Development of WEP Model and Its Application to an Urban Watershed

HYDROLOGICAL PROCESSES Hydrol. Process. 15, 2175–2194 (2001) DOI: 10.1002/hyp.275

Development of WEP model and its application to an urban watershed

Yangwen Jia,1* Guangheng Ni,1 Yoshihisa Kawahara2 and Tadashi Suetsugi3 1 Urban River Division, Public Works Research Institute (PWRI), Asahi, Tsukuba City 305-0804, Ibaraki Prefecture, Japan 2 Department of Safety Systems Construction Engineering, Kagawa University, Kagawa 761-0396, Japan 3 River Hydraulics Division, Public Works Research Institute, Tsukuba, Japan

Abstract: A distributed hydrological model, water and energy transfer processes (WEP) model, is developed to simulate spatially variable water and energy processes in watersheds with complex land covers. In the model, state variables include depression storage on land surfaces and canopies, soil moisture content, land surface temperature, groundwater tables and water stages in rivers, etc. The subgrid heterogeneity of land use is also taken into consideration by using the mosaic method. For hydrological processes, evapotranspiration is computed by the Penman–Monteith equation, infiltration excess during heavy rains is simulated by a generalized Green–Ampt model, whereas saturation excess during the remaining periods is obtained by doing balance analysis in unsaturated soil layers. A two-dimensional simulation of multilayered aquifers is performed for groundwater flow. Flow routing is conducted by using the kinematic wave method in a one-dimensional scheme. For energy processes, short-wave radiation is based on observation or deduced from sunshine duration, long-wave radiation is calculated according to temperatures, latent and sensible fluxes are computed by the aerodynamic method and surface temperature is solved by the force–restore method. In addition, anthropogenic components, e.g. water supply, groundwater lift, sewerage drainage and energy consumption, etc. are also taken into account. The model is applied to the Ebi River watershed (27 km2) with a grid size of 50 m and a time step of 1 h. The model is verified through comparisons of simulated river discharges, groundwater levels and land surface temperatures with the observed values. A comparison between water balance at present (1993) and that in the future (2035) is also conducted. It is found that the hydrological cycle in the future can be improved through the implementation of infiltration trenches for the storm water from urban canopies. Copyright  2001 John Wiley & Sons, Ltd.

KEY WORDS hydrological processes; energy processes; urbanization; distributed model

INTRODUCTION With the change of land surface and living styles in urban river watersheds, the hydrological cycle has been greatly changed and this change still continues or even accelerates in some watersheds. In urban rivers, discharges are increased and concentration times become shorter during ﬂood periods. On the other hand, discharges become much less and water quality deteriorates during dry seasons. In addition, the microclimate in urban areas is also changed, e.g. the urban heat island and dry weather phenomena become more and more evident. Ensuring sustainable developments in urban areas requires understanding the real situation of water and energy budgets in watersheds and taking systematic and effective countermeasures. Distributed physically-based hydrological models can take account of spatial variations of all variables and parameters involved in the basic mathematical equations of the water ﬂows for a watershed. In addition, the used parameters are physically measurable. Therefore, they give a detailed and potentially more correct description of the hydrological processes in the watershed than empirical and conceptual hydrological models.

* Correspondence to: Y. Jia, Hydrologic Engineering, Public Works Research Institute (PWRI), Minamihara 1–6, Tsukuba City 305-8516, Ibaraki Prefecture, Japan. E-mail: [email protected] Received 3 April 2000 Copyright  2001 John Wiley & Sons, Ltd. Accepted 18 August 2000 2176 Y. JIA ET AL.

With more available data, especially with the development of GIS and remote sensing technology, the study and application of these types of models will surely be promoted. Today, several popular models are of this type, such as SHE (Abbott et al., 1986), IHDM (Beven et al., 1987) and MIKE SHE (Refsgaard and Storm, 1995), etc. In this paper, the water and energy transfer processes (WEP) model developed at PWRI is described, which adds more detailed energy balance analysis in hydrological modelling. The model is based on Jia and Tamai (1998) and is improved by adding the simulation of multilayered aquifers, direct computation of groundwater outflow to rivers and simulation of infiltration trenches. The paper consists of two main parts: (1) model development and (2) its application to the Ebi River watershed. In the first part, a distributed and physically-based model is developed to explain spatially variable water and energy processes with complex land covers, which is not only applicable to natural watersheds but also applicable to urbanized watersheds. Evapotranspiration and latent heat flux are computed by combining the Penman–Monteith equation (Monteith, 1973) with the force–restore method (Hu and Islam, 1995) instead of the potential value method. More efficient and reasonable modelling of infiltration is also conducted by using a generalized Green–Ampt model (Jia and Tamai, 1997). In addition, the mosaic method (Avissar and Pielke, 1989) is used to consider the subgrid heterogeneity of land use. In the second part, the model is applied to simulate the hydrological cycle in the Ebi River watershed with a grid size of 50 m and a time step of 1 h. A 6-year simulation from 1992 to 1997 is performed. The model is verified through comparisons of simulated river discharges, groundwater levels and land surface temperatures with the observed values. The comparison of water balance at present (1993) with that in the future (2035) is also conducted and it shows the impact of urbanization. Finally, the effect of installing infiltration trenches is assessed. Although the WEP model simulates most of the hydrological processes by similar methods to the distributed physically-based models mentioned above, its main differences from those models are as follows. (1) The energy transfer processes are also simulated in detail in addition to hydrological processes. Because of its detailed consideration of heat flux partitions on land surface, the model not only enhances the computations of interception and evapotranspiration, but also is easy to couple to atmospheric models. (2) The subgrid heterogeneity of land use is considered by using the mosaic method, which is believed to be more reasonable than the usual dominant land use method, especially in urbanized areas with complex land covers. (3) The generalized Green–Ampt model is developed to simulate infiltration and infiltration excess during heavy rains to save computation time. (4) The infiltration trenches are simulated in the model, which makes it possible to evaluate their effect on the hydrological cycle.

