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We proposed unit flood discharge model that defined as the discharge into end-order (smallest) drainage canals. The discharge acts an important role for estimating regional flooding by big rainfall events which leading roughly estimation of flood discharge associated with land use changes as urbanization. In some areas of Japan, increased urbanization with insufficient drainage canal capacity has led to increasingly frequent flooding and flood damage. The aim of this study was to investigate the effect of urbanization on unit flood discharge using a runoff model for the Tedori River alluvial fan area, Japan. The discharge was studied as collecting runoff from paddy fields, upland crop fields, and residential lots. A runoff model for various land use types in the study area was developed using actual and physical properties of the runoff sites, and parameters for paddy fields. The model was tested using 54 big events and inputted those. The maximum total runoff ratio among different land use types was observed for residential lots, and the ratio remained relatively constant across different flood events. The minimum total runoff ratio was observed for irrigated paddy fields. There was a positive relationship between the total runoff ratio and total precipitation for all land use types. Whereas, the relationship between the peak runoff ratio and peak precipitation was variable. The runoff analysis was carried out using 60-min and 10-min precipitation data. For agricultural land, data for both intervals produced similar results.

Rapid urbanization in Japan since the late 1960s has been associated with increasingly frequent flood events and flood damage, primarily as a result of insufficient drainage canal capacity. This phenomenon of increased flood discharge likely reflects the widespread change in land use from paddy fields and upland crop fields to residential areas. The relevant researches have been performed widely [

While previous studies investigated changes in runoff related to cultivation, the effect of urbanization was not directly considered. Furthermore, runoff models of outflow from areas with different land use types have only been proposed conceptually (e.g., Maruyama et al. [

Using the unit flood discharge, total discharge can be estimated by flood routing according to discharge systems and the changes in land use associated with urbanization that will be describe next research. A runoff model for various land use types was developed based on actual and physical properties and historic precipitation data were used to estimate total and peak discharge ratios. Another feature of the present research was the consideration of depression storage of precipitation as part of the runoff analysis. Special features of the Tedori River alluvial fan area where the study was conducted were that the residential areas were reclaimed from paddy fields on very steep hillsides. Most of the upland field areas were cultivated with soybean or wheat in rotation with rice paddies by rice production control.

In summary, a runoff model based on actual and physical properties of various land use types was developed [

The site selected for the present study, the Tedori River alluvial fan area, is bounded by the cities of Kanazawa to the northeast and Komatsu to the southwest. The study area is representative of the steep landscapes cultivated as rice paddies in the region of Hokuriku (

Region | Paddy | Upland | Residential | River/canal | Road | Total |
---|---|---|---|---|---|---|

Right side | 5674 | 391 | 5399 | 532 | 2177 | 14,173 |

Left side | 1865 | 111 | 650 | 406 | 477 | 3509 |

Total | 7539 | 502 | 6049 | 938 | 2654 | 17,682 |

Ratio | 42.6% | 2.8% | 34.2% | 5.3% | 15.0% | 100.0% |

unit: ha |

Cultivated paddy fields are enclosed by levees and each individual field (lot) has a drainage outlet (

The continuity equation and discharge from a rectangular weir are expressed as follows [

where H_{t−1} and H_{t} are, respectively, water depth (mm) on the paddy field before and after calculation. q is the discharge from the weir (m^{3}∙h^{−1}), A is area of an individual paddy field (set as 1760 m^{2} based on the average size of paddy fields in the study area), R is precipitation (mm∙h^{−1}), ET is evapotranspiration (mm∙h^{−1}), P is percolation rate (mm∙h^{−1}), ∆t is time difference (h) and H_{min} is height of the outlet (mm). α is the discharge coefficient of the weir (set as 1.838), and b is the width of the weir (m) set as [b − 0.2 (H_{t} − H_{min})] [

Even at times when paddy fields and upland crop fields are not irrigated, some water from precipitation builds up in the depressions between levees. When this water exceeds the storage capacity of the fields, it is discharged into drainage channels. The volume of depression storage varies depending on the land use type (see the section on Depression storage in Results below).

