such as shape, size, and volume. The statistics of Ziarat river basin showed that the results produced by the model were very good in the calibration and validation periods.

Rainfall-runoff models are used to perform various water resource assessments based on current and future changes in the watersheds and also in flood forecasting. Particularly, the Distributed Model Intercomparison Project (DMIP) provides a forum to examine the suitability of distributed rainfall-runoff models in flood forecasting using operational quality data in order to improve the flow modeling and prediction along the whole of the river system [

The WetSpa model simulates the runoff and river flow in a watershed basin on an hourly time step [

d θ d t = P − I − S − E − R − F (1)

where D [L] implicate the root depth, h [L^{3}L^{−3}] show the soil moisture, I, [LT^{−1}] is the initial loss consist of interception and depression storage, S [LT^{−1}] is the surface runoff, E [LT^{−1}] is the evapotranspiration from the soil, R [LT^{−1}] is the percolation out of the root zone, F [LT^{−1}] implicate the interflow, and t is the time [T]. The surface runoff is computed by a moisture-related modified rational method with a runoff coefficient dependent on the land cover, soil type and slope:

S = C ( P − I ) ( θ θ s ) a (2)

where: θ_{s} = saturated soil moisture content [L^{3}L^{−1}], Cr = potential runoff coefficient [−] depending on slope, land use and soil type, and α = empirical parameter [−]. Exponent α [−] in the formula is a variable reflecting the effect of rainfall intensity on runoff generation.

∂ Q ∂ t + c i ∂ Q ∂ x − d i ∂ 2 Q ∂ x 2 = 0 (3)

where Q [L^{3}T^{−1}] implicates the discharge, t [T] shows the time, x [L] shows the distance along the flow direction, c [LT^{−1}] is the location dependent on the kinematic wave celerity, is interpreted as the velocity by which a disturbance travels along the flow path, and d [L^{2}T^{−1}] is the location dependent on the dispersion coefficient, which measures the tendency of the disturbance to disperse longitudinally as it travels to the downstream. Assuming that the water level gradient equals the bottom slope and the hydraulic radius approaches the average flow depth for overland flow, c and d can be approximated by c = (5/3)v, and = (vH)/(2S0) [^{−1}] is the flow velocity computed by the Manning equation, and H [L] shows the hydraulic radius or the average flow depth. An approximate solution to the diffusive wave equation in the form of a first passage time distribution is applied [

u i ( t ) = l i 2 π d i t 3 exp [ − ( c i t − l i ) 2 4 d i t ] (4)

where U(t) [T^{−1}] implicates the flow path unit response function, serving as an instantaneous unit hydrograph (IUH) of the flow path, which makes it possible to direct the excess water from any grid cell to the outlet of the basin or to the any downstream convergent point, t_{0} [T] shows the flow time, and σ [T] is the standard deviation of the average flowtime. Two parameters t_{0} and σ are spatially distributed and can be obtained through integration along the topographic determined flow paths as a function of flow celerity and dispersion coefficient.

t 0 = ∫ c − 1 d x (5)

σ = ∫ ( 2 d / c 3 ) d x (6)

As the groundwater movement is much slower than the surface water and near surface water system movements and the understandings about the bedrock is little, groundwater flow is simplified as a lumped linear reservoir in small GIS derived subwatershed scale. With considering the river damping effect for all flow components, overland flow and interflow are directed firstly from each grid cell to the main channel, and are joined with groundwater flow at the outlet of the subwatershed. Then the total hydrograph is routed to the outlet of the basin by the channel response function derived from Equation (4). The amount of total discharge is sum of the overland flow, interflow, and groundwater flow, and is obtained by convolution of the flow responses of all grid cells. One advantage of this approach is allowing to the spatially distributed runoff and hydrological parameters of the basin for using as inputs for the model. Inputs of the model consist of digital elevation data, soil type, land use data, and measured climatological data. Stream discharge data are optional for model calibration. All hydrological processes are simulated within a GIS framework. Because a large part of the annual precipitation is in the form of snow, snow melt simulating is done by a model based on hourly temperature data. The conceptual temperature index or degree-day method is used in this study because of its simplicity but it has not a strong physical foundation. The method replaces the full energy balance with a term linked to air temperature. It is physically sound in the absence of shortwave radiation when much of the energy supplied to the snowpack is atmospheric long wave radiation [

M = max [ 0 , ( K s n o w + K r a i n P ) ( T a − T o ) ] (7)

where M implicates the daily snowmelt [mm], Ta [˚C] shows the mean air temperature, To [˚C] shows a threshold melt temperature, Ksnow is a melt-rate factor [md^{−1}˚・C^{−1}], and Krain is a degree-day coefficient that shows the heat contribution from rainfall [d^{−1}˚・C^{−1}]. The critical melt temperature To is often intuitively set to 0˚C. The melt-rate factor Ks now is an effective parameter and may vary with location and characteristics of the snow. However, Ks now, To and K rain can be calibrated.

