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Warning, /doc/phys_pkgs/fizhi.rst is written in an unsupported language. File is not indexed.
view on githubraw file Latest commit 0bad585a on 2022-02-16 18:55:09 UTC8679f9097b Jeff*0001 .. include:: ../defs.hrst 0002 0003 .. _sub_phys_pkg_fizhi: 0004 0005 Fizhi: High-end Atmospheric Physics 0006 ----------------------------------- 0007 0008 0009 Introduction 0010 ++++++++++++ 0011 0012 The fizhi (high-end atmospheric physics) package includes a collection 0013 of state-of-the-art physical parameterizations for atmospheric 0014 radiation, cumulus convection, atmospheric boundary layer turbulence, 0015 and land surface processes. The collection of atmospheric physics 0016 parameterizations were originally used together as part of the GEOS-3 0017 (Goddard Earth Observing System-3) GCM developed at the NASA/Goddard 0018 Global Modelling and Assimilation Office (GMAO). 0019 0020 Equations 0021 +++++++++ 0022 0023 Moist Convective Processes: 0024 0025 0026 .. _para_phys_pkg_fizhi_mc: 0027 0028 Sub-grid and Large-scale Convection 0029 ################################### 0030 0031 Sub-grid scale cumulus convection is parameterized using the Relaxed 0032 Arakawa Schubert (RAS) scheme of :cite:`moorsz:92`, which is a linearized Arakawa 0033 Schubert type scheme. RAS predicts the mass flux from an ensemble of 0034 clouds. Each subensemble is identified by its entrainment rate and level 0035 of neutral bouyancy which are determined by the grid-scale properties. 0036 0037 The thermodynamic variables that are used in RAS to describe the grid 0038 scale vertical profile are the dry static energy, :math:`s=c_pT +gz`, 0039 and the moist static energy, :math:`h=c_p T + gz + Lq`. The conceptual 0040 model behind RAS depicts each subensemble as a rising plume cloud, 0041 entraining mass from the environment during ascent, and detraining all 0042 cloud air at the level of neutral buoyancy. RAS assumes that the 0043 normalized cloud mass flux, :math:`\eta`, normalized by the cloud base 0044 mass flux, is a linear function of height, expressed as: 0045 0046 .. math:: 0047 0bad585a21 Navi*0048 \pp{\eta(z)}{z} = \lambda \hspace{0.4cm} \text{or} \hspace{0.4cm} \pp{\eta(P^{\kappa})}{P^{\kappa}} = 0049 -\frac{c_p}{g} \theta \lambda 8679f9097b Jeff*0050 0051 where we have used the hydrostatic equation written in the form: 0052 0bad585a21 Navi*0053 .. math:: \pp{z}{P^{\kappa}} = -\frac{c_p}{g} \theta 8679f9097b Jeff*0054 0055 The entrainment parameter, :math:`\lambda`, characterizes a particular 0056 subensemble based on its detrainment level, and is obtained by assuming 0057 that the level of detrainment is the level of neutral buoyancy, ie., the 0058 level at which the moist static energy of the cloud, :math:`h_c`, is 0059 equal to the saturation moist static energy of the environment, 0060 :math:`h^*`. Following :cite:`moorsz:92`, :math:`\lambda` may be written as 0061 0bad585a21 Navi*0062 .. math:: \lambda = \frac{h_B - h^*_D}{\frac{c_p}{g} \int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}} 8679f9097b Jeff*0063 0064 where the subscript :math:`B` refers to cloud base, and the subscript 0065 :math:`D` refers to the detrainment level. 0066 0067 The convective instability is measured in terms of the cloud work 0068 function :math:`A`, defined as the rate of change of cumulus kinetic 0069 energy. The cloud work function is related to the buoyancy, or the 0070 difference between the moist static energy in the cloud and in the 0071 environment: 0072 0073 .. math:: 0074 0075 A = \int_{P_D}^{P_B} \frac{\eta}{1 + \gamma} 0076 \left[ \frac{h_c-h^*}{P^{\kappa}} \right] dP^{\kappa} 0077 0078 where :math:`\gamma` is :math:`\frac{L}{c_p}\pp{q^*}{T}` obtained from 0079 the Claussius Clapeyron equation, and the subscript :math:`c` refers to 0080 the value inside the cloud. 0081 0082 To determine the cloud base mass flux, the rate of change of :math:`A` 0083 in time *due to dissipation by the clouds* is assumed to approximately 0084 balance the rate of change of :math:`A` *due to the generation by the 0085 large scale*. This is the quasi-equilibrium assumption, and results in 0086 an expression for :math:`m_B`: 0087 0bad585a21 Navi*0088 .. math:: m_B = \dfrac{- \left. \frac{dA}{dt} \right|_{\rm ls}}{K} 8679f9097b Jeff*0089 0090 where :math:`K` is the cloud kernel, defined as the rate of change of 0091 the cloud work function per unit cloud base mass flux, and is currently 0092 obtained by analytically differentiating the expression for :math:`A` in 0093 time. The rate of change of :math:`A` due to the generation by the large 0094 scale can be written as the difference between the current 0bad585a21 Navi*0095 :math:`A(t+\Delta t)` and its equilibrated value after the previous 8679f9097b Jeff*0096 convective time step :math:`A(t)`, divided by the time step. 0bad585a21 Navi*0097 :math:`A(t)` is approximated as some critical :math:`A_{\rm crit}`, computed 0098 by Lord (1982) from in situ observations. 8679f9097b Jeff*0099 0100 The predicted convective mass fluxes are used to solve grid-scale 0101 temperature and moisture budget equations to determine the impact of 0102 convection on the large scale fields of temperature (through latent 0103 heating and compensating subsidence) and moisture (through precipitation 0104 and detrainment): 0105 0106 .. math:: \left.{\pp{\theta}{t}}\right|_{c} = \alpha \frac{ m_B}{c_p P^{\kappa}} \eta \pp{s}{p} 0107 0108 and 0109 0bad585a21 Navi*0110 .. math:: \left.{\pp{q}{t}}\right|_{c} = \alpha \frac{m_B}{L} \eta \left( \pp{h}{p}-\pp{s}{p} \right) 8679f9097b Jeff*0111 0112 where :math:`\theta = \frac{T}{P^{\kappa}}`, :math:`P = (p/p_0)`, and 0113 :math:`\alpha` is the relaxation parameter. 0114 0115 As an approximation to a full interaction between the different 0116 allowable subensembles, many clouds are simulated frequently, each 0117 modifying the large scale environment some fraction :math:`\alpha` of** Warning **
Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 119.