In upland crop fields previously used as paddy fields, outlets into drainage weirs are usually opened. In this case, H_{min} in Equation (3) is replaced by depression storage (Dep) and discharge q is calculated using Equation (2) and Equation (3) with percolation rate P (irrigated paddy) replaced by infiltration rate I (non-irrigated paddy, upland and residential area) as follows:

The area of individual fields A is again set as 1760 m^{2}.

For runoff analysis for residential areas, to determine the unit time (∆t) runoff analysis was estimated before the runoff model was generated. First, the size of the average residential lot was estimated based on statistical data from the 2010 national census [^{2}. Second, the stream length in residential areas was estimated by assuming the shape of a standard residential lot to be a 25 m × 18 m rectangle. Third, the runoff time from waterways upstream of residential areas to drainage ditches below residential areas was estimated. The runoff time was calculated using a kinematic wave model [

The results for precipitation rates of 10, 30, and 50 mm∙h^{−1}; lot gradients of 0.001 and 0.01 m∙m^{−1}; and roughness of 0.03 and 0.05, are shown in

The runoff from residential lots was estimated using Equation (2) and Equation (6) with percolation rate P replaced by infiltration rate I in Equation (2), to satisfy Equation (4) and Equation (5). The units of some of the parameters in each equation had to be changed to account for the 10-min precipitation data. A' in Equation (6) is the area of the average residential lot (449 m^{2}).

The percolation rate was surveyed at 135 lots (3-lot per 1 point) in irrigated paddy fields

Gradient | Rainfall intensity | N = 0.03 | N = 0.05 |
---|---|---|---|

(mm∙h^{−1}) | (min) | (min) | |

0.01 | 10 | 9.3 | 12.7 |

30 | 6.0 | 8.2 | |

50 | 4.9 | 6.7 | |

0.001 | 10 | 18.6 | 25.3 |

30 | 12.0 | 16.3 | |

50 | 9.8 | 13.3 |

Note: Slope length: 25 m, N is roughness coefficient.

(^{th}-30^{th} May and 30^{th} June-3^{th} July 2014) and after midsummer drainage (31^{st} July-1^{st} August 2014). The percolation rate was observed as the change in the distance from the standing water level in the paddy field to the top of outlet height into the drainage weir over 24 h, minus the evaporation when no precipitation period. At the same time, the height of the levee, and the width and height of the drainage weirs were also measured. The evaporation was measured using a pan with 30 cm of diameter placed in standing water among rice plants in the paddy fields.

Infiltration rate was measured at five sites for each land use type in September 2014 using infiltrometers. The infiltrometers had a diameter of 27 - 30 cm and a height of 35 cm, and were inserted about 20 cm into the ground. The measurement conducted at non-irrigation paddy lots, upland crop lots and residential area. The infiltration rate was calculated based on the method of Philip using Equation (7) [

where I is the infiltration rate (mm∙h^{−1}), S is the sorptivity (mm∙h^{−1/2}), t is the time (h) from the start of the measurement, and a is the final percolation rate (mm∙h^{−1}).

Precipitation data were obtained from the Kanazawa Meteorological Observation Station. The station has data for 1883-2015. The data interval has increased over that time from 6 hourly in 1883-1885, to 4 hourly in 1886-1939, to hourly in 1940-2015. Since 2009, 10-min data have also been collected. For the present study, hourly precipitation data from 1940-2015 were used for paddy fields and upland crop fields, and 10-min data for 2009-2015 were used for residential areas. Events that met the flood-planning standard [

For the analysis of paddy fields and upland crop fields, 26 flood events with rainfall > 130 mm∙24-h^{−1} and seven events with rainfall > 100 mm∙24-h^{−1} including 10 min. intensity precipitation data were selected. For residential areas, 21 flood events with rainfall > 80 mm∙24-h^{−1} including 10 min. intensity precipitation data were selected. There- fore, the analysis included 33 events with hourly data and 21 events with 10-min data for a total of 54 flood events. Most of the flood events occurred from June to September (81%), with one event in May, eight in June, 11 in July, nine in August, 16 in September, four each in October and November, and one in December.