MODEL DEVELOPMENT Model structure The diagram of the model structure within a grid cell utilized in this study is shown in Figure 1a. To consider the subgrid heterogeneity of land use, the mosaic method is used which reflects composition of different land uses within a grid cell. The areal average of water and heat fluxes from all land uses in a grid cell produces the averaged fluxes in the grid cell. Land use is at first divided into three groups, namely a water body group, a soil–vegetation group and an impervious area group. The soil–vegetation group is further classified into bare soil, tall vegetation (forest or urban trees) and short vegetation (grass or crops). The impervious area group consists of impervious urban cover and urban canopy. For the soil–vegetation group, nine vertical layers, namely an interception layer, a depression layer, three upper soil layers, a transition layer, an unconfined aquifer and two confined aquifers, are included in the model structure. The energy balance of each land use is also analysed. The interaction of radiation between soil and vegetation is considered by use of the fraction of transmitted short-wave radiation of vegetation, whereas the interaction between urban cover and urban canopy is considered by using the sky view factor of urban cover.

(a)

Precipitation Shortwave Longwave radiation radiation

Water Body Soil-Vegetation Impervious Group Group Area Group Anthropogenic Interception Transpiration energy source Layer heat Surface Depression fluxes runoff τ Layer Top Soil Layer Evaporation Suction Water use heat diffusion Infiltration 2nd Soil Layer leakage Pumped

fluxes runoff ground

Subsurface 3rd Soil Layer water Recharge Transition Layer Exchange by Flow Unconfined Aquifer Flow in seepage or out outflow Aquitard 1 Flow in Confined Aquifer 1 Percolation 1 Flow out Aquitard 2 Flow in Percolation 2 Flow Confined Aquifer 2 out (b) Multi-layered Groundwater Flow 1D River Flow

j+1

j Lateral inflow j−1 Sub-Watershed

Tributary

Main River

i−1i i+1

Figure 1. The structure of the proposed model : (a) vertical structure within a grid cell and (b) horizontal structure

The diagram of the model horizontal structure within a watershed is shown in Figure 1b. River flow routing is conducted for every tributary and a main river by using the kinematic wave method. Overland flow is simplified as lateral inflow to rivers because the concentration time is estimated to be shorter than the simulation time interval in this study. In addition, a two-dimensional simulation of multilayered aquifers, i.e. quasi-3D simulation, is performed for groundwater flow.

Hydrological processes Evapotranspiration. Evapotranspiration in a grid cell consists of interception of vegetation canopies (evaporation from the wet part of leaves), evaporation from water body, soil, urban cover and urban canopy and transpiration from the dry fraction of leaves with the source from the three soil layers. The averaged evapotranspiration E is expressed as:

E D FWEW C FSVESV C FUEU 1 where FW,FSV and FU are the area fractions of water body, soil–vegetation and impervious area respectively, EW,ESV and EU the evaporation or evapotranspiration from them respectively. The evaporation from the water body group is calculated with the Penman equation: RN G C C υ /r E D a p e a 2 W  C where RN is the net radiation, G the heat conduction,  the gradient of saturated vapour pressure to temperature, υe the air vapour pressure deﬁcit, ra the aerodynamic resistance, a the air density, Cp the air speciﬁc heat, the latent heat of water and the psychometric constant. The evaporation from the impervious area group is taken as the smaller one of current depression storage and the potential evaporation (also calculated with the Penman equation). The maximum depression storage of impervious area is assumed as 2 mm in this study. The evapotranspiration from the soil–vegetation group is calculated as follows:

ESV D Ei1 C Ei2 C Etr1 C Etr2 C Es 3 where Ei is the interception of vegetation, Etr the transpiration from the dry part of vegetation leaves with numbers 1 and 2 representing tall vegetation and short vegetation respectively and Es the evaporation from soils. The computation of interception is referred to as the following model (Noilhan and Planton, 1989):

Ei D Veg Ð υ Ð Ev 4 ∂W /∂t D Veg Ð P E R 5 r i r 0Wr Ä Wrmax Rr D 6 Wr Wrmax Wr > Wrmax 2Ð3 υ D Wr/Wrmax ;Wrmax D 0Ð2Veg Ð LAI 7 where Veg is the fraction of tall (or short) vegetation in the soil–vegetation group, υ the fraction coefﬁcient of the foliage covered by a water ﬁlm, Ev the potential evaporation on vegetation surface, Wr the storage of the interception reservoir, Wrmax the maximum Wr (mm), P the precipitation, Rr the drainage rate from the canopy when Wr exceeds Wrmax and LAI the leaf area index. The transpiration is expressed as:

Etr D Veg Ð 1 υ Ð EPM 8

RN G C aCpυe/ra EPM D 9 [ C 1 C rc/ra]

