Noah MP地表能量计算

能量计算

Noah-MP能量模块的计算包括地表能量平衡、辐射传输与湍流输送。通常，可以使用传统或者修改后的二流辐射物理计算方案计算。

$$netRad+PH=SH+LH+G$$

$$netRad=SW_{down}+SW_{up}+LW_{down}-LW_{up}$$

在每一个格点计算能量平衡时，分为裸地与冠层计算，再根据所占比例权重相加、

影响能量的关键参数与过程

1. 参考风速（$U_{ref}$）：参考高度上的风速。( defined as the 10 min mean wind velocity at 10 m above ground )
2. 是否有植被覆盖。
3. 积雪覆盖 $f_{snow}$

$$\begin{cases} \rho_{snow}=\frac {m_{snow}}{n_{snow}} \\ f_{melt}={\frac {\rho_{snow}}{\rho_{new}=100 kg/m^3}}^m \\ f_{snow}=tanh(\frac {h_{snow}}{F_{sno}×f_{melt}}) \end{cases}$$

Fsno与m为相关参数，在MPTBL文件中。
4. 粗糙度计算
5. 热学特性
积雪热特性：与积雪密度相关

积雪 影响：温度、土壤特性、水相变过程。

6. 积雪对地表温度的影响(opt_stc=3)

! if snow on ground and TG > TFRZ: reset TG = TFRZ. reevaluate ground fluxes.
 ！TG     !ground temperature (k) TFRZ   = 273.16    !freezing/melting point
     IF(OPT_STC == 1 .OR. OPT_STC == 3) THEN
     IF (SNOWH > 0.05 .AND. TG > TFRZ) THEN
        IF(OPT_STC == 1) TG  = TFRZ
        IF(OPT_STC == 3) TG  = (1.-FSNO)*TG + FSNO*TFRZ   ! MB: allow TG>0C during melt v3.7
        IRG = CIR*TG**4 - EMG*(1.-EMV)*LWDN - EMG*EMV*SB*TV**4
        SHG = CSH * (TG         - TAH)
        EVG = CEV * (ESTG*RHSUR - EAH)
        GH  = SAG+PAHG - (IRG+SHG+EVG)
     END IF
     END IF

! if snow on ground and TG > TFRZ: reset TG = TFRZ. reevaluate ground fluxes.

     IF(OPT_STC == 1 .OR. OPT_STC == 3) THEN
     IF (SNOWH > 0.05 .AND. TGB > TFRZ) THEN
          IF(OPT_STC == 1) TGB = TFRZ
          IF(OPT_STC == 3) TGB  = (1.-FSNO)*TGB + FSNO*TFRZ  ! MB: allow TG>0C during melt v3.7
          IRB = CIR * TGB**4 - EMG*LWDN
          SHB = CSH * (TGB        - SFCTMP)
          EVB = CEV * (ESTG*RHSUR - EAIR )          !ESTG reevaluate ?
          GHB = SAG+PAHB - (IRB+SHB+EVB)
     END IF
     END IF

7. 积雪相变(opt_frz=1)

First, define a phase change indicator (𝐼𝑝ℎ𝑎𝑠𝑒): 0-none;1-melt;2-refreeze.(根据是否大于重冻温度判断)

If 𝐼𝑝ℎ𝑎𝑠𝑒 > 0 (melting or refreezing active), the energy residual (surplus or loss) ($𝐻_{𝑀,𝑝ℎ𝑎𝑠𝑒}$, [W/m2]) is computed for each snow/soil layer (i) as:

$$H_{m,phase}(i)=\frac {T_{snso}(i)-T_{frz}} {f_{phase}(i)}$$

where 𝑓𝑝ℎ𝑎𝑠𝑒 is the phase change factor computed in GroundThermalProperty mod.

积雪相变除了能量改变外，其对于雪中冰水含量的影响也会影响其反照率。

8. 积雪水文过程

The snow hydrological processes include snowfall after canopy interception,
snowpack compaction, snow layer combination, snow layer division, and snow water state
updates. These processes are driven by the energy fluxes and snow temperature changes computed
in EnergyMainMod.F90. The change in snowpack SWE is balanced by the input snowfall and frost
and the output snowmelt and sublimation. Only snowpack with explicit snow layers (snow depth>= 2.5cm) will go through snow layer compaction, combination, and division processes.