The statistical data of drainage weir height and levee height above the soil surface is shown in

The percolation of standing water in paddy fields was calculated by dividing before and after midsummer drainage. The mean percolation rate before midsummer drainage was 12.5 mm∙d^{−1} ± 12.5mm∙d^{−1} (range 0 - 62.0 mm∙d^{−1}). The mean percolation rate after midsummer drainage was 20.5 ± 14.6 mm∙d^{−1} (range, 0 - 57 mm∙d^{−1}). The values for

Item | Average | Sd^{*} | RSD^{**} |
---|---|---|---|

(mm) | (mm) | (%) | |

Weir height | 84.5 | 27.4 | 32.4 |

Levee height | 196.6 | 43.6 | 22.2 |

Storage capacity | |||

Before mid-summer | 43.1 | 37.1 | 86.1 |

After mid summer | 58.5 | 39.9 | 68.2 |

Percolation rate | |||

Before mid-summer | 12.5 | 12.5 | 100.0 |

After mid summer | 20.5 | 14.6 | 71.2 |

^{*}Standard deviation, ^{**}relative standard deviation.

percolation rate were not normally distributed despite the regular distribution of survey points (

In addition, comparisons were carried out between percolation rates on the right side and left side of the Tedori River, among different elevations, and before and after midsummer drainage. There was a significant difference in percolation rate before and after midsummer drainage (P-value is 0.06% < 5.0%). Therefore, the analysis was conducted separately for the periods before and after midsummer drainage.

Based on the infiltration equation, the related parameters determined using observed data by least square method and averaged at five points of those. The estimated sorptivity rate S and the final percolation rate a were, respectively, 4.6 mm∙h^{−1/2} and 3.4 mm∙h^{−1} for paddy fields, 4.1 mm∙h^{−1/2} and 1.7 mm∙h^{−1} for upland crop fields, and 11.3 mm∙h^{−1/2} and 1.58 mm∙h^{−1} for residential lots. However, if these estimations are applied directly to the runoff model, there is likely to be considerable error because of the large differences between sites [^{−1} after midsummer drainage because the examined events occurs mainly after mid-summer drainage. Therefore, this percolation rate was applied for irrigated areas. Based on the percolation rate of irrigated area, the infiltration test was used for relative values of non-irrigated paddy fields, upland crop fields, and residential areas.

In previous studies, Ando et al. [^{−1}, and Watanabe and Toyokuni [^{−1} for their runoff recharge model for residential areas. However, if the total amount of rainfall is > 100 mm∙d^{−1}, the accuracy of the percolation estimation has a minimal effect on the estimated peak discharge.

If outlet weirs are removed from non-irrigated paddy fields and upland crop fields, the surface drainage is incomplete because of depression storage. There is also a small amount of depression storage in some residential areas. Therefore, depression storage must be included in runoff analysis. Maruyama [

In the present study area, there is non-irrigation of paddy fields and upland crop fields. Therefore, depression storage should be divided into two categories; cultivation that requires furrows, such as soybean crops; and cultivation that does not require furrows, such as wheat crops. Non-irrigated paddy fields can be included in the non-fur- rowed category. Maruyama and Tomita [

For residential area, previous research of depression storage in residential was applied in which lots have 4 - 6 mm [

The shape of generated hydrographs differs not only in terms of the amount of the precipitation input into the runoff model but also in terms of the initial conditions. The initial conditions used in the present study to investigate the unit discharge for various land use types were based on the different sites and periods of major flooding (

Weir height | Storage capacity | Depression storage | Initial depth | Percolation rate | |
---|---|---|---|---|---|