where EPM is the Penman–Monteith transpiration (Monteith, 1973), rc the canopy resistance and the others as denoted above. The transpiration is actually supplied from soil layers by roots. A root uptake model is adopted which assumes that the root uptake intensity linearly decreases with the increase of root depth and the uptake in the upper half root zone accounts for 70% of the total uptake. The transpiration of tall vegetation is assumed to originate from the three upper soil layers in Figure 1 while that of short vegetation from only the two upper ones. The aerodynamic resistance ra under neutral atmospheric conditions can be represented as follows (Monteith, 1973): n[z d/z ] Ð n[z d/z ] r D om ox 9a a Ä2U where z is the measurement height of wind speed, humidity and temperature, Ä the von Karman constant, U the wind speed, d the displacement height, zom the roughness height of momentum, and zox D zom for momentum transfer, zov (the roughness height of vapour) for vapour transfer or zoh (the roughness height of heat) for heat transfer respectively. The Monin–Obukhov similarity theory is used to modify the computation of aerodynamic resistance (Brutsaert, 1982) under unstable and stable atmospheric conditions. The canopy resistance rc is also called the surface resistance. Noilhan and Planton (1989) are followed to calculate it. It is a summation of the contributions of stomatal resistance of individual leaves: r r D sminf Tf VPDf PARf Â 9b c LAI 1 2 3 4 where rsmin is the canopy minimum stomatal resistance, LAI the canopy leaf area index, f1 the dependence on the air temperature T, f2 the dependence on the vapour pressure deficit (VPD) of the air, f3 the influence of the photosynthetically active radiation flux (PAR) and f4 the effect of the soil moisture content Â. Evaporation from soils is assumed to come only from the top layer. It is usually estimated by multiplying the potential evaporation (based on the Penman equation) with an evaporation coefficient, which is called the potential method hereafter. However, the potential method may cause theoretical nonconsistency of heat flux partition on soil surface because the net radiation and soil heat flux corresponding to the saturated vapour pressure of soil are used in the Penman equation while the actual soil may be unsaturated. Based on the energy balance on the soil surface, aerodynamic diffusion equations of latent and sensible heat fluxes and the wetness function concept, we derived the following modified Penman equation to compute actual soil evaporation directly: RN G C C υ /r E D a p e a 10 s  C /ˇ where ˇ is the wetness function and the other notations are the same as mentioned above. The wetness function is defined as in Equation (10a) (Lee and Pielke, 1992) and it is estimated by Equation (10b), which is a modified version of Lee and Pielke’s ˇ-equation:

ˇ D [eTs eTa]/[esTs eTa] 10a 0 Â Ä Âm 1 2 ˇ D 4 [1 cos Â Âm/Âfc Âm] Âm <Â<Âfc 10b 1 Â ½ Âfc where eTs is the surface vapour pressure, esTs the saturated surface vapour pressure, eTa the air vapour pressure, Ts the surface temperature, Ta the air temperature, Â is the volumetric soil moisture content, Âfc the ﬁeld capacity of the top soil layer and Âm the moisture content correspondent to the monomolecular suction. The difference between Equation (10b) and the Lee and Pielke’s ˇ-equation is that Âm terms are added here. Âm should be considered because soil evaporation cannot continue when the soil suction becomes equal to

θ θ initial value o saturated value s moisture content q

L1 F1 1st layer t1

L2 F2 2nd layer t2

− Lm−1 Fm−1 (m 1) th layer tm−1

Fp tp Lm m-th layer wetting front

depth L

Figure 2. The diagram of inﬁltration into multilayered soil proﬁle or larger than the monomolecular suction (pF 6Ð0–7Ð0). The Kanto loam’s Âm is about 0Ð111 according to Nakaegawa (1996).

Infiltration. Considering infiltration into a vertical uniform soil column when the surface is ponded, Green and Ampt proposed an infiltration model by assuming there is a wetting front which separates saturated soil above from soil below and by using Darcy’s law. Compared with the other infiltration models, the Green–Ampt model has the advantages of simplicity, physically-based characteristics and measurable parameters. Mein and Larson (1973) extended it to model infiltration into uniform soil during a steady rain and Moore and Eigel (1981) extended it to model infiltration into two-layered soil profiles during steady rains. Moreover, Jia and Tamai (1997) suggested a generalized Green–Ampt model for infiltration into multilayered soil profiles during unsteady rains. The generalized Green–Ampt model is summarized as follows. Supposing that the wetting front is in the mth soil layer (see Figure 2), the infiltration rate can be expressed in the following equation: Am1 f D km Ð 1 C 11 Bm1 C F where f is the infiltration rate, F the accumulated infiltration and the others are described later. The calculation of accumulated infiltration includes two cases. The accumulated infiltration is calculated in Equation (12) if the surface ponding occurs with the wetting front at the m 1th layer and continues since then: Am1 C Bm1 C F F Fm1 D kmt tm1 C Am1 Ð n 12 Am1 C Bm1 C Fm1 whereas it is calculated using Equation (13) if the surface ponding begins at the present time step tn with no ponding at the last time step t : n1 Am1 C Bm1 C F F Fp D kmt tp C Am1 Ð n 13 Am1 C Bm1 C Fp

Fp Fn1 Fp Fn1 D Iptp tn1;tp D tn1 C 14 Ip

m1 m1 Am1 D Li Likm/ki C SWm Âm 15 1 1 m1 m1 m1 Bm1 D Likm/ki Âm LiÂi;Fm1 D LiÂi 16 1 1 1 where SW is the capillary suction at the wetting front, k the hydraulic conductivity in the wetted zone, Âs the moisture content in the wetted zone, Â0 the initial moisture content, t the time, Fp the accumulated inﬁltration at the instant of surface ponding, tp the time to surface ponding, Ip the rain intensity during the nth time step when surface ponding occurs, tm1 the time when the wetting front reached the interface of mth and m 1th, L the depth of wetting front, Li the thickness of the ith soil layer and Â D Âs Â0.