0118 the total adjustment. The parameterization thereby “relaxes” the large 0bad585a21 Navi*0119 scale environment towards equilibrium. 8679f9097b Jeff*0120 0121 In addition to the RAS cumulus convection scheme, the fizhi package 0122 employs a Kessler-type scheme for the re-evaporation of falling rain :cite:`sudm:88`, 0123 which correspondingly adjusts the temperature assuming :math:`h` is 0124 conserved. RAS in its current formulation assumes that all cloud water 0125 is deposited into the detrainment level as rain. All of the rain is 0126 available for re-evaporation, which begins in the level below 0127 detrainment. The scheme accounts for some microphysics such as the 0128 rainfall intensity, the drop size distribution, as well as the 0129 temperature, pressure and relative humidity of the surrounding air. The 0130 fraction of the moisture deficit in any model layer into which the rain 0131 may re-evaporate is controlled by a free parameter, which allows for a 0132 relatively efficient re-evaporation of liquid precipitate and larger 0133 rainout for frozen precipitation. 0134 0135 Due to the increased vertical resolution near the surface, the lowest 0136 model layers are averaged to provide a 50 mb thick sub-cloud layer for 0137 RAS. Each time RAS is invoked (every ten simulated minutes), a number of 0138 randomly chosen subensembles are checked for the possibility of 0139 convection, from just above cloud base to 10 mb. 0140 0141 Supersaturation or large-scale precipitation is initiated in the fizhi 0142 package whenever the relative humidity in any grid-box exceeds a 0bad585a21 Navi*0143 critical value, currently 100%. The large-scale precipitation 8679f9097b Jeff*0144 re-evaporates during descent to partially saturate lower layers in a 0145 process identical to the re-evaporation of convective rain. 0146 0bad585a21 Navi*0147 .. _fizhi_clouds: 0148 8679f9097b Jeff*0149 Cloud Formation 0150 ############### 0151 0152 Convective and large-scale cloud fractons which are used for 0153 cloud-radiative interactions are determined diagnostically as part of 0154 the cumulus and large-scale parameterizations. Convective cloud 0155 fractions produced by RAS are proportional to the detrained liquid water 0156 amount given by 0157 0bad585a21 Navi*0158 .. math:: F_{\rm RAS} = \min\left[ \frac{l_{\rm RAS}}{l_c}, 1 \right] 8679f9097b Jeff*0159 0160 where :math:`l_c` is an assigned critical value equal to :math:`1.25` 0161 g/kg. A memory is associated with convective clouds defined by: 0162 0bad585a21 Navi*0163 .. math:: F_{\rm RAS}^n = \min\left[ F_{\rm RAS} + \left(1-\frac{\Delta t_{\rm RAS}}{\tau}\right) F_{\rm RAS}^{n-1} \, , \, 1 \right], 8679f9097b Jeff*0164 0bad585a21 Navi*0165 where :math:`F_{\rm RAS}` is the instantaneous cloud fraction and 0166 :math:`F_{\rm RAS}^{n-1}` is the cloud fraction from the previous RAS 8679f9097b Jeff*0167 timestep. The memory coefficient is computed using a RAS cloud 0168 timescale, :math:`\tau`, equal to 1 hour. RAS cloud fractions are 0bad585a21 Navi*0169 cleared when they fall below 5%. 8679f9097b Jeff*0170 0171 Large-scale cloudiness is defined, following Slingo and Ritter (1985), 0172 as a function of relative humidity: 0173 0bad585a21 Navi*0174 .. math:: F_{\rm ls} = \min\left[ { \left( \frac{\textrm{RH}-\textrm{RH}_c}{1-\textrm{RH}_c} \right) }^2 \, , \, 1 \right] 8679f9097b Jeff*0175 0176 where 0177 0bad585a21 Navi*0178 .. math:: 0179 \begin{aligned} 0180 \textrm{RH}_c & = 1-s(1-s)(2-\sqrt{3}+2\sqrt{3}s)r \\ 0181 s & = p/p_{\rm surf} \\ 0182 r & = \left(\frac{1.0-\textrm{RH}_{\rm min}}{\alpha}\right) \\ 0183 \textrm{RH}_{\rm min} & = 0.75 \\ 0184 \alpha & = 0.573285 \end{aligned} 8679f9097b Jeff*0185 0186 These cloud fractions are suppressed, however, in regions where the 0187 convective sub-cloud layer is conditionally unstable. The functional 0bad585a21 Navi*0188 form of :math:`\textrm{RH}_c` is shown in :numref:`rhcrit` 8679f9097b Jeff*0189 0190 0191 0192 .. figure:: figs/rhcrit.* 0193 :width: 70% 0194 :align: center 0195 :alt: critical relative humidity for clouds 0196 :name: rhcrit 0197 0198 Critical Relative Humidity for Clouds. 0199 0200 0201 0202 The total cloud fraction in a grid box is determined by the larger of 0203 the two cloud fractions: 0204 0bad585a21 Navi*0205 .. math:: F_{\rm cld} = \max \left[ F_{\rm RAS} \, , \, F_{\rm ls} \right] 8679f9097b Jeff*0206 0207 Finally, cloud fractions are time-averaged between calls to the 0208 radiation packages. 0209 0210 Radiation: 0211 0212 The parameterization of radiative heating in the fizhi package includes 0213 effects from both shortwave and longwave processes. Radiative fluxes are 0214 calculated at each model edge-level in both up and down directions. The 0215 heating rates/cooling rates are then obtained from the vertical 0216 divergence of the net radiative fluxes. 0217 0218 The net flux is 0219 0220 .. math:: F = F^\uparrow - F^\downarrow 0221 0222 where :math:`F` is the net flux, :math:`F^\uparrow` is the upward flux 0223 and :math:`F^\downarrow` is the downward flux. 0224 0225 The heating rate due to the divergence of the radiative flux is given by 0226 0227 .. math:: \pp{\rho c_p T}{t} = - \pp{F}{z} 0228 0229 or 0230 0231 .. math:: \pp{T}{t} = \frac{g}{c_p \pi} \pp{F}{\sigma} 0232 0233 where :math:`g` is the accelation due to gravity and :math:`c_p` is the 0234 heat capacity of air at constant pressure. 0235 0236 The time tendency for Longwave Radiation is updated every 3 hours. The 0237 time tendency for Shortwave Radiation is updated once every three hours 0238 assuming a normalized incident solar radiation, and subsequently 0239 modified at every model time step by the true incident radiation. The 0bad585a21 Navi*0240 solar constant value used in the package is equal to 1365 W m\ :sup:`--2` 0241 and a CO\ :sub:`2` mixing ratio of 330 ppm. For the ozone mixing ratio, 8679f9097b Jeff*0242 monthly mean zonally averaged climatological values specified as a 0243 function of latitude and height :cite:`rosen:87` are linearly interpolated to the 0244 current time. 0245 0246 Shortwave Radiation 0247 ################### 0248 0249 The shortwave radiation package used in the package computes solar 0250 radiative heating due to the absoption by water vapor, ozone, carbon 0251 dioxide, oxygen, clouds, and aerosols and due to the scattering by 0252 clouds, aerosols, and gases. The shortwave radiative processes are 0253 described by :cite:`chou:90,chou:92`. This shortwave package uses the Delta-Eddington 0254 approximation to compute the bulk scattering properties of a single 0255 layer following King and Harshvardhan (JAS, 1986). The transmittance and 0256 reflectance of diffuse radiation follow the procedures of Sagan and 0257 Pollock (JGR, 1967) and :cite:`lhans:74`. 0258 0259 Highly accurate heating rate calculations are obtained through the use 0260 of an optimal grouping strategy of spectral bands. By grouping the UV 0261 and visible regions as indicated in :numref:`tab_phys_pkg_fizhi_solar1`, the 0262 Rayleigh scattering and the ozone absorption of solar radiation can be 0263 accurately computed in the ultraviolet region and the photosynthetically 0264 active radiation (PAR) region. The computation of solar flux in the 0265 infrared region is performed with a broadband parameterization using the 0266 spectrum regions shown in :numref:`tab_phys_pkg_fizhi_solar2`. The solar radiation 0267 algorithm used in the fizhi package can be applied not only for climate 0268 studies but also for studies on the photolysis in the upper atmosphere 0269 and the photosynthesis in the biosphere. 0270 0271 0bad585a21 Navi*0272 .. table:: UV and visible spectral regions used in shortwave radiation package. 8679f9097b Jeff*0273 :name: tab_phys_pkg_fizhi_solar1 0274 0275 +----------+--------+-----------------------+ 0276 | **UV and Visible Spectral Regions** | 0277 +----------+--------+-----------------------+ 0278 | Region | Band | Wavelength (micron) | 0279 +==========+========+=======================+ 0280 | UV-C | 1. | .175 - .225 | 0281 +----------+--------+-----------------------+ 0282 | | 2. | .225 - .245 | 0283 +----------+--------+-----------------------+ 0284 | | | .260 - .280 | 0285 +----------+--------+-----------------------+ 0286 | | 3. | .245 - .260 | 0287 +----------+--------+-----------------------+ 0288 | UV-B | 4. | .280 - .295 | 0289 +----------+--------+-----------------------+ 0290 | | 5. | .295 - .310 | 0291 +----------+--------+-----------------------+ 0292 | | 6. | .310 - .320 | 0293 +----------+--------+-----------------------+ 0294 | UV-A | 7. | .320 - .400 | 0295 +----------+--------+-----------------------+ 0296 | PAR | 8. | .400 - .700 | 0297 +----------+--------+-----------------------+ 0298 0299 0300 0301 0bad585a21 Navi*0302 .. table:: Infrared spectral regions used in shortwave radiation package. 