(mm) | (mm) | (mm) | (mm) | (mm/hr) | |

Irrigating paddy | 84.5 | 58.5 | - | 26.0 | 0.85^{*} |

Non-irrigating and upland for wheat | 0.0 | - | 0 ~ 38.6 | 0.0 | 0.43 |

Upland for soybean | 0.0 | - | 0 ~ 17.6 | 0.0 | 0.43 |

Permeable residential lot | 0.0 | - | 0 ~ 6.4 | 0.0 | 0.46 |

^{*}Before mid-summer percolation is 0.52 (mm/hr).

minus mean ponding depth of 26.0 mm. For non-irrigated paddy fields, upland crop fields, and residential areas, the initial condition was the depression storage. The standing water depth before precipitation was assumed to be 0 mm. In addition, evapotranspiration having limited effect on runoff discharge estimated by complementary relationship using Penman equation [

The runoff model for the Tedori River alluvial fan area was based on the data described above. If precipitation data are entered into this model, the flood discharge (potential) can be estimated for various land use types. The following is an overview of simulated potential flood discharge for various land use types.

The relationship between total precipitation and total runoff ratio (total runoff/total precipitation) was relatively smooth except for residential areas (

An example of the analysis of a flood event estimated by 10-min and 60-min is shown in ^{th}-7^{th} of July 2012. The total discharge and

peak discharge increased in the following order with 10-min and 60-min precipitation intensity together: irrigated paddy fields, non-irrigated paddy fields and upland wheat fields, upland soybean fields, and residential lots. The initial loss from irrigated paddy fields was larger than that for other land use types which can be observed the runoff ratio and peak runoff ratio. Especially upland crop fields with non-furrowed crops had larger initial loss than upland crop fields with furrowed crops. The hydrograph estimated by 10-min and 60-min precipitation intensity is quite similar.

In the previous sections, the flood discharge analysis was conducted using precipitation data with a time interval of 60-min, except for residential lots for which a time interval of 10-min was used. In this section, the entire analysis was carried out with precipitation data at an interval of 10-min and 60-min to determine whether the results would be the same because of the large storage capacity of agricultural land. The 21 precipitation events for which 10-min data was available were used. The 21 events were classified as flood events based on The Disaster Recovery Project [^{−1} and > 20 mm∙h^{−1}.

The analysis was conducted as follows: For agricultural land, hourly and 10-min and 60-min precipitation data were entered into the runoff model expressed as outlined in Equation (2) and Equation (3), and the results were compared. For residential lots, the analysis was conducted using 10-min precipitation data input into Equation (2) and Equation (6) and the kinematic wave model [

The hydrographs obtained from this analysis are shown in

except residential lot. For residential lots, the latitudinal axes describe flood discharge calculated as precipitation minus infiltration and depression storage, that is, the effective precipitation calculated using Equation (6), while the abscise axis describe the discharge estimated by the kinematic model analysis. There was no difference between the results using the 10-min and 60-min precipitation data for all land use types.

Consequently, 60-min precipitation data are sufficient for practical estimation of agricultural land discharge. In addition, in residential lots, the effective precipitation was almost equal to the flood discharge.

Estimation of the peak discharge is very important for drainage planning. The peak runoff ratio and lag time (the time between peak precipitation and peak discharge t_{p}), are important parameters to determine the peak discharge. However, the estimation of lag time is very difficult because the hyetograph shows random variation i.e., not smooth variation.

The peak runoff ratio can be estimated in two ways. The first is the ratio Fp1 between the average effective precipitation intensity (r_{pe}) and the peak precipitation intensity (r_{p}) during the unit time (∆t) of the analysis (Fp1 = r_{pe}/r_{p}). The second is the ratio Fp2 between the average effective precipitation intensity (r_{pe}) and the average precipitation intensity (r_{ae}) during the lag time t_{p} (Fp2 = r_{pe}/r_{ae}). The average effective precipitation intensity (r_{pe}) is reciprocally determined using the rational formula [_{p} is estimated usually using observation data but not here. The t_{p} was relatively longer in paddy fields and upland crop fields, and shorter in residential lots. There was little difference between upland wheat fields and upland soybean fields.