积雪平衡公式：

$$\frac {\Delta W_{snow}}{\Delta t}=Q_{snow}+Q_{sno,frost}-Q_{sno,melt}-Q_{sno,subl}$$

Qsnow为降雪，Qsno,frost 冻雪， metl融化，sublmation，升华。

积雪融化为最重要过程，其公式为：

$$Q_{sno,melt}=\frac 1{C_{LH,fus}}(SW_{net}+LW_{net}+H_{pr}-H_L-H_S-G_{sno2soil})$$

where $𝐶_{𝐿𝐻,𝑓𝑢𝑠}$ [J/kg] is the specific latent heat of fusion. 𝑆𝑊𝑛𝑒𝑡 , 𝐿𝑊𝑛𝑒𝑡 , 𝐻𝑝𝑟, 𝐻𝐿 , and 𝐻𝑆, [W/m2
] are the net shortwave radiation flux, net longwave radiation flux, precipitation
advected heat flux, latent heat flux, and sensible heat flux at the snowpack surface. 𝐺𝑠𝑛𝑜2𝑠𝑜𝑖𝑙[W/m2] is the heat flux advected from snowpack to soil at the snow-soil interface (neglected).

积雪层厚度变化与划分：由于降雪(overburden)、融化等过程造成的雪压实(compaction)

积雪内冰水变化：

对于不存在积雪与积雪较浅，无清晰雪层的情况，积雪内的冰水含量与土壤的冰水含量相关。

对于有明显雪层：

顶部雪层：

$$W_{ice,sno}(I_{n,sno}+1)=W_{ice,sno}(I_{n,sno}+1)+(Q_{sno,frost}-Q_{sno,subl})×\Delta t$$

当顶部积雪冰含量过小，则雪层会重新合并

$$W_{liq,sno}(I_{n_sno}+1)=max(0,W_{liq,sno}(I_{n_sno})+1)+Q_{rain}×\Delta t$$

对于里层积雪：

$$V_{ice}(i)=min(1.0,\frac {W_{ice,sno}(i)}{D_{zsno}(i)×\rho _{ice}})$$

$$P_{eff,sno}(i)=1-V_{ice}(i)$$

where i is the snow layer index, 𝑉𝑖𝑐𝑒 is the ice partial volume, and 𝑃𝑒𝑓𝑓,𝑠𝑛𝑜 is the snow effective porosity

里层雪水当量：

The liquid water in each snow layer is computed based on the input water (Qin, [mm]) and
snowpack liquid water holding capacity (𝑊𝑙𝑖𝑞,𝑐𝑎𝑝,𝑠𝑛𝑜, a parameter in NoahmpTable.TBL)

感热计算

$$H_s=\rho_a×C_h×C_{\rho}×U×(\theta_s-\theta_a)$$

$$C_h=\frac {\kappa^2}{[ln(\frac {z-d_0}{z_{0m}})-\phi_m(\frac {z-d_0}{L_{MO}})][ln(\frac {z-d_0}{z_{0h}})-\phi_h(\frac {z-d_0}{L_{MO}})]}$$

𝐶𝑝,𝑎𝑖𝑟 [J/kg/K] is the air heat capacity (CONST),Where $\kappa$ is the von Karman constant, Z is the height above the ground, $𝑑_0$
[m] is the zero-displacement height, and $𝐿_{𝑀𝑂}$ [m] is the M-O length. $\phi_𝑚$ and $\phi_ℎ$ are the stability functions for
momentum and heat transfer, respectively. $𝑧_{0𝑚}$ [m] and $𝑧_{0ℎ}$ [m] are the surface roughness length
for momentum and heat, respectively.

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WRF代码相关：

SHB !bare ground sensible heat flux [+ to atm]

SHC !canopy sensible heat flux [+ to atm]

SHG !vegetated ground sensible heat flux [+ to atm]

HFX      (I,J)                = FSH
FSH    !total sensible heat (w/m2) 
有植被时：FSH= FVEG * SHG   + (1.0 - FVEG) * SHB + SHC
无植被：FSH=SHB
SHB计算函数：

潜热变化

感热包括：蒸发热量与蒸腾热量

$$H_L=\rho_a×C_w×C_{LH}×U×(q_s-q_a)$$

𝑞𝑠[kg/kg] and 𝑞𝑎 [kg/kg] are the specific humidity at the surface and in the air, respectively. 𝐶ℎ and 𝐶𝑤 are the surface exchange
coefficients for heat and moisture, respectively. Noah-MP assumes that 𝐶𝑤 is equal to 𝐶ℎ (Chen and Zhang, 2009).𝐶𝐿𝐻 [J/kg] is the specific latent heat of water vaporization (CONST)