8679f9097b Jeff*0303 :name: tab_phys_pkg_fizhi_solar2 0304 0305 +--------+---------------------------------+-----------------------+ 0306 | **Infrared Spectral Regions** | 0307 +--------+---------------------------------+-----------------------+ 0308 | Band | Wavenumber (cm\ :sup:`--1`) | Wavelength (micron) | 0309 +========+=================================+=======================+ 0310 | 1 | 1000-4400 | 2.27-10.0 | 0311 +--------+---------------------------------+-----------------------+ 0312 | 2 | 4400-8200 | 1.22-2.27 | 0313 +--------+---------------------------------+-----------------------+ 0314 | 3 | 8200-14300 | 0.70-1.22 | 0315 +--------+---------------------------------+-----------------------+ 0316 0317 0318 Within the shortwave radiation package, both ice and liquid cloud 0319 particles are allowed to co-exist in any of the model layers. Two sets 0320 of cloud parameters are used, one for ice paticles and the other for 0321 liquid particles. Cloud parameters are defined as the cloud optical 0322 thickness and the effective cloud particle size. In the fizhi package, 0323 the effective radius for water droplets is given as 10 microns, while 65 0324 microns is used for ice particles. The absorption due to aerosols is 0325 currently set to zero. 0326 0327 To simplify calculations in a cloudy atmosphere, clouds are grouped into 0328 low (:math:`p>700` mb), middle (700 mb :math:`\ge p > 400` mb), and high 0329 (:math:`p < 400` mb) cloud regions. Within each of the three regions, 0330 clouds are assumed maximally overlapped, and the cloud cover of the 0331 group is the maximum cloud cover of all the layers in the group. The 0332 optical thickness of a given layer is then scaled for both the direct 0333 (as a function of the solar zenith angle) and diffuse beam radiation so 0334 that the grouped layer reflectance is the same as the original 0335 reflectance. The solar flux is computed for each of eight cloud 0336 realizations possible within this low/middle/high classification, and 0337 appropriately averaged to produce the net solar flux. 0338 0339 Longwave Radiation 0340 ################## 0341 0342 The longwave radiation package used in the fizhi package is thoroughly 39fa6219cc Oliv*0343 described by :cite:`chsz:94`. As described in that document, IR fluxes are 0344 computed due to absorption by water vapor, carbon dioxide, and ozone. The 0345 spectral bands together with their absorbers and parameterization methods, 0346 configured for the fizhi package, are shown in 0347 :numref:`tab_phys_pkg_fizhi_longwave`. 8679f9097b Jeff*0348 0bad585a21 Navi*0349 .. table:: IR spectral bands, absorbers, and parameterization method 8679f9097b Jeff*0350 :name: tab_phys_pkg_fizhi_longwave 0351 0352 +----------------+------------------------------------+------------------------------+----------+ 0353 | **IR Spectral Bands** | 0354 +----------------+------------------------------------+------------------------------+----------+ 0355 | Band | Spectral Range (cm\ :sup:`--1`) | Absorber | Method | 0356 +================+====================================+==============================+==========+ 0bad585a21 Navi*0357 | 1 | 0-340 | H\ :sub:`2`\ O line | T | 8679f9097b Jeff*0358 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0359 | 2 | 340-540 | H\ :sub:`2`\ O line | T | 8679f9097b Jeff*0360 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0361 | 3a | 540-620 | H\ :sub:`2`\ O line | K | 8679f9097b Jeff*0362 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0363 | 3b | 620-720 | H\ :sub:`2`\ O continuum | S | 8679f9097b Jeff*0364 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0365 | 3b | 720-800 | CO\ :sub:`2` | T | 8679f9097b Jeff*0366 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0367 | 4 | 800-980 | H\ :sub:`2`\ O line | K | 8679f9097b Jeff*0368 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0369 | | | H\ :sub:`2`\ O continuum | S | 8679f9097b Jeff*0370 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0371 | | | H\ :sub:`2`\ O line | K | 8679f9097b Jeff*0372 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0373 | 5 | 980-1100 | H\ :sub:`2`\ O continuum | S | 8679f9097b Jeff*0374 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0375 | | | O\ :sub:`3` | T | 8679f9097b Jeff*0376 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0377 | 6 | 1100-1380 | H\ :sub:`2`\ O line | K | 8679f9097b Jeff*0378 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0379 | | | H\ :sub:`2`\ O continuum | S | 8679f9097b Jeff*0380 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0381 | 7 | 1380-1900 | H\ :sub:`2`\ O line | T | 8679f9097b Jeff*0382 +----------------+------------------------------------+------------------------------+----------+ 0bad585a21 Navi*0383 | 8 | 1900-3000 | H\ :sub:`2`\ O line | K | 8679f9097b Jeff*0384 +----------------+------------------------------------+------------------------------+----------+ 0385 | K: :math:`k`-distribution method with linear pressure scaling | 0386 +----------------+------------------------------------+------------------------------+----------+ 0387 | T: Table look-up with temperature and pressure scaling | 0388 +----------------+------------------------------------+------------------------------+----------+ 0389 | S: One-parameter temperature scaling | 0390 +----------------+------------------------------------+------------------------------+----------+ 0391 0392 0393 The longwave radiation package accurately computes cooling rates for the 0394 middle and lower atmosphere from 0.01 mb to the surface. Errors are 0bad585a21 Navi*0395 < 0.4 C day\ :sup:`--1` in cooling rates and < 1% in 8679f9097b Jeff*0396 fluxes. From Chou and Suarez, it is estimated that the total effect of 0397 neglecting all minor absorption bands and the effects of minor infrared 0bad585a21 Navi*0398 absorbers such as nitrous oxide (N\ :sub:`2`\ O), methane 0399 (CH\ :sub:`4`), and the chlorofluorocarbons (CFCs), is an underestimate 0400 of :math:`\approx 5` W m\ :sup:`--2` in the downward flux at the surface 0401 and an overestimate of :math:`\approx 3` W m\ :sup:`--2` in the upward 8679f9097b Jeff*0402 flux at the top of the atmosphere. 0403 0404 Similar to the procedure used in the shortwave radiation package, clouds 0405 are grouped into three regions catagorized as low/middle/high. The net 0406 clear line-of-site probability :math:`(P)` between any two levels, 0407 :math:`p_1` and :math:`p_2 \quad (p_2 > p_1)`, assuming randomly 0408 overlapped cloud groups, is simply the product of the probabilities 0409 within each group: 0410 0bad585a21 Navi*0411 .. math:: P_{\rm net} = P_{\rm low} \times P_{\rm mid} \times P_{\rm hi} 8679f9097b Jeff*0412 0413 Since all clouds within a group are assumed maximally overlapped, the 0414 clear line-of-site probability within a group is given by: 0415 0bad585a21 Navi*0416 .. math:: P_{\rm group} = 1 - F_{\rm max} 8679f9097b Jeff*0417 0bad585a21 Navi*0418 where :math:`F_{\rm max}` is the maximum cloud fraction encountered between 8679f9097b Jeff*0419 :math:`p_1` and :math:`p_2` within that group. For groups and/or levels 0420 outside the range of :math:`p_1` and :math:`p_2`, a clear line-of-site 0421 probability equal to 1 is assigned. 0422 0423 Cloud-Radiation Interaction 0424 ########################### 0425 0426 The cloud fractions and diagnosed cloud liquid water produced by moist 0427 processes within the fizhi package are used in the radiation packages to 0428 produce cloud-radiative forcing. The cloud optical thickness associated 0429 with large-scale cloudiness is made proportional to the diagnosed 0430 large-scale liquid water, :math:`\ell`, detrained due to 0431 super-saturation. Two values are used corresponding to cloud ice 0432 particles and water droplets. The range of optical thickness for these 0433 clouds is given as 0434 0bad585a21 Navi*0435 .. math:: 0.0002 \le \tau_{\rm ice} (\text{mb}^{-1}) \le 0.002 \quad\mbox{for}\quad 0 \le \ell \le 2 \; \text{mg/kg} 8679f9097b Jeff*0436 0bad585a21 Navi*0437 .. math:: 0.02 \le \tau_{\rm H_2O} (\text{mb}^{-1}) \le 0.2 \quad\mbox{for}\quad 0 \le \ell \le 10 \; \text{mg/kg} 8679f9097b Jeff*0438 0439 The partitioning, :math:`\alpha`, between ice particles and water 0440 droplets is achieved through a linear scaling in temperature: 0441 0bad585a21 Navi*0442 .. math:: 0 \le \alpha \le 1 \quad\mbox{for}\quad 233.15 \le T \le 253.15 8679f9097b Jeff*0443 0444 The resulting optical depth associated with large-scale cloudiness is 0445 given as 0446 0bad585a21 Navi*0447 .. math:: \tau_{\rm ls} = \alpha \tau_{\rm H_2O} + (1-\alpha) \tau_{\rm ice} 8679f9097b Jeff*0448 0449 The optical thickness associated with sub-grid scale convective clouds 0450 produced by RAS is given as 0451 0bad585a21 Navi*0452 .. math:: \tau_{\rm RAS} = 0.16 \; \text{mb}^{-1} 8679f9097b Jeff*0453 0454 The total optical depth in a given model layer is computed as a weighted 0455 average between the large-scale and sub-grid scale optical depths, 0456 normalized by the total cloud fraction in the layer: 0457 0bad585a21 Navi*0458 .. math:: \tau = \left( \frac{F_{\rm RAS} \,\,\, \tau_{\rm RAS} + F_{\rm ls} \,\,\, \tau_{\rm ls} }{ F_{\rm RAS}+F_{\rm ls} } \right) \Delta p 8679f9097b Jeff*0459 0bad585a21 Navi*0460 where :math:`F_{\rm RAS}` and :math:`F_{\rm ls}` are the time-averaged cloud 8679f9097b Jeff*0461 fractions associated with RAS and large-scale processes described in 0bad585a21 Navi*0462 :numref:`fizhi_clouds`. The optical thickness for the longwave 0463 radiative feedback is assumed to be 75% of these values. 8679f9097b Jeff*0464 0465 The entire Moist Convective Processes Module is called with a frequency 0466 of 10 minutes. The cloud fraction values are time-averaged over the 0467 period between Radiation calls (every 3 hours). Therefore, in a 0468 time-averaged sense, both convective and large-scale cloudiness can 0469 exist in a given grid-box. 0470 0471 Turbulence 0472 ########## 0473 0474 Turbulence is parameterized in the fizhi package to account for its 0475 contribution to the vertical exchange of heat, moisture, and momentum. 