Theoretically, the peak runoff ratio Fp2 is more appropriate for runoff analysis than Fp1. However, as shown in the left and center column in

Fp1 is more practical for the runoff analysis because the estimation of lag time tp is very difficult. However, since the relationship between Fp1 and Fp2 and peak precipitation is not smooth, which indicate that there are limitations of the use of peak discharge estimation for individual precipitation events. To accurately estimate potential flood discharge, actual precipitation data must be input into the runoff model. In addition, the maximum runoff intensity in upland crop fields is 32 mm∙h^{−1}. There is no overflow of levee because the depth is set as 102 mm at the outlet.

We proposed the unit flood discharge concept as a measure of flooding discharge potential to investigate the impact of urbanization on flooding and flood damage. First, a runoff model for paddy fields was proposed. This model differed from models proposed in previous research at that point actual and physical properties of the runoff sites were used. In other word, the previous research on runoff analysis of agricultural land is limited in to conceptual model rather than physical model, but the proposed model is basing on physical properties of agricultural land including depression storage. The discharge acts an important role for estimating regional flooding by big rainfall event and is roughly estimate of flood discharge associated with land use changes as urbanization.

Data on the area and shape of paddy fields, upland crop fields, and residential lots, the height of drainage outlets, and standing water before and after midsummer drainage were collected from 135 lots and used as input for the runoff model. The paddy field storage capacity was 40.3 mm before midsummer drainage and 58.5 mm after midsummer drainage. Percolation of 12.5 and 20.5 mm∙d^{−1}, respectively, was observed in paddy fields before and after midsummer drainage. Second, the runoff model as expressed in Equation (2) and Equation (3) was used to analyze 54 rainfall events using 74 years of rainfall data from the Kanazawa Metrological Observation Station. In addition, parameters such as the initial standing water depth and percolation rate were determined by observation at each survey site.

The relationship between total runoff ratio and total precipitation was relatively smooth. The ratio increased in the following order: irrigated paddy fields, non-irrigated paddy fields, upland wheat fields, upland soybean fields, and residential lots. The initial runoff from paddy fields was smaller than that from other land use types and the runoff from upland crop fields was larger for crops requiring furrows (e.g., soybean) than for those that did not require furrows (e.g., wheat). The total runoff ratio is very useful to estimate the impact of urbanization on total runoff.

Runoff analysis for agricultural land was conducted using 60-min and 10-min precipitation data. There was little difference between the results using the two data intervals. Therefore, the use of 60-min precipitation data is practical and there are abundant data available. For residential lots, kinematic wave analysis was compared with analysis based on 10-min precipitation data. There was little difference between the results of the two methods. Therefore, 10-min precipitation data can be used to directly estimate potential flood discharge in residential areas.

The relationship between peak runoff ratio and peak precipitation was not as smooth as the relationship between total runoff ratio and total precipitation. There was a difference between the peak runoff ratio calculated using 60-min precipitation data (Fp1) and the peak runoff ratio calculated using the lag time between peak precipitation and peak discharge (Fp2). For the runoff analysis, Fp2 is more theoretically appropriate. However, Fp1 is more practical because estimation of lag time is very difficult. The peak runoff ratio is very useful to estimate peak discharge from precipitation; in particular, the highest peak runoff ratio is useful to estimate the maximum potential flood discharge.

It was not possible to compare observed and estimated flood discharge in the present study. However, this study confirms the value of unit flood discharge to measure the potential for flooding and flood damage in areas with various land use types, and to assess the impact of urbanization on flooding.

We wish to thank the staff of Ishikawa Prefectural Government for providing valuable information and the students of the Prefectural University for help with the infiltration investigation.

Segawa, M., Maruyama, T. and Takase, K. (2016) Estimation of Unit Flood Discharge for Various Land Use Types with a Focus on Urbanization. Open Journal of Modern Hydrology, 6, 195- 211. http://dx.doi.org/10.4236/ojmh.2016.64016