The Ziarat watershed places in the north of Iran. The watershed has an area of 95.15 km^{2} which is a small watershed, with elevation ranging from 488 to 3027 m. The mean elevation and slope of the watershed are 1714 m and about 41.4%, respectively, from which the drainage system and area were determined as shown in

Area (km^{2}) | 95.15 |
---|---|

Perimeter (km) | 51.40 |

Min. elevation (m) | 488 |

Max. elevation (m) | 3027 |

Mean elevation (m) | 1714 |

Mean basin slope (%) | 41.4 |

Stream order at outlet | 4 |

Max. flow length (km) | 23 |

The grid size of DEM of the river basin was 30 m from which the drainage system and area were determined. The topographic data were provided from the numerical elevation data sets of National cartographic center. All GIS data are raster based with a 30 m grid size.

For this study, precipitation, temperature, discharge and potential evapotranspiration (PET) data were provided from Water Research Institute of Golestan Province, The sets include hourly precipitation for two stations, temperature for one station, PET at one station, and hourly discharge data at one gauging station. All of the data are available for a 3-year period from 2008 to 2010.

Identification of the spatial model parameters is undertaken after collecting and processing of required data for use in the WetSpa model. DEM is first used to extract the terrain features at each grid cell including elevation, flow direction, flow accumulation, stream network, stream link, stream order, slope, and hydraulic radius. The threshold of stream network delineating is set to 10 namely when the upstream drained area is greater than 0.1 km^{2} a cell is considered be drained by a stream. The value of subwatersheds determining threshold is set to 3000, by which 17 subwatersheds are identified with an average subwatershed area of 5.5 km^{2}. A threshold value of minimum slope of 0.01% is considered in creating the grid of surface slope. If the calculated slope is less than the threshold value, the slope will set to 0.01% in order to avoid stagnant water or extreme low velocities.

The grid of hydraulic radius is generated with an exceeding frequency of 0.5 (2-years return period) which is resulted in an average hydraulic radius of 0.007 m for the upland cells and 0.5 m at the outlet of the main river channel (The related formula and calculation method are discussed in the documentation and user manual of the model by [

Finally, the flow routing parameters include flow velocity, average travel time and its standard deviation from cells to the watershed outlet and to the subwatershed outlet.

Model calibration and validation is done by the 3 years (2008-2010) measured hourly precipitation, temperature, PET, and discharge data. The 3-years period is divided into a 2-years and a 1-year period that the former is used for the model calibration and the second is used for the model validation. The calibration process is only performed manually for the global model parameters, whereas the spatial model parameters are kept as they are. Initial global model parameters are specifically chosen according to the basin characteristics as discussed in the documentation and user manual of the model [

of the hourly stream flow for the second part of the data namely from 2010 is done using the calibrated global parameters in order to the model validation.

parameter values, the PEST program is applied to calibrate the WetSpa model. The statistical criteria used in the Model analysis are ModelBias (MB), reflecting the ability of reproducing the water balance, the Modified Correlation Coefficient (r_{mod}), which reflects differences both in hydrograph size and in hydrograph shape [

r mod = r × [ min { σ o , σ s } max { σ o , σ s } ] (8)

where σ o and σ s show the standard deviations of the observed and simulated discharges respectively, r indicates the correlation coefficient between observed and simulated hydrographs. The perfect value for this criterion is 1.

M B = ∑ i − 1 n ( Q s i − Q o i ) ∑ i − 1 n Q o i (9)

where, MB is the model bias, Qsi and Qoi are the simulated and observed streamflows at time step i (m^{3}/s), and N is the number of time steps over the simulation period. Model bias measures the systematic under or over prediction for a set of predictions. A lower MB value indicates a better fit, and the value 0.0 represents the perfect simulation of observed flow volume.

N S = 1 − ∑ i − 1 N ( Q s i − Q o i ) 2 ∑ i − 1 N ( Q o i − Q o ) 2 (10)

where, NS is the Nash-Sutcliffe efficiency used for evaluating the ability of reproducing the time evolution of streamflows. The NS value can range from a negative value to 1, which 1 indicates a perfect fit between the simulated and observed hydrographs. Aggregated Measure (AM) is used to measure the different aspects of the simulated hydrograph such as shape, size and volume

AM = r mod + N S + ( 1 − | M B | ) 3 (11)

A value of 1 for AM shows a perfect fit. To categorize the goodness of the model performance, the intervals listed in

It has been proven that the distributed models are useful in scenario analyses because of their ability to predict the effect of spatially changing variables. To avoid the inherent complexity in estimating the surface runoff a simple but effective approach is presented wherein the whole basin is divided into grid cells, giving the possibility to simulate the hydrologic processes at reasonably small scale [

Category | Aggregated Measure (AM) |
---|---|

Excellent | >0.85 |

Very good | 0.70 - 0.85 |

Good | 0.55 - 0.70 |

Poor | 0.40 - 0.55 |

Very poor | <0.40 |

Criteria | Calibration | Validation |
---|---|---|

r mod | 0.78 | 0.79 |

MB | −0.04 | 0.1 |

NS | 0.74 | 0.62 |

AM | 0.73 | 0.71 |

complexities of a watershed and temporal variation of river flows, especially peak discharges [

Azizi, M., Mohajerani, A. and Akhavan, M. (2018) Simulating and Prediction of Flow Using by WetSpa Model in Ziyarat River Basin, Iran. Open Journal of Geology, 8, 298-312. https://doi.org/10.4236/ojg.2018.83019