PCSE模型中，土壤水分入渗的分层计算过程及代码

PCSE（Python Crop Simulation Environment）是一个基于Python的农作物模拟环境，用于模拟农作物生长、发育和产量。在PCSE中，土壤水分模型使用了分层计算方法，其原理是将土壤分成若干层，每层的水分含量和通透性都不同，然后计算每层的水分入渗量和排水量，以及水分在土壤中的移动和储存情况。以下是土壤水分入渗的分层计算过程及代码：

1. 初始化土壤参数

def initialize_states(self, day, weather, CO2, soil_parameters):
    self.soil_parameters = soil_parameters
    self.layer_thickness = soil_parameters['thickness']
    self.layer_depth = np.cumsum(self.layer_thickness) - 0.5 * self.layer_thickness
    self.layer_depth = np.insert(self.layer_depth, 0, 0.0)
    self.layer_depth = np.append(self.layer_depth, soil_parameters['depth'])
    self.theta_fc = soil_parameters['theta_fc']
    self.theta_wp = soil_parameters['theta_wp']
    self.theta_sat = soil_parameters['theta_sat']
    self.Ksat = soil_parameters['Ksat']
    self.S = soil_parameters['S']
    self.psi_b = soil_parameters['psi_b']
    self.psi_sat = soil_parameters['psi_sat']
    self.psi_air_entry = soil_parameters['psi_air_entry']
    self.psi_min = soil_parameters['psi_min']
    self.theta = np.zeros_like(self.layer_thickness)
    self.theta[:] = self.theta_wp
    self.psi = np.zeros_like(self.layer_thickness)

2. 计算每层的水分入渗

def compute_water_infiltration(self, day, weather, CO2, et0, Ke, Kcb, soil_parameters):
    dt = 1.0
    P = weather['precip']
    Ep = et0 * Ke * Kcb
    P -= Ep
    P = max(P, 0.0)
    for i in range(self.n_layers):
        if P > 0.0:
            P_i = min(P, self.Ksat[i] * dt)
            P_i = min(P_i, self.theta_sat[i] - self.theta[i])
            self.theta[i] += P_i
            self.psi[i] = self.compute_soil_water_potential(self.theta[i], i)
            P -= P_i
        else:
            break

3. 计算每层的水分排水

def compute_water_drainage(self, day, weather, CO2, et0, Ke, Kcb, soil_parameters):
    dt = 1.0
    Ep = et0 * Ke * Kcb
    for i in range(self.n_layers-1, -1, -1):
        if self.theta[i] > self.theta_fc[i]:
            D_i = min(self.S[i] * (self.psi[i] - self.psi_b[i])**self.S[i], (self.theta[i] - self.theta_fc[i])/dt)
            D_i = min(D_i, self.theta[i] - self.theta_fc[i])
            self.theta[i] -= D_i
            self.psi[i] = self.compute_soil_water_potential(self.theta[i], i)
            if i < self.n_layers-1:
                self.theta[i+1] += D_i
            else:
                self.soil_drainage += D_i

4. 计算每层的水分移动和储存

def compute_water_storage(self, day, weather, CO2, et0, Ke, Kcb, soil_parameters):
    for i in range(self.n_layers):
        if i == 0:
            self.theta[i] += self.soil_drainage
            self.theta[i] = max(self.theta[i], 0.0)
            self.psi[i] = self.compute_soil_water_potential(self.theta[i], i)
        else:
            q = self.Ksat[i-1] * (self.psi[i-1] - self.psi[i]) / self.layer_thickness[i-1]
            q = max(q, 0.0)
            self.theta[i-1] -= q * dt
            self.theta[i] += q * dt
            self.psi[i-1] = self.compute_soil_water_potential(self.theta[i-1], i-1)
            self.psi[i] = self.compute_soil_water_potential(self.theta[i], i)

其中，`theta`表示每层土壤的水分含量，`psi`表示每层土壤的水势，`Ksat`表示每层土壤的饱和导水率，`S`表示van Genuchten方程中的参数，`psi_b`表示土壤下限水势，`psi_sat`表示土壤饱和水势，`psi_air_entry`表示空气入渗水势，`psi_min`表示最小水势。在计算水分入渗、排水、移动和储存时，还需要考虑天气、CO2浓度和农作物参数等因素。

以上是PCSE模型中土壤水分入渗的分层计算过程及代码。