Surface runoff. In the water body group, surface runoff is estimated as precipitation minus evaporation. In the impervious area group, surface runoff can be obtained by doing balance analysis of depression storage, precipitation and evaporation on land surfaces. It is assumed that there is no infiltration in these two groups. In the soil–vegetation group, surface runoff consists of two parts, namely the infiltration excess (Hortan- type runoff) during heavy rainfall periods and the saturation excess (Dunne-type runoff) during the other periods. A heavy rainfall period is defined as a period during which the rainfall intensity is larger than the saturated soil hydraulic conductivity. The infiltration excess R1ie is solved by applying the generalized Green–Ampt model to infiltration in three soil layers during heavy rainfall periods. The equations to compute the infiltration excess are as follows:

∂Hs D P E0 f R1ie 17 ∂t 0Hs Ä Hsmax R1ie D 18 Hs Hsmax Hs > Hsmax where Hs is the depression storage on soil surface, Hsmax the maximum depression storage (set as 15 mm for paddy and 5 mm for other pervious land in this study), P the rainfall, E0 the evaporation, f the inﬁltration rate calculated with Equation (11). In Equation (17), the gradual variation of R1ie after Hs > Hsmax is neglected because a time step of 1 h is adopted in this study, which is believed to be long enough to justify the approximation. In addition, the interception storage of vegetation is assumed to be full, E0 equals the potential evaporation and transpiration is neglected during heavy rainfall periods. The saturation excess R1se during the left periods may occur if the groundwater level in the unconﬁned aquifer rises and the top soil layer becomes nearly saturated. It can be deduced by doing balance analysis in every soil layer (the Richards model) as follows:

(1) Depression storage layer

∂H /∂t D P1 Veg Veg C Veg Ð R C Veg Ð R E Q R1 19 s 1 2 1 r1 2 r2 0 0 se 0Hs Ä Hsmax R1se D 20 Hs Hsmax Hs > Hsmax (2) Top soil layer ∂Â1 1 D Q0 C QD12 Q1 R21 E1 Etr11 Etr2121 ∂t d1 (3) Second soil layer ∂Â2 1 D Q1 C QD23 QD12 Q2 R22 Etr12 Etr2222 ∂t d2

(4) Third soil layer

∂Â3 1 D Q2 QD23 Q3 Etr1323 ∂t d3

Qj D kjÂjj D 1, 2, 324

E0 D minfEp,Hs C PinEp/Ep C Qpg;E1 D Es E0;Pin D P1 Veg 1 Veg 2

C Veg 1Rr1 C Veg 2Rr225

Q0 D minfQp,Hs C PinQp/Ep C Qpg;Qp D minfk1Âs, Q0maxg;Q0max D W1max

W10 Q1 26

jÂj jC1ÂjC1 dj Ł kjÂj C djC1 Ł kjC1ÂjC1 QDj,jC1 D kj,jC1 Ð ;kj,jC1 D j D 1, 227 dj C djC1/2 dj C djC1

In the above equations, Hs is the depression storage on soil surface, Hsmax the maximum Hs,Veg1 and Veg 2 the fraction of tall and short vegetation respectively, Rr1 and Rr2 the drainage rate from tall and short vegetation respectively, Q the gravity drainage, QDj,jC1 the suction diffusion from the j C 1th soil layer to the jth layer, E0 and E1 the evaporation from the depression storage layer and top soil layer respectively, Etr the transpiration with the ﬁrst subscript representing vegetation type (1 D tall vegetation and 2 D short vegetation) and the second one representing soil layer, R2 the subsurface runoff, Â the moisture content, Âs the saturated moisture content, kÂ the hydraulic conductivity correspondent to Â, Â the soil suction correspondent to Â, d the thickness of the soil layer, W D Âd the water storage of the soil layer, W10 the initial water storage of the top soil layer and the other notations are the same as mentioned above. Except where especially mentioned, the numbers or subscripts of all variables mean layer numbers with 0, 1, 2 and 3 representing depression storage layer, top soil layer, second soil layer and third soil layer respectively. The continuity of water movement is considered when the application of the generalized Green–Ampt model [Equations (11)–(18)] is switched into that of the Richards model [Equations (19)–(27)] and vice versa. When the application of the generalized Green–Ampt model is switched into that of the Richards model, the initial moisture contents of three unsaturated soil layers for the Richards model are computed based on the depth of the wetting front from the generalized Green–Ampt model. However, when the application of the Richards model is switched into that of the generalized Green–Ampt model, the moisture contents of the three soil layers from the Richards model provide initial values for the generalized Green–Ampt model and no special treatment is required. It should be mentioned that there are some approximations in the application of the generalized Green–Ampt model. Though heat ﬂux partition and surface temperature solution are also carried out, soil evaporation, canopy transpiration and the redistribution of soil moisture below the wetting front are neglected. It is believed that these factors can be neglected during heavy rainfalls.

Subsurface runoff. The subsurface runoff is calculated according to the land slope and the soil hydraulic conductivity: R2 D kÂ sinslope d 28 where R2 is the subsurface runoff from the unsaturated soil layers, is the channel length in the grid and others as denoted above.

Groundwater flow and groundwater outflow. Taking account of the recharge from unsaturated soil layers and lifted groundwater as source terms, a quasi-3D simulation is performed for groundwater flow to consider the

Copyright  2001 John Wiley & Sons, Ltd. Hydrol. Process. 15, 2175–2194 (2001) DEVELOPMENT OF WEP 2183 interactions between surface water and groundwater by using the following Boussinesq equations (Zaradny, 1993): ∂h ∂ ∂h ∂ ∂h unconfined aquifer : C u D k h u C k h u C Q C WUL RG Per E29 u ∂t ∂x u u ∂x ∂y u u ∂y 3 ∂h ∂ ∂h ∂ ∂h confined aquifers : C D kD C kD C Per GWP Perc30 ∂t ∂x ∂x ∂y ∂y where Cu is the specific yield, C the storage coefficient, hu and h the groundwater heads in the unconfined aquifer and confined aquifers respectively, ku and k the hydraulic conductivities of the unconfined aquifer and confined aquifers respectively, D the thickness of confined aquifers, Q3 the recharge from unsaturated soil layers, RG the groundwater outflow to rivers, WUL the water use leakage, GWP the pumped groundwater, Per and Perc the percolation to the aquifer below and E the evapotranspiration from groundwater when the unconfined groundwater level rises above the third soil layer in Figure 1a. E D FSVEtr13 if hu rises to the third soil layer, E D FSVEtr12 C Etr13 C Etr22 if hu rises to the second soil layer or E D FSVEs C Etr11 C Etr12 C Etr13 C Etr21 C Etr22 if hu rises to the top soil layer with the notations as described above. Groundwater outflow is calculated according to the hydraulic conductivity kb of riverbed material and the difference between river water stage Hr and groundwater level hu: kbAbhu Hr/db hu ½ Hr RG D 31 kbAb[1 C Hr Zb/db]hu < Hr where Ab is the seepage area of the riverbed, Zb the elevation of the riverbed and db is the thickness of the riverbed material.

River ﬂow. The river ﬂow is routed for every subwatershed and a main channel by using the kinematic wave method:

∂A ∂Q C D q 32 ∂t ∂x L A Q D R2/3S1/2 33 n 0 where A is the area of lateral section, Q the discharge, qL the lateral inﬂow of unit channel length, n the Manning roughness, R the hydraulic radius, S0 the longitudinal slope of the river bed. In addition, qL D [R1 C R2 C RG C RsewDxDy]/L, where denotes summation of all grids in the subwatershed, Rsew the sewerage in a grid of the subwatershed, Dx,Dy the grid size in x and y directions, L the channel length and the others as mentioned before.

Anthropogenic components. The water use in every grid is deduced by using population and water use per capita. The water use per capita is decided according to statistics of water use in a watershed. In addition, water use leakage is deduced from water use and the leakage rate of water supply system. The sewerage is equal to water use subtracted by leakage. It is set as one part of the lateral inﬂow to the channel because the coverage rate of the combined sewer system is as low as 10% in the study watershed. The groundwater lift has twofold utilization, the drinking water and the irrigation water. The drinking water is calculated according to the annual drinking water lift and the population distribution. The irrigation water is calculated based on the annual lift, paddy area and irrigation period.

The inﬁltration trenches are simulated using the following equations (Herath, 1994):

∂St/∂t D Qin Qinf Qovf 34

St D nLWH 35

Qinf D K0LaH C b36 3/2 Qovf D cLH Hm 37 where St is the storage in infiltration trenches, Qin the inflow discharge, Qinf the infiltration, Qovf the overflow, n the porosity of filled material in the trench, L the length of infiltration trenches, W the width, H the depth, Hm the maximum design depth, K0 the saturated hydraulic conductivity of the soil below the trench, a, b and c the constants. In addition, Qin D R1 Ð A with A denoting the control area of the infiltration trench, the recharge to unconfined aquifer Q3 is changed to Qinf/A and the surface runoff to Qovf/A. If infiltration trenches are installed only for the storm water from urban canopies, A D Fu1 FrDxDy where Fr is the fraction of urban cover in the impervious area of a grid and the others as mentioned before.

Energy processes

Energy balance on land surface. The energy balance equation on land surface is expressed as:

RN C Ae D E C H C G 38 RN D RSN C RLN 39 where RN is the net radiation, Ae the anthropogenic energy source, E the latent heat ﬂux, H the sensible heat ﬂux, G the heat conduction into soil, RSN the net short-wave radiation and RLN the net long-wave radiation.

Short-wave radiation. If there is no direct observation of the incoming short-wave radiation it can be estimated from the sunshine hours. Shimazaki (1996) is referred to in order to deduce the hourly incoming short-wave radiation from the sunshine data in this study. It at ﬁrst deduces the direct short-wave radiation and the diffusion short-wave radiation based on the sunshine levels in current and prior hours, and then adds them up to obtain the total short-wave radiation after considering the solar zenith angle. The equations are as follows:

RS D IcosÂ C S 40 I/I D 0Ð0011N C 0Ð0482N C 0Ð0021N N 41 max p c c p 2 0Ð5517 C 0Ð0482Nc 0Ð0056Nc Nc > 0 S/Smax D 42 0Ð267 Nc D 0 where RS is the incoming short-wave radiation, I the direct short-wave radiation, Imax the maximum direct short-wave radiation on clear days, Â the solar zenith angle, S the diffusion short-wave radiation, Smax the maximum diffusion short-wave radiation, Nc the sunshine level (0–10) in the current hour and Np the sunshine level in the prior hour. The maximum direct short-wave radiation and the maximum diffusion short-wave radiation depend on the Julian day number and the solar zenith angle, whereas the solar zenith angle depends on the latitude of the observation site, the solar temporal angle, and the Julian day number. The related equations are neglected here. The net short-wave radiation on each land use is as follows after considering the albedo and the sheltering factors.

(1) Water body RSNw D RS 1 ˛w43 (2) Soil–vegetation group

soil: RSNs D RS1 ˛sFsoil C 1 Ð Veg 1 C 2 Ð Veg 244

tall vegetation: RSNv1 D RS1 ˛v1Veg 1 RS1 ˛s1 Ð Veg 1 45

short vegetation: RSNv2 D RS1 ˛v2Veg 2 RS1 ˛s2 Ð Veg 2 46 1 D exp0Ð5LAI12 D exp0Ð5LAI247 (3) Impervious group

urban cover: RSNu1 D RS1 ˛u1Frˇ48

urban canopy: RSNu2 D RS1 ˛u21 Frˇ 49 where RSN is the net short-wave radiation, ˛ the albedo, 1 the transmission of short-wave radiation of tall vegetation, 2 the transmission of short-wave radiation of short vegetation, Fsoil,Veg1 and Veg2 the area fractions of bare soil, tall vegetation and short vegetation in the soil–vegetation group respectively, LAI the leaf area index, Fr the area fraction of urban cover in the impervious area group, ˇ the sky view factor of urban cover. Subscripts w, s, v1, v2, u1and u2 denote water body, bare soil, tall vegetation, short vegetation, urban cover and urban canopy respectively. The sky view factor of urban cover is referred to Kawamata (1994). Except where the albedo of water body is set as 0Ð08, those of other land uses are related to solar zenith angle, soil moisture content or canopy heights.

Long-wave radiation. The long-wave radiation is calculated by using the following equations (Kondo,1994):

4 RLD D [1 1 εacFc]Ta C 273Ð2 50 4 RLU D 0Ð98Ts C 273Ð2 51 4 2 εac D 1 0Ð261 exp7Ð77 ð 10 Ð Ta52 3 2 Fc D 0Ð826Nc 1Ð234Nc C 1Ð135Nc C 0Ð298 53 where RLN is the net long-wave radiation, RLD the downward long-wave radiation from atmosphere to landsurface, RLU the upward long-wave radiation from landsurface to atmosphere, Fc the cloudiness factor, the Stefan–Boltzmann constant, εac the atmosphere emmisivity on clear days, Nc the sunshine level (0–10) in the current hour, Ta the air temperature and Ts the landsurface temperature. Net long-wave radiation is equal to the downward long-wave radiation subtracted by the upward one. Its expression for each land use is as follows:

(1) Water body RLNw D RLD RLUw 54 (2) soil–vegetation group

soil: RLNs D RLD RLUsFsoil C RLUv1 RLUsVeg 1 C RLUv2 RLUsVeg 2 55

tall vegetation: RLNv1 D RLD C RLUs 2RLUv1Veg 1 56

short vegetation: RLNv2 D RLD C RLUs 2RLUv2Veg 2 57

(3) Impervious group

urban cover: RLNu1 D [RLDˇ RLUu1 C RLUu21 ˇ]Fr 58

urban canopy: RLNu2 D RLD1 Frˇ RLUu2[1 Fr C 2Fr1 ˇ] C RLUu1Fr1 ˇ 59 where the notations are the same as described above.

Antropogenic energy consumption. Statistic energy consumption indices on various types of urban land use are used to consider the impact of human activities on energy balance in an urban area (Kawamata,1994). Half of the energy consumption is assumed to emit to land surfaces and the other half to the air.

Latent heat ﬂux. In the hydrological processes part, the computation of evapotranspiration has been described in detail. The latent heat ﬂux E and the evapotranspiration E have the following relation:

E D Ð E 60 where is the latent heat of the water.

Sensible heat ﬂux. The sensible heat ﬂux H depends on the aerodynamic resistance and the temperature difference between the air and the land surface, and can be expressed as:

H D aCpTs T/ra 61 where a is the density of the air, Cp the speciﬁc heat of the air, T the air temperature, Ts the surface temperature and ra the aerodynamic resistance.

Heat conduction into soil. Based on the energy balance equation we get:

G D RN C Ae E C H62

Surface temperature. The force–restore method (FRM) is used to solve the surface temperature of different land covers. This method is a better approximation to the classical heat diffusion equation compared with other methods. Hu and Islam (1995) suggested an optimal parameter ˛, which cannot only ensure minimum distortion of FRM to sinusoidal diurnal forcing but also makes distortion to higher harmonics negligible. They are followed in this research with the equations as follows:

∂Ts 2 ˛ D G ωTs Td63 ∂t ch Ð d0 ∂T 1 d D T T 64 ∂t s d υ υ 2 3 4 ˛ D 1 C 0Ð943 C 0Ð223 C 0Ð0168 υ 0Ð00527 υ 65 d d d0 d0 0 0 d0 D 2kh/chω 66 where G is the heat conduction into soil, Ts the surface temperature, Td the deep soil temperature (approximated as the daily average of Ts), υ the considered soil depth (selected as the thickness of top soil layer), d0 the damping depth of the diurnal temperature wave, kh the soil heat conductivity, ch the soil volumetric heat capacity, ω D 2/ and D 86400. The soil thermal properties depend on the water content and the mineral

composition of the soil. The soil heat capacity ch and the soil heat conductivity kh are referred to Kondo (1994).

APPLICATION Study area and input data The map of the Ebi River watershed is shown in Figure 3. It is located in the Funabashi and Kamagaya Cities, Chiba Prefecture, Japan. It is one of the pilot watersheds set by the Ministry of Construction to study hydrological cycles in detail. It has an area of 27 km2. There are six rain gauges within or near the watershed, one of which is the Funabashi AMeDAS station with observations of temperature, wind and sunshine besides precipitation. The annual average precipitation over the past 10 years is 1360 mm. The Thiessen method, namely the nearest gauge station method, is used to estimate the meteorological data for each grid. In addition, there are two gauges of river water stage and discharge, one of which is the Yasakaebashi station of the Ebi main river and another is the Ichiba station of the Maehara tributary. The land use and elevation data are based on the Fine Digital Information System (FDIS). The watershed is adjacent to Tokyo Bay and the land elevations are quite low (0–33 m). There are four kinds of soils (see Figure 4) considered in the study, the dominant ones being Kanto loam and alluvial soil. The geological boring data indicates that the aquifers in the watershed have a multilayered structure. The boundary of groundwater ﬂow is a little larger than the watershed boundary according to the measurement of groundwater levels as shown in Figure 3.

Rain Gauge

W2 Discharge Gauge Nichida Groundwater Gauge Ground Catchment Boundary Kitayatsu River River W4 Groundwater Nenda Boundary AMeDAS River Takane Funobashi River W3 Nagatsu Miyamae River River Hasama River Yasakae -bashi Ichiba Maehara River W1 N Ebi River W E

2 0 2 4 km

Figure 3. The map of the Ebi River watershed

Alluvial soil

Kanto loam

Joso clay

Narita sand

No data

2 0 2 4 km

Figure 4. The classiﬁcation of surface soils

The distributions of land use at present and in the future are shown in Figure 5. According to the prediction by the local government, forest, paddy or drought farmland of about 5Ð7km2 will be developed for housing areas from 1993 to 2035, the population will reach 261 000 from 203 000 and the coverage rate of the sewer system will attain 100% from 10% (in population).

Model parameters Many parameters are used in the model. The setting of main parameters is summarized as follows.

(a) (b)

Forest Paddy Dry crops Idle/Park Industrial Residential River/Pond

Figure 5. The distributions of land use: (a) at present (1993) and (b) in the future (2035)

Soil parameters and aquifer parameters are shown in Tables I and II respectively. The soil parameters are referred to Herath et al. (1992) who conducted on-site borehole tests for representative soils within or near the watershed. In addition, the depths of top, second and third soil layers in the model are set as 0Ð2m,0Ð4m and 1Ð4 m respectively considering the variation characteristic of soil moisture, the distribution of vegetation roots and the damping depth of diurnal temperature wave in the watershed. Aquifer parameters are based on geological investigations in the watershed, although there are some adjustments after model calibration. Vegetation parameters are species-dependent and referred to Wilson et al. (1987), etc. Their seasonal variations are considered in this study according to the growing characteristics of trees and crops in the watershed. Furthermore, the area fractions of land use classiﬁcation are speciﬁed through sample analysis using a large-scale residential map. The aerodynamic and thermal parameters of land covers are referred to Kondo (1994).

Table I. The soil parameters

Parameter Kanto loam Joso clay Narita sand Alluvial soil

Saturated moisture content Âs 0Ð772 0Ð394 0Ð400 0Ð707 Residual moisture content Âr 0Ð589 0Ð120 0Ð077 0Ð598 Field capacity Âf 0Ð676 0Ð384 0Ð174 0Ð622 6 7 4 6 Saturated hydraulic conductivity ks (m/s) 5Ð0 ð 10 5Ð0 ð 10 2Ð0 ð 10 3Ð0 ð 10

Table II. The aquifer parameters

Parameter Unconfined Aquitard 1 Confined Aquitard 2 Confined aquifer aquifer 1 aquifer 2

Hydraulic conductivity (m/s) 5Ð0 ð 106 1–10 ð 108 5Ð0 ð 106 2Ð0 ð 109 5Ð0 ð 106 Speciﬁc yield/speciﬁc0Ð01–0Ð1 — 5Ð0 ð 104 — 5Ð0 ð 104 storage (1/m) Thickness (m) 2Ð0–16Ð72Ð0–7Ð880Ð6–96Ð010Ð0 391–424

1000 0

100 30 Rain (AMeDAS) Simulated Observed /s) 3 10 60

1 90 Rain (mm) Discharge (m 0.1 120

0.01 150 1 169 337 505 673 841 1009

Hours from Aug.17 1:00 AM, 1994 Figure 6. Hourly discharges at the Yasakaebashi station of the Ebi River

Calibration and veriﬁcation The model is warmed up by using the data in 1992 and calibrated by using the data in 1993. Figure 6 shows the comparison of hourly discharges at the Yasakaebashi station, which is located at the middle reach of the Ebi River and has a control area of 8Ð3km2. It can be seen that the simulated discharges show overall agreement with the observed ones. Since the daily-averaged sewerage is used in the application, the simulated result does not capture diurnal variations during periods of low ﬂow.

12 0

9 50

6 Rain Observed Simulated 100 Daily rain (mm)

Groundwater level (m) 3 150

0 200 1995/1/1 1995/5/1 1995/8/29 1995/12/27 1996/4/25 1996/8/23 1996/12/21 Figure 7. Groundwater levels at the W1 well

simulated 20W2 observed 18 16 well 14 catchment 12 18W4 boundary groundwater boundary 10

8 W3 22

24 6 20 18 4 16 20 14 98

W1 12 2 10 8 6 4 N 0 2 WE

8 S

Figure 8. Contour lines of groundwater levels on 25 January 1996 (Unit: m)

Figure 7 shows the comparison of simulated groundwater level with the observed one at the W1 well (its position is referred to in Figure 8). It can be seen that the variation patterns are almost the same. Here the groundwater level is the elevation above the sea level of the Tokyo Bay. Contour lines of groundwater levels in the watershed are shown in Figure 8. The simulated result of the top conﬁned aquifer is compared with the measurement at 112 private wells in the winter of 1996. Though there are obvious differences between them, the distribution patterns are similar, namely the groundwater level becomes lower from the upstream area to the downstream area (refer to Figure 3 at the same time). The net radiation on land surface is depicted in Figure 9. The surface temperature at the Nichidai Ground (its position is referred to in Figure 3) is shown in Figure 10. From these ﬁgures it can be seen that the simulated results generally have good matches with the observed ones.

Impact of urbanization and effect of infiltration trenches The comparison of water balance at present with that in the future in the whole watershed is shown in Figure 11a and b. The land use and population data in 1993 are used in the simulation of water balance at present, whereas those data predicted for 2035 are used for that in the future. The land use and population data for 2035 are prepared based on the urban development plan and the population density control plan of Chiba Prefecture as well as the data in 1993. The meteorological data in 1993 are used for both cases. It can be seen that with further urbanization in the future, evapotranspiration will decrease by 90 mm, infiltration lessen by 97 mm and groundwater outflow be reduced by 21 mm. On the other hand, surface runoff will increase by 140 mm. In the case where separate sewer systems are installed and the treated sewage drains directly into the sea, a great change in the river flow is predicted, namely the river base flow will decrease to 178 mm (the value within brackets in the figure), which means a deterioration in the water environment.

600 ) 2 500 Observed Simulated 400 300 200 100

Net radiation (W/m 0 −100 1 25 49 73 97 121 145 169 193 Hours from Jan. 1st 1:00 AM, 1997 Figure 9. Net radiation on land surface at the Nichidai Ground

C) 30 ° Simulated (top layer averaged) Observed (3cm below surface) 25 20 15 10 5 0 Soil temperature ( −5 1 25 49 73 97 121 145 169 193 217 Hours from Nov.26 1:00 AM, 1997 Figure 10. Surface temperature at the Nichidai Ground

(a) (b)

Precipitation Evapotranspiration Precipitation Evapotranspiration

1463 Diversion Diversion 1463 471 59 381 Water Water 36 supply Drainage supply Drainage Impervious 79 47 Pervious Paddy Impervious Pervious Paddy 811 area area 1048 area Fast % 121 Surface Fast area 75 Surface 46.7 64.5% flow run off flow runoff 779 919 579 779 797 919 Sewerage 332 235 Sewerage 1019 34 792 44 Treat- Infiltration Infiltration ment Leakage Leakage

Unsaturated soils Unsaturated soils Inter flow Inter flow Base Recharge 3 Base Recharge 2

277 flow 363 flow Flow Flow 1197 Unconfined aquifer 992 Unconfined aquifer in Groundwater in Groundwater (178)

0 River discharge 2116 (1112)

River discharge 1771 1 outflow

96 outflow

Recharge 72 Recharge Lift 15

Lift 41 176 Lift 15 197 Lift 25 Flow Flow Confined aquifer 1 Confined aquifer 1 in in 16 Recharge 19

40 Recharge 38 Lift 19 Lift 11 Confined aquifer 2 Confined aquifer 2

Diversion 1463 388 Water 36 supply Drainage Impervious Pervious Paddy 47 1048 area area Fast 75 Surface 64.5% flow runoff 727 Infiltration 605 trench 727 Sewerage 235 185 1019 44 Treat- Infiltration Artifical

Infiltration ment Leakage

Unsaturated soils Inter flow Recharge 2

462 Base flow Flow Unconfined aquifer 1222 in Groundwater 1 outflow River discharge 1949 82 Recharge 201 Flow Lift 15 Lift 25 Confined aquifer 1 in 17 Recharge 43 Lift 11 Confined aquifer 2

Figure 11. Water balances in the whole wathershed: (a) at present, (b) in the future without inﬁltration trenches and (c) in the future with inﬁltration trenches

In the case without a sewer system, though the river base flow can increase from 992 mm to 1197 mm, the water environment will also deteriorate because the sewage will account for 85% of the base flow. Therefore, to conserve the hydrological cycle and the water environment, infiltration facilities, sewer systems and wastewater treatment plants should be installed, and the treated wastewater should be drained back into local rivers.

10 0

8 10 /s) 3 Rain Present 6 20 Future without trench Future with trench 4 30

2 40 Rain(mm/hour) Discharge (m

0 50 1 25 49 73 97 121 145 Hours from June 1st 1:00 AM, 1993 Figure 12. Comparison of river discharges at the Yesakaebashi station of the Ebi River

The installation effect of infiltration trenches for the storm water from urban canopies (building roofs) is studied by using the present model. The guideline promulgated by the Japan Association for Rainwater Storage and Infiltration Technology is followed to make a layout and design scheme of infiltration trenches. It is required that the land slope should be lower than 10%, the soil should not be clay, the ground water table should be 2 m or more below the land surface and the trench density should be less than 450 m/ha, etc. In the Ebi River watershed, the urban canopies account for about 20% of the whole area. The installation effect of infiltration trenches is shown in Figure 11c and Figure 12. Figure 11c shows that, compared with the case without infiltration trenches, the annual surface runoff shows a decrease of about 200 mm, the groundwater outflow shows an increase of 25 mm though the evapotranspiration shows less difference. In a general sense, the hydrological cycle in the watershed can be much improved with the installation of infiltration trenches for storm water from urban canopies. From Figure 12, it can be seen that the discharge peak in the future is about 20% higher than that at present at the Yasakaebashi station of the Ebi River, however, it can be improved to the present level or even better if infiltration trenches are implemented for the storm water from urban canopies.

CONCLUSIONS To ensure sustainable developments in urban areas, it is required to adopt an integrated analysis of the hydrological and energy processes and to evaluate the effects of countermeasures. In this study, a model for this purpose (WEP model) is developed. The model is grid-based and able to simulate spatially variable water and energy processes in watersheds with complex land covers. The model is applied to the Ebi River watershed with reasonable results obtained. The model is verified through comparisons of simulated river discharges, groundwater levels and land surface temperatures with the observed values. A comparison between water balance at present (1993) and that in the future (2035) is conducted and it shows the impact of urbanization. The effect of infiltration trenches is also studied. It is found that the hydrological cycle can be improved to the same level or even better in the future than now if infiltration trenches are implemented for the storm water from urban canopies. In addition, to conserve the water environment in rivers, sewer systems and wastewater treatment plants should also be installed, and the treated wastewater should be drained back into local rivers.

ACKNOWLEDGEMENTS The authors give their sincere thanks to Professor K. Musiake and Professor S. Herath of the University of Tokyo, Urban River Division of Chiba Prefecture and the Japan Association for Rainwater Storage and Inﬁltration Technology (ARSIT) for providing valuable observation data in the Ebi River watershed. Their

Copyright  2001 John Wiley & Sons, Ltd. Hydrol. Process. 15, 2175–2194 (2001) 2194 Y. JIA ET AL. sincere appreciation is also given to the two referees for their detailed, strict and important comments on this paper. Their deep appreciation is extended to Chief Researcher T. Kinouchi in PWRI for his kind opinions on this paper. Finally, the ﬁrst author is grateful to the Japanese Science and Technology Foundation (JST) for its ﬁnancial support.

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