0476 The turbulence scheme is invoked every 30 minutes, and employs a 0477 backward-implicit iterative time scheme with an internal time step of 5 0478 minutes. The tendencies of atmospheric state variables due to turbulent 0479 diffusion are calculated using the diffusion equations: 0480 0481 .. math:: 0bad585a21 Navi*0482 \begin{aligned} 0483 {\pp{u}{t}}_{\rm turb} &= {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} 0484 = {\pp{}{z} }{\left(K_m \pp{u}{z}\right)} \nonumber \\ 0485 {\pp{v}{t}}_{\rm turb} &= {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} 0486 = {\pp{}{z} }{\left(K_m \pp{v}{z}\right)} \nonumber \\ 0487 {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{\rm turb} &= 8679f9097b Jeff*0488 P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} 0bad585a21 Navi*0489 = P^{\kappa}{\pp{}{z} }{\left(K_h \pp{\theta_v}{z}\right)} \nonumber \\ 0490 {\pp{q}{t}}_{\rm turb} &= {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} 0491 = {\pp{}{z} }{\left(K_h \pp{q}{z}\right)} 0492 \end{aligned} 8679f9097b Jeff*0493 0494 Within the atmosphere, the time evolution of second turbulent moments is 0495 explicitly modeled by representing the third moments in terms of the 0496 first and second moments. This approach is known as a second-order 0497 closure modeling. To simplify and streamline the computation of the 0498 second moments, the level 2.5 assumption of Mellor and Yamada (1974) and :cite:`yam:77` 0499 is employed, in which only the turbulent kinetic energy (TKE), 0500 0bad585a21 Navi*0501 .. math:: {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}} 8679f9097b Jeff*0502 0503 is solved prognostically and the other second moments are solved 0504 diagnostically. The prognostic equation for TKE allows the scheme to 0505 simulate some of the transient and diffusive effects in the turbulence. 0506 The TKE budget equation is solved numerically using an implicit backward 0507 computation of the terms linear in :math:`q^2` and is written: 0508 0509 .. math:: 0510 0bad585a21 Navi*0511 {\dd{}{t} \left({{\h} q^2}\right)} - { \pp{}{z} \left[{ \frac{5}{3} {{\lambda}_1} q { \pp {}{z} 0512 \left({\h}q^2\right)} }\right]} = 8679f9097b Jeff*0513 {- \overline{{u^{\prime}}{w^{\prime}}} { \pp{U}{z} }} - {\overline{{v^{\prime}}{w^{\prime}}} 0514 { \pp{V}{z} }} + {\frac{g}{\Theta_0}{\overline{{w^{\prime}}{{{\theta}_v}^{\prime}}}} 0515 - \frac{ q^3}{{\Lambda}_1} } 0516 0517 where :math:`q` is the turbulent velocity, :math:`{u^{\prime}}`, 0518 :math:`{v^{\prime}}`, :math:`{w^{\prime}}` and 0519 :math:`{{\theta}^{\prime}}` are the fluctuating parts of the velocity 0520 components and potential temperature, :math:`U` and :math:`V` are the 0521 mean velocity components, :math:`{\Theta_0}^{-1}` is the coefficient of 0522 thermal expansion, and :math:`{{\lambda}_1}` and :math:`{{\Lambda} _1}` 0523 are constant multiples of the master length scale, :math:`\ell`, which 0524 is designed to be a characteristic measure of the vertical structure of 0525 the turbulent layers. 0526 0527 The first term on the left-hand side represents the time rate of change 0528 of TKE, and the second term is a representation of the triple 0529 correlation, or turbulent transport term. The first three terms on the 0530 right-hand side represent the sources of TKE due to shear and bouyancy, 0531 and the last term on the right hand side is the dissipation of TKE. 0532 0533 In the level 2.5 approach, the vertical fluxes of the scalars 0534 :math:`\theta_v` and :math:`q` and the wind components :math:`u` and 0535 :math:`v` are expressed in terms of the diffusion coefficients 0536 :math:`K_h` and :math:`K_m`, respectively. In the statisically 0537 realizable level 2.5 turbulence scheme of :cite:`helflab:88`, these diffusion coefficients 0538 are expressed as 0539 0540 .. math:: 0541 0542 K_h 0543 = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) \, & \mbox{decaying turbulence} 0bad585a21 Navi*0544 \\ \frac{ q^2 }{ q_{\rm eq} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. 8679f9097b Jeff*0545 0546 and 0547 0548 .. math:: 0549 0550 K_m 0551 = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) \, & \mbox{decaying turbulence} 0bad585a21 Navi*0552 \\ \frac{ q^2 }{ q_{\rm eq} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. 8679f9097b Jeff*0553 0bad585a21 Navi*0554 where the subscript 'eq' refers to the value under conditions of 0555 local equilibrium (obtained from the Level 2.0 Model), :math:`\ell` is 8679f9097b Jeff*0556 the master length scale related to the vertical structure of the 0557 atmosphere, and :math:`S_M` and :math:`S_H` are functions of :math:`G_H` 0558 and :math:`G_M`, the dimensionless buoyancy and wind shear parameters, 0559 respectively. Both :math:`G_H` and :math:`G_M`, and their equilibrium 0560 values :math:`G_{H_e}` and :math:`G_{M_e}`, are functions of the 0561 Richardson number: 0562 0563 .. math:: 0bad585a21 Navi*0564 \textrm{RI} = \frac{ \frac{g}{\theta_v} \pp{\theta_v}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 } 0565 = \frac{c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 } 8679f9097b Jeff*0566 0567 Negative values indicate unstable buoyancy and shear, small positive 0bad585a21 Navi*0568 values (<0.2) indicate dominantly unstable shear, and large 8679f9097b Jeff*0569 positive values indicate dominantly stable stratification. 0570 0571 Turbulent eddy diffusion coefficients of momentum, heat and moisture in** Warning **
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0572 the surface layer, which corresponds to the lowest GCM level (see *—** Warning **
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0573 missing table —*), are calculated using stability-dependant functions 0574 based on Monin-Obukhov theory: 0575 0bad585a21 Navi*0576 .. math:: {K_m} ({\rm surface}) = C_u \times u_* = C_D W_s 8679f9097b Jeff*0577 0578 and 0579 0bad585a21 Navi*0580 .. math:: {K_h} ({\rm surface}) = C_t \times u_* = C_H W_s 8679f9097b Jeff*0581 0582 where :math:`u_*=C_uW_s` is the surface friction velocity, :math:`C_D` 0583 is termed the surface drag coefficient, :math:`C_H` the heat transfer 0584 coefficient, and :math:`W_s` is the magnitude of the surface layer wind. 0585 0586 :math:`C_u` is the dimensionless exchange coefficient for momentum from 0587 the surface layer similarity functions: 0588 0589 .. math:: {C_u} = \frac{u_* }{ W_s} = \frac{ k }{ \psi_{m} } 0590 0591 where k is the Von Karman constant and :math:`\psi_m` is the surface 0592 layer non-dimensional wind shear given by 0593 0bad585a21 Navi*0594 .. math:: \psi_{m} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{m} }{ \zeta} d \zeta} 8679f9097b Jeff*0595 0596 Here :math:`\zeta` is the non-dimensional stability parameter, and 0597 :math:`\phi_m` is the similarity function of :math:`\zeta` which 0598 expresses the stability dependance of the momentum gradient. The 0599 functional form of :math:`\phi_m` is specified differently for stable 0600 and unstable layers. 0601 0602 :math:`C_t` is the dimensionless exchange coefficient for heat and 0603 moisture from the surface layer similarity functions: 0604 0605 .. math:: 0606 0607 {C_t} = -\frac{( \overline{w^{\prime}\theta^{\prime}}) }{ u_* \Delta \theta } = 0608 -\frac{( \overline{w^{\prime}q^{\prime}}) }{ u_* \Delta q } = 0609 \frac{ k }{ (\psi_{h} + \psi_{g}) } 0610 0611 where :math:`\psi_h` is the surface layer non-dimensional temperature 0612 gradient given by 0613 0bad585a21 Navi*0614 .. math:: \psi_{h} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{h} }{ \zeta} d \zeta} 8679f9097b Jeff*0615 0616 Here :math:`\phi_h` is the similarity function of :math:`\zeta`, which 0617 expresses the stability dependance of the temperature and moisture 0618 gradients, and is specified differently for stable and unstable layers 0619 according to :cite:`helfschu:95`. 0620 0621 :math:`\psi_g` is the non-dimensional temperature or moisture gradient 0622 in the viscous sublayer, which is the mosstly laminar region between the 0623 surface and the tops of the roughness elements, in which temperature and 0624 moisture gradients can be quite large. Based on :cite:`yagkad:74`: 0625 0626 .. math:: 0627 0bad585a21 Navi*0628 \psi_{g} = \frac{ 0.55 ({\rm Pr}^{2/3} - 0.2) }{ \nu^{1/2} } 0629 (h_{0}u_{*} - h_{0_{\rm ref}}u_{*_{\rm ref}})^{1/2} 8679f9097b Jeff*0630 0631 where Pr is the Prandtl number for air, :math:`\nu` is the molecular 0632 viscosity, :math:`z_{0}` is the surface roughness length, and the 0bad585a21 Navi*0633 subscript 'ref' refers to a reference value. :math:`h_{0} = 30z_{0}` 0634 with a maximum value over land of 0.01. 8679f9097b Jeff*0635 0636 The surface roughness length over oceans is is a function of the 0637 surface-stress velocity, 0638 0639 .. math:: {z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + \frac{c_5 }{ u_*} 0640 0641 where the constants are chosen to interpolate between the reciprocal 0642 relation of :cite:`kondo:75` for weak winds, and the piecewise linear relation of :cite:`larpond:81` for 0643 moderate to large winds. Roughness lengths over land are specified from 0644 the climatology of :cite:`dorsell:89`. 0645 0646 For an unstable surface layer, the stability functions, chosen to 0647 interpolate between the condition of small values of :math:`\beta` and 0648 the convective limit, are the KEYPS function :cite:`pano:73` for momentum, and its 0649 generalization for heat and moisture: 0650 0651 .. math:: 0652 0653 {\phi_m}^4 - 18 \zeta {\phi_m}^3 = 1 \hspace{1cm} ; \hspace{1cm} 0bad585a21 Navi*0654 {\phi_h}^2 - 18 \zeta {\phi_h}^3 = 1 \hspace{1cm} 8679f9097b Jeff*0655 0656 The function for heat and moisture assures non-vanishing heat and 0657 moisture fluxes as the wind speed approaches zero. 0658 0659 For a stable surface layer, the stability functions are the 0660 observationally based functions of :cite:`clarke:70`, slightly modified for the momemtum 0661 flux: 0662 0663 .. math:: 0664 0665 {\phi_m} = \frac{ 1 + 5 {{\zeta}_1} }{ 1 + 0.00794 {\zeta}_1 0666 (1+ 5 {\zeta}_1) } \hspace{1cm} ; \hspace{1cm} 0667 {\phi_h} = \frac{ 1 + 5 {{\zeta}_1} }{ 1 + 0.00794 {\zeta} 0bad585a21 Navi*0668 (1+ 5 {{\zeta}_1}) } 8679f9097b Jeff*0669 0670 The moisture flux also depends on a specified evapotranspiration 0671 coefficient, set to unity over oceans and dependant on the 0672 climatological ground wetness over land. 0673 0674 Once all the diffusion coefficients are calculated, the diffusion 0675 equations are solved numerically using an implicit backward operator. 0676 0677 Atmospheric Boundary Layer 0678 ########################## 0679 0680 The depth of the atmospheric boundary layer (ABL) is diagnosed by the 0681 parameterization as the level at which the turbulent kinetic energy is 0682 reduced to a tenth of its maximum near surface value. The vertical 0683 structure of the ABL is explicitly resolved by the lowest few (3-8) 0684 model layers. 0685 0686 Surface Energy Budget 0687 ##################### 0688 0689 The ground temperature equation is solved as part of the turbulence 0690 package using a backward implicit time differencing scheme: 0691 0bad585a21 Navi*0692 .. math:: C_g\pp{T_g}{t} = R_{\rm sw} - R_{\rm lw} + Q_{\rm ice} - H - LE 8679f9097b Jeff*0693 0bad585a21 Navi*0694 where :math:`R_{\rm sw}` is the net surface downward shortwave radiative 0695 flux and :math:`R_{\rm lw}` is the net surface upward longwave radiative 8679f9097b Jeff*0696 flux. 0697 0698 :math:`H` is the upward sensible heat flux, given by: 0699 0700 .. math:: 0bad585a21 Navi*0701 {H} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{\rm surface} - \theta_{\rm NLAY}) 0702 \hspace{1cm}\text{where}: \hspace{.2cm}C_H = C_u C_t 8679f9097b Jeff*0703 0704 where :math:`\rho` = the atmospheric density at the surface, 0705 :math:`c_{p}` is the specific heat of air at constant pressure, and 0706 :math:`\theta` represents the potential temperature of the surface and 0707 of the lowest :math:`\sigma`-level, respectively. 0708 0bad585a21 Navi*0709 The upward latent heat flux, :math:`\textrm{LE}`, is given by 8679f9097b Jeff*0710 0711 .. math:: 0712 0bad585a21 Navi*0713 \textrm{LE} = \rho \beta L C_{H} W_s (q_{\rm surface} - q_{\rm NLAY}) 0714 \hspace{1cm}\text{where}: \hspace{.2cm}C_H = C_u C_t 8679f9097b Jeff*0715 0716 where :math:`\beta` is the fraction of the potential evapotranspiration 0717 actually evaporated, L is the latent heat of evaporation, and 0bad585a21 Navi*0718 :math:`q_{\rm surface}` and :math:`q_{\rm NLAY}` are the specific humidity of 8679f9097b Jeff*0719 the surface and of the lowest :math:`\sigma`-level, respectively. 0720 0bad585a21 Navi*0721 The heat conduction through sea ice, :math:`Q_{\rm ice}`, is given by 8679f9097b Jeff*0722 0bad585a21 Navi*0723 .. math:: {Q_{\rm ice}} = \frac{C_{\rm ti} }{ H_i} (T_i-T_g) 8679f9097b Jeff*0724 0bad585a21 Navi*0725 where :math:`C_{\rm ti}` is the thermal conductivity of ice, :math:`H_i` is 0726 the ice thickness, assumed to be 3 m where sea ice 8679f9097b Jeff*0727 is present, :math:`T_i` is 273 degrees Kelvin, and :math:`T_g` is the 0728 surface temperature of the ice. 0729 0730 :math:`C_g` is the total heat capacity of the ground, obtained by 0731 solving a heat diffusion equation for the penetration of the diurnal 0bad585a21 Navi*0732 cycle into the ground (Blackadar 1977), and is given by: 8679f9097b Jeff*0733 0734 .. math:: 0735 0736 C_g = \sqrt{ \frac{\lambda C_s }{ 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3} 0bad585a21 Navi*0737 \frac{86400}{2\pi} } 8679f9097b Jeff*0738 0739 Here, the thermal conductivity, :math:`\lambda`, is equal to 0bad585a21 Navi*0740 :math:`2\times10^{-3}` :math:`\frac{\text{ly}}{\text{sec}}\frac{\text{cm}}{\text{K}}`, 0741 the angular velocity of the earth, :math:`\omega`, is 0742 written as 86400 sec day\ :sup:`--1` divided by :math:`2 \pi` 0743 radians day\ :sup:`--1`, and the expression for :math:`C_s`, the heat capacity per unit 8679f9097b Jeff*0744 volume at the surface, is a function of the ground wetness, :math:`W`. 0745 0746 Land Surface Processes: 0747 0748 Surface Type 0749 ############ 0750 0751 The fizhi package surface Types are designated using the Koster-Suarez 0752 :cite:`ks:91,ks:92` Land Surface Model (LSM) mosaic philosophy which allows multiple** Warning **
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0753 “tiles”, or multiple surface types, in any one grid cell. The 0754 Koster-Suarez LSM surface type classifications are shown in :numref:`tab_phys_pkg_fizhi_surface_type_designation`. The surface types and the percent of the grid cell 0755 occupied by any surface type were derived from the surface 0756 classification of :cite:`deftow:94`, and information about the location of permanent ice 0757 was obtained from the classifications of :cite:`dorsell:89`. The surface type map for a 0758 :math:`1^\circ` grid is shown in :numref:`fig_phys_pkg_fizhi_surftype`. The 0759 determination of the land or sea category of surface type was made from** Warning **
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0760 NCAR’s 10 minute by 10 minute Navy topography dataset, which includes 0761 information about the percentage of water-cover at any point. The data** Warning **
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0762 were averaged to the model’s grid resolutions, and any grid-box whose 0763 averaged water percentage was :math:`\geq 60 \%` was defined as a water 0764 point. The Land-Water designation was further modified subjectively to 0765 ensure sufficient representation from small but isolated land and water 0766 regions. 0767 0768 .. table:: Surface Type Designation 0769 :name: tab_phys_pkg_fizhi_surface_type_designation 0770 0771 +--------+-----------------------------+ 0772 | Type | Vegetation Designation | 0773 +========+=============================+ 0774 | 1 | Broadleaf Evergreen Trees | 0775 +--------+-----------------------------+ 0776 | 2 | Broadleaf Deciduous Trees | 0777 +--------+-----------------------------+ 0778 | 3 | Needleleaf Trees | 0779 +--------+-----------------------------+ 0780 | 4 | Ground Cover | 0781 +--------+-----------------------------+ 0782 | 5 | Broadleaf Shrubs | 0783 +--------+-----------------------------+ 0784 | 6 | Dwarf Trees (Tundra) | 0785 +--------+-----------------------------+ 0786 | 7 | Bare Soil | 0787 +--------+-----------------------------+ 0788 | 8 | Desert (Bright) | 0789 +--------+-----------------------------+ 0790 | 9 | Glacier | 0791 +--------+-----------------------------+ 0792 | 10 | Desert (Dark) | 0793 +--------+-----------------------------+ 0794 | 100 | Ocean | 0795 +--------+-----------------------------+ 0796 0797 0798 0799 .. figure:: figs/surftype.* 0800 :width: 70% 0801 :align: center 0802 :alt: surface type combinations 0803 :name: fig_phys_pkg_fizhi_surftype 0804 0805 Surface type combinations 0806 0807 0808 0809 Surface Roughness 0810 ################# 0811 0812 The surface roughness length over oceans is computed iteratively with 0813 the wind stress by the surface layer parameterization :cite:`helfschu:95`. It employs an 0814 interpolation between the functions of :cite:`larpond:81` for high winds and of :cite:`kondo:75` for weak 0815 winds. 0816 0817 0818 Albedo 0819 ###### 0820** Warning **
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0821 The surface albedo computation, described in , employs the “two stream”** Warning **
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0822 approximation used in Sellers’ (1987) Simple Biosphere (SiB) Model which 0823 distinguishes between the direct and diffuse albedos in the visible and 0824 in the near infra-red spectral ranges. The albedos are functions of the 0825 observed leaf area index (a description of the relative orientation of 0826 the leaves to the sun), the greenness fraction, the vegetation type, and 0827 the solar zenith angle. Modifications are made to account for the 0828 presence of snow, and its depth relative to the height of the vegetation 0829 elements. 0830 0831 Gravity Wave Drag 0832 ################# 0833 0834 The fizhi package employs the gravity wave drag scheme of :cite:`zhouetal:95`. This scheme 0835 is a modified version of Vernekar et al. (1992), which was based on 0836 Alpert et al. (1988) and Helfand et al. (1987). In this version, the 0837 gravity wave stress at the surface is based on that derived by 0838 Pierrehumbert (1986) and is given by: 0839 0840 .. math:: 0bad585a21 Navi*0841 |\vec{\tau}_{\rm sfc}| = \frac{\rho U^3}{N \ell^*} \left( \frac{F_r^2}{1+F_r^2}\right) 8679f9097b Jeff*0842 0843 0844 where :math:`F_r = N h /U` is the Froude number, :math:`N` is the *Brunt 0845 - Visl* frequency, :math:`U` is the surface wind speed, :math:`h` is 0846 the standard deviation of the sub-grid scale orography, and 0847 :math:`\ell^*` is the wavelength of the monochromatic gravity wave in 0848 the direction of the low-level wind. A modification introduced by Zhou 0849 et al. allows for the momentum flux to escape through the top of the 0850 model, although this effect is small for the current 70-level model. The 0851 subgrid scale standard deviation is defined by :math:`h`, and is not 0852 allowed to exceed 400 m. 0853 0854 The effects of using this scheme within a GCM are shown in :cite:`taksz:96`. Experiments 0855 using the gravity wave drag parameterization yielded significant and 0856 beneficial impacts on both the time-mean flow and the transient 0857 statistics of the a GCM climatology, and have eliminated most of the 0858 worst dynamically driven biases in the a GCM simulation. An examination 0859 of the angular momentum budget during climate runs indicates that the 0860 resulting gravity wave torque is similar to the data-driven torque 0861 produced by a data assimilation which was performed without gravity wave 0862 drag. It was shown that the inclusion of gravity wave drag results in 0863 large changes in both the mean flow and in eddy fluxes. The result is a 0864 more accurate simulation of surface stress (through a reduction in the 0865 surface wind strength), of mountain torque (through a redistribution of 0866 mean sea-level pressure), and of momentum convergence (through a 0867 reduction in the flux of westerly momentum by transient flow eddies). 0868 0bad585a21 Navi*0869 Boundary Conditions and other Input Data 0870 ######################################## 8679f9097b Jeff*0871 0872 Required fields which are not explicitly predicted or diagnosed during 0873 model execution must either be prescribed internally or obtained from 0874 external data sets. In the fizhi package these fields include: sea 0875 surface temperature, sea ice estent, surface geopotential variance, 0876 vegetation index, and the radiation-related background levels of: ozone, 0877 carbon dioxide, and stratospheric moisture. 0878** Warning **
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0879 Boundary condition data sets are available at the model’s resolutions 0880 for either climatological or yearly varying conditions. Any frequency of 0881 boundary condition data can be used in the fizhi package; however, the 0882 current selection of data is summarized in :numref:`tab_phys_pkg_fizhi_inputs`. The 0883 time mean values are interpolated during each model timestep to the 0884 current time. 0885 0886 .. table:: Boundary conditions and other input data used in the fizhi package. Also noted are the current years and frequencies available. 0887 :name: tab_phys_pkg_fizhi_inputs 0888 0889 +-----------------------------------------+-----------+-----------------------------+ 0890 | **Fizhi Input Datasets** | 0891 +-----------------------------------------+-----------+-----------------------------+ 0892 | Sea Ice Extent | monthly | 1979-current, climatology | 0893 +-----------------------------------------+-----------+-----------------------------+ 0894 | Sea Ice Extent | weekly | 1982-current, climatology | 0895 +-----------------------------------------+-----------+-----------------------------+ 0896 | Sea Surface Temperature | monthly | 1979-current, climatology | 0897 +-----------------------------------------+-----------+-----------------------------+ 0898 | Sea Surface Temperature | weekly | 1982-current, climatology | 0899 +-----------------------------------------+-----------+-----------------------------+ 0900 | Zonally Averaged Upper-Level Moisture | monthly | climatology | 0901 +-----------------------------------------+-----------+-----------------------------+ 0902 | Zonally Averaged Ozone Concentration | monthly | climatology | 0903 +-----------------------------------------+-----------+-----------------------------+ 0904 0905 0906 Topography and Topography Variance 0907 ################################## 0908 0909 Surface geopotential heights are provided from an averaging of the Navy 0910 10 minute by 10 minute dataset supplied by the National Center for** Warning **
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0911 Atmospheric Research (NCAR) to the model’s grid resolution. The original 0912 topography is first rotated to the proper grid-orientation which is 0913 being run, and then averages the data to the model resolution. 0914 0915 The standard deviation of the subgrid-scale topography is computed by** Warning **
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0916 interpolating the 10 minute data to the model’s resolution and 0917 re-interpolating back to the 10 minute by 10 minute resolution. The 0918 sub-grid scale variance is constructed based on this smoothed dataset. 0919 0920 0921 Upper Level Moisture 0922 #################### 0923 0924 The fizhi package uses climatological water vapor data above 100 mb from 0925 the Stratospheric Aerosol and Gas Experiment (SAGE) as input into the** Warning **
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0926 model’s radiation packages. The SAGE data is archived as monthly zonal 0927 means at :math:`5^\circ` latitudinal resolution. The data is** Warning **
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0928 interpolated to the model’s grid location and current time, and blended** Warning **
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0929 with the GCM’s moisture data. Below 300 mb, the model’s moisture data is 0930 used. Above 100 mb, the SAGE data is used. Between 100 and 300 mb, a 0931 linear interpolation (in pressure) is performed using the data from SAGE 0932 and the GCM. 0933 9ce7d74115 Jeff*0934 0935 .. _fizhi_diagnostics: 0936 8679f9097b Jeff*0937 Fizhi Diagnostics 0938 +++++++++++++++++ 0939 0bad585a21 Navi*0940 Fizhi Diagnostic Menu: 8679f9097b Jeff*0941 0942 +--------+----------------------------------+---------+--------------------------------------------------+ 0943 | NAME | UNITS | LEVELS | DESCRIPTION | 0944 +--------+----------------------------------+---------+--------------------------------------------------+ 0945 | UFLUX | N m\ :sup:`--2` | 1 | Surface U-Wind Stress on the atmosphere | 0946 +--------+----------------------------------+---------+--------------------------------------------------+ 0947 | VFLUX | N m\ :sup:`--2` | 1 | Surface V-Wind Stress on the atmosphere | 0948 +--------+----------------------------------+---------+--------------------------------------------------+ 0949 | HFLUX | W m\ :sup:`--2` | 1 | Surface Flux of Sensible Heat | 0950 +--------+----------------------------------+---------+--------------------------------------------------+ 0951 | EFLUX | W m\ :sup:`--2` | 1 | Surface Flux of Latent Heat | 0952 +--------+----------------------------------+---------+--------------------------------------------------+ 0953 | QICE | W m\ :sup:`--2` | 1 | Heat Conduction through Sea-Ice | 0954 +--------+----------------------------------+---------+--------------------------------------------------+ 0955 | RADLWG | W m\ :sup:`--2` | 1 | Net upward LW flux at the ground | 0956 +--------+----------------------------------+---------+--------------------------------------------------+ 0957 | RADSWG | W m\ :sup:`--2` | 1 | Net downward SW flux at the ground | 0958 +--------+----------------------------------+---------+--------------------------------------------------+ 0959 | RI | dimensionless | Nrphys | Richardson Number | 0960 +--------+----------------------------------+---------+--------------------------------------------------+ 0961 | CT | dimensionless | 1 | Surface Drag coefficient for T and Q | 0962 +--------+----------------------------------+---------+--------------------------------------------------+ 0963 | CU | dimensionless | 1 | Surface Drag coefficient for U and V | 0964 +--------+----------------------------------+---------+--------------------------------------------------+ 0965 | ET | m\ :sup:`2` s\ :sup:`--1` | Nrphys | Diffusivity coefficient for T and Q | 0966 +--------+----------------------------------+---------+--------------------------------------------------+ 0967 | EU | m\ :sup:`2` s\ :sup:`--1` | Nrphys | Diffusivity coefficient for U and V | 0968 +--------+----------------------------------+---------+--------------------------------------------------+ 0969 | TURBU | m s\ :sup:`--1` day\ :sup:`--1` | Nrphys | U-Momentum Changes due to Turbulence | 0970 +--------+----------------------------------+---------+--------------------------------------------------+ 0971 | TURBV | m s\ :sup:`--1` day\ :sup:`--1` | Nrphys | V-Momentum Changes due to Turbulence | 0972 +--------+----------------------------------+---------+--------------------------------------------------+ 0973 | TURBT | deg day\ :sup:`--1` | Nrphys | Temperature Changes due to Turbulence | 0974 +--------+----------------------------------+---------+--------------------------------------------------+ 0975 | TURBQ | g/kg/day | Nrphys | Specific Humidity Changes due to Turbulence | 0976 +--------+----------------------------------+---------+--------------------------------------------------+ 0977 | MOISTT | deg day\ :sup:`--1` | Nrphys | Temperature Changes due to Moist Processes | 0978 +--------+----------------------------------+---------+--------------------------------------------------+ 0979 | MOISTQ | g/kg/day | Nrphys | Specific Humidity Changes due to Moist Processes | 0980 +--------+----------------------------------+---------+--------------------------------------------------+ 0981 | RADLW | deg day\ :sup:`--1` | Nrphys | Net Longwave heating rate for each level | 0982 +--------+----------------------------------+---------+--------------------------------------------------+ 0983 | RADSW | deg day\ :sup:`--1` | Nrphys | Net Shortwave heating rate for each level | 0984 +--------+----------------------------------+---------+--------------------------------------------------+ 0985 | PREACC | mm/day | 1 | Total Precipitation | 0986 +--------+----------------------------------+---------+--------------------------------------------------+ 0987 | PRECON | mm/day | 1 | Convective Precipitation | 0988 +--------+----------------------------------+---------+--------------------------------------------------+ 0989 | TUFLUX | N m\ :sup:`--2` | Nrphys | Turbulent Flux of U-Momentum | 0990 +--------+----------------------------------+---------+--------------------------------------------------+ 0991 | TVFLUX | N m\ :sup:`--2` | Nrphys | Turbulent Flux of V-Momentum | 0992 +--------+----------------------------------+---------+--------------------------------------------------+ 0993 | TTFLUX | W m\ :sup:`--2` | Nrphys | Turbulent Flux of Sensible Heat | 0994 +--------+----------------------------------+---------+--------------------------------------------------+ 0995 0996 0997 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 0998 | NAME | UNITS | LEVELS | DESCRIPTION | 0999 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1000 | TQFLUX | W m\ :sup:`--2` | Nrphys | Turbulent Flux of Latent Heat | 1001 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1002 | CN | dimensionless | 1 | Neutral Drag Coefficient | 1003 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1004 | WINDS | m s\ :sup:`--1` | 1 | Surface Wind Speed | 1005 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1006 | DTSRF | deg | 1 | Air/Surface virtual temperature difference | 1007 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1008 | TG | deg | 1 | Ground temperature | 1009 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1010 | TS | deg | 1 | Surface air temperature (Adiabatic from lowest model layer) | 1011 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1012 | DTG | deg | 1 | Ground temperature adjustment | 1013 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1014 | QG | g kg\ :sup:`--1` | 1 | Ground specific humidity | 1015 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1016 | QS | g kg\ :sup:`--1` | 1 | Saturation surface specific humidity | 1017 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1018 | TGRLW | deg | 1 | Instantaneous ground temperature used as input to the Longwave radiation subroutine | 1019 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1020 | ST4 | W m\ :sup:`--2` | 1 | Upward Longwave flux at the ground (:math:`\sigma T^4`) | 1021 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1022 | OLR | W m\ :sup:`--2` | 1 | Net upward Longwave flux at the top of the model | 1023 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1024 | OLRCLR | W m\ :sup:`--2` | 1 | Net upward clearsky Longwave flux at the top of the model | 1025 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1026 | LWGCLR | W m\ :sup:`--2` | 1 | Net upward clearsky Longwave flux at the ground | 1027 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1028 | LWCLR | deg day\ :sup:`--1` | Nrphys | Net clearsky Longwave heating rate for each level | 1029 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1030 | TLW | deg | Nrphys | Instantaneous temperature used as input to the Longwave radiation subroutine | 1031 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1032 | SHLW | g g\ :sup:`--1` | Nrphys | Instantaneous specific humidity used as input to the Longwave radiation subroutine | 1033 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1034 | OZLW | g g\ :sup:`--1` | Nrphys | Instantaneous ozone used as input to the Longwave radiation subroutine | 1035 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1036 | CLMOLW | :math:`0-1` | Nrphys | Maximum overlap cloud fraction used in the Longwave radiation subroutine | 1037 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1038 | CLDTOT | :math:`0-1` | Nrphys | Total cloud fraction used in the Longwave and Shortwave radiation subroutines | 1039 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1040 | LWGDOWN| W m\ :sup:`--2` | 1 | Downwelling Longwave radiation at the ground | 1041 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1042 | GWDT | deg day\ :sup:`--1` | Nrphys | Temperature tendency due to Gravity Wave Drag | 1043 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1044 | RADSWT | W m\ :sup:`--2` | 1 | Incident Shortwave radiation at the top of the atmosphere | 1045 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1046 | TAUCLD | per 100 mb | Nrphys | Counted Cloud Optical Depth (non-dimensional) per 100 mb | 1047 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1048 | TAUCLDC| Number | Nrphys | Cloud Optical Depth Counter | 1049 +--------+---------------------+---------+-------------------------------------------------------------------------------------+ 1050 1051 +--------+-----------------+----------+---------------------------------------------------------------+ 1052 | NAME | UNITS | LEVELS | Description | 1053 +--------+-----------------+----------+---------------------------------------------------------------+ 1054 | CLDLOW | 0-1 | Nrphys | Low-Level ( 1000-700 hPa) Cloud Fraction (0-1) | 1055 +--------+-----------------+----------+---------------------------------------------------------------+ 1056 | EVAP | mm/day | 1 | Surface evaporation | 1057 +--------+-----------------+----------+---------------------------------------------------------------+ 1058 | DPDT | hPa/day | 1 | Surface Pressure time-tendency | 1059 +--------+-----------------+----------+---------------------------------------------------------------+ 1060 | UAVE | m/sec | Nrphys | Average U-Wind | 1061 +--------+-----------------+----------+---------------------------------------------------------------+ 1062 | VAVE | m/sec | Nrphys | Average V-Wind | 1063 +--------+-----------------+----------+---------------------------------------------------------------+ 1064 | TAVE | deg | Nrphys | Average Temperature | 1065 +--------+-----------------+----------+---------------------------------------------------------------+ 1066 | QAVE | g/kg | Nrphys | Average Specific Humidity | 1067 +--------+-----------------+----------+---------------------------------------------------------------+ 1068 | OMEGA | hPa/day | Nrphys | Vertical Velocity | 1069 +--------+-----------------+----------+---------------------------------------------------------------+ 1070 | DUDT | m/sec/day | Nrphys | Total U-Wind tendency | 1071 +--------+-----------------+----------+---------------------------------------------------------------+ 1072 | DVDT | m/sec/day | Nrphys | Total V-Wind tendency | 1073 +--------+-----------------+----------+---------------------------------------------------------------+ 1074 | DTDT | deg/day | Nrphys | Total Temperature tendency | 1075 +--------+-----------------+----------+---------------------------------------------------------------+ 1076 | DQDT | g/kg/day | Nrphys | Total Specific Humidity tendency | 1077 +--------+-----------------+----------+---------------------------------------------------------------+ 1078 | VORT | 10^{-4}/sec | Nrphys | Relative Vorticity | 1079 +--------+-----------------+----------+---------------------------------------------------------------+ 1080 | DTLS | deg/day | Nrphys | Temperature tendency due to Stratiform Cloud Formation | 1081 +--------+-----------------+----------+---------------------------------------------------------------+ 1082 | DQLS | g/kg/day | Nrphys | Specific Humidity tendency due to Stratiform Cloud Formation | 1083 +--------+-----------------+----------+---------------------------------------------------------------+ 1084 | USTAR | m/sec | 1 | Surface USTAR wind | 1085 +--------+-----------------+----------+---------------------------------------------------------------+ 1086 | Z0 | m | 1 | Surface roughness | 1087 +--------+-----------------+----------+---------------------------------------------------------------+ 1088 | FRQTRB | 0-1 | Nrphys-1 | Frequency of Turbulence | 1089 +--------+-----------------+----------+---------------------------------------------------------------+ 1090 | PBL | mb | 1 | Planetary Boundary Layer depth | 1091 +--------+-----------------+----------+---------------------------------------------------------------+ 1092 | SWCLR | deg/day | Nrphys | Net clearsky Shortwave heating rate for each level | 1093 +--------+-----------------+----------+---------------------------------------------------------------+ 1094 | OSR | W m\ :sup:`--2` | 1 | Net downward Shortwave flux at the top of the model | 1095 +--------+-----------------+----------+---------------------------------------------------------------+ 1096 | OSRCLR | W m\ :sup:`--2` | 1 | Net downward clearsky Shortwave flux at the top of the model | 1097 +--------+-----------------+----------+---------------------------------------------------------------+ 1098 | CLDMAS | kg / m^2 | Nrphys | Convective cloud mass flux | 1099 +--------+-----------------+----------+---------------------------------------------------------------+ 1100 | UAVE | m/sec | Nrphys | Time-averaged :math:`u`-Wind | 1101 +--------+-----------------+----------+---------------------------------------------------------------+ 1102 1103 1104 1105 +--------+-------------------+--------+---------------------------------------------------------------+ 1106 | NAME | UNITS | LEVELS | DESCRIPTION | 1107 +--------+-------------------+--------+---------------------------------------------------------------+ 1108 | VAVE | m/sec | Nrphys | Time-averaged :math:`v`-Wind | 1109 +--------+-------------------+--------+---------------------------------------------------------------+ 1110 | TAVE | deg | Nrphys | Time-averaged Temperature` | 1111 +--------+-------------------+--------+---------------------------------------------------------------+ 1112 | QAVE | g/g | Nrphys | Time-averaged Specific Humidity | 1113 +--------+-------------------+--------+---------------------------------------------------------------+ 1114 | RFT | deg/day | Nrphys | Temperature tendency due Rayleigh Friction | 1115 +--------+-------------------+--------+---------------------------------------------------------------+ 1116 | PS | mb | 1 | Surface Pressure | 1117 +--------+-------------------+--------+---------------------------------------------------------------+ 1118 | QQAVE | (m/sec)\ :sup:`2` | Nrphys | Time-averaged Turbulent Kinetic Energy | 1119 +--------+-------------------+--------+---------------------------------------------------------------+ 1120 | SWGCLR | W m\ :sup:`--2` | 1 | Net downward clearsky Shortwave flux at the ground | 1121 +--------+-------------------+--------+---------------------------------------------------------------+ 1122 | PAVE | mb | 1 | Time-averaged Surface Pressure | 1123 +--------+-------------------+--------+---------------------------------------------------------------+ 1124 | DIABU | m/sec/day | Nrphys | Total Diabatic forcing on :math:`u`-Wind | 1125 +--------+-------------------+--------+---------------------------------------------------------------+ 1126 | DIABV | m/sec/day | Nrphys | Total Diabatic forcing on :math:`v`-Wind | 1127 +--------+-------------------+--------+---------------------------------------------------------------+ 1128 | DIABT | deg/day | Nrphys | Total Diabatic forcing on Temperature | 1129 +--------+-------------------+--------+---------------------------------------------------------------+ 1130 | DIABQ | g/kg/day | Nrphys | Total Diabatic forcing on Specific Humidity | 1131 +--------+-------------------+--------+---------------------------------------------------------------+ 1132 | RFU | m/sec/day | Nrphys | U-Wind tendency due to Rayleigh Friction | 1133 +--------+-------------------+--------+---------------------------------------------------------------+ 1134 | RFV | m/sec/day | Nrphys | V-Wind tendency due to Rayleigh Friction | 1135 +--------+-------------------+--------+---------------------------------------------------------------+ 1136 | GWDU | m/sec/day | Nrphys | U-Wind tendency due to Gravity Wave Drag | 1137 +--------+-------------------+--------+---------------------------------------------------------------+ 1138 | GWDU | m/sec/day | Nrphys | V-Wind tendency due to Gravity Wave Drag | 1139 +--------+-------------------+--------+---------------------------------------------------------------+ 1140 | GWDUS | N m\ :sup:`--2` | 1 | U-Wind Gravity Wave Drag Stress at Surface | 1141 +--------+-------------------+--------+---------------------------------------------------------------+ 1142 | GWDVS | N m\ :sup:`--2` | 1 | V-Wind Gravity Wave Drag Stress at Surface | 1143 +--------+-------------------+--------+---------------------------------------------------------------+ 1144 | GWDUT | N m\ :sup:`--2` | 1 | U-Wind Gravity Wave Drag Stress at Top | 1145 +--------+-------------------+--------+---------------------------------------------------------------+ 1146 | GWDVT | N m\ :sup:`--2` | 1 | V-Wind Gravity Wave Drag Stress at Top | 1147 +--------+-------------------+--------+---------------------------------------------------------------+ 1148 | LZRAD | mg/kg | Nrphys | Estimated Cloud Liquid Water used in Radiation | 1149 +--------+-------------------+--------+---------------------------------------------------------------+ 1150 1151 +--------+-------------------+--------+-----------------------------------------------------+ 1152 | NAME | UNITS | LEVELS | DESCRIPTION | 1153 +--------+-------------------+--------+-----------------------------------------------------+ 1154 | SLP | mb | 1 | Time-averaged Sea-level Pressure | 1155 +--------+-------------------+--------+-----------------------------------------------------+ 1156 | CLDFRC | 0-1 | 1 | Total Cloud Fraction | 1157 +--------+-------------------+--------+-----------------------------------------------------+ 1158 | TPW | gm cm\ :sup:`--2` | 1 | Precipitable water | 1159 +--------+-------------------+--------+-----------------------------------------------------+ 1160 | U2M | m/sec | 1 | U-Wind at 2 meters | 1161 +--------+-------------------+--------+-----------------------------------------------------+ 1162 | V2M | m/sec | 1 | V-Wind at 2 meters | 1163 +--------+-------------------+--------+-----------------------------------------------------+ 1164 | T2M | deg | 1 | Temperature at 2 meters | 1165 +--------+-------------------+--------+-----------------------------------------------------+ 1166 | Q2M | g/kg | 1 | Specific Humidity at 2 meters | 1167 +--------+-------------------+--------+-----------------------------------------------------+ 1168 | U10M | m/sec | 1 | U-Wind at 10 meters | 1169 +--------+-------------------+--------+-----------------------------------------------------+ 1170 | V10M | m/sec | 1 | V-Wind at 10 meters | 1171 +--------+-------------------+--------+-----------------------------------------------------+ 1172 | T10M | deg | 1 | Temperature at 10 meters | 1173 +--------+-------------------+--------+-----------------------------------------------------+ 1174 | Q10M | g/kg | 1 | Specific Humidity at 10 meters | 1175 +--------+-------------------+--------+-----------------------------------------------------+ 1176 | DTRAIN | kg m\ :sup:`--2` | Nrphys | Detrainment Cloud Mass Flux | 1177 +--------+-------------------+--------+-----------------------------------------------------+ 1178 | QFILL | g/kg/day | Nrphys | Filling of negative specific humidity | 1179 +--------+-------------------+--------+-----------------------------------------------------+ 1180 | DTCONV | deg/sec | Nr | Temp Change due to Convection | 1181 +--------+-------------------+--------+-----------------------------------------------------+ 1182 | DQCONV | g/kg/sec | Nr | Specific Humidity Change due to Convection | 1183 +--------+-------------------+--------+-----------------------------------------------------+ 1184 | RELHUM | percent | Nr | Relative Humidity | 1185 +--------+-------------------+--------+-----------------------------------------------------+ 1186 | PRECLS | g/m^2/sec | 1 | Large Scale Precipitation | 1187 +--------+-------------------+--------+-----------------------------------------------------+ 1188 | ENPREC | J/g | 1 | Energy of Precipitation (snow, rain Temp) | 1189 +--------+-------------------+--------+-----------------------------------------------------+ 1190 1191 1192 Fizhi Diagnostic Description 1193 ++++++++++++++++++++++++++++ 1194 1195 In this section we list and describe the diagnostic quantities available 1196 within the GCM. The diagnostics are listed in the order that they appear 1197 in the Diagnostic Menu, Section [sec:pkg:fizhi:diagnostics]. In all 1198 cases, each diagnostic as currently archived on the output datasets is 1199 time-averaged over its diagnostic output frequency: 1200 1201 .. math:: {\bf DIAGNOSTIC} = \frac{1}{TTOT} \sum_{t=1}^{t=TTOT} diag(t) 1202 1203 where :math:`TTOT = \frac{ {\bf NQDIAG} }{\Delta t}`, **NQDIAG** is the 1204 output frequency of the diagnostic, and :math:`\Delta t` is the timestep 1205 over which the diagnostic is updated. 1206 1207 Surface Zonal Wind Stress on the Atmosphere (:math:`Newton/m^2`) 1208 ################################################################ 1209 1210 The zonal wind stress is the turbulent flux of zonal momentum from the 1211 surface. 1212 1213 .. math:: {\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u 1214 1215 where :math:`\rho` = the atmospheric density at the surface, 1216 :math:`C_{D}` is the surface drag coefficient, :math:`C_u` is the 1217 dimensionless surface exchange coefficient for momentum (see diagnostic 1218 number 10), :math:`W_s` is the magnitude of the surface layer wind, and 1219 :math:`u` is the zonal wind in the lowest model layer. 1220 1221 Surface Meridional Wind Stress on the Atmosphere (:math:`Newton/m^2`) 1222 ###################################################################### 1223 1224 The meridional wind stress is the turbulent flux of meridional 1225 momentum from the surface. 1226 1227 .. math:: {\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u 1228 1229 where :math:`\rho` = the atmospheric density at the surface, 1230 :math:`C_{D}` is the surface drag coefficient, :math:`C_u` is the 1231 dimensionless surface exchange coefficient for momentum (see diagnostic 1232 number 10), :math:`W_s` is the magnitude of the surface layer wind, and 1233 :math:`v` is the meridional wind in the lowest model layer. 1234 1235 Surface Flux of Sensible Heat (W m\ :sup:`--2`) 1236 ################################################ 1237 1238 The turbulent flux of sensible heat from the surface to the atmosphere 1239 is a function of the gradient of virtual potential temperature and the 1240 eddy exchange coefficient: 1241 1242 .. math:: 1243 0bad585a21 Navi*1244 {\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{\rm surface} - \theta_{Nrphys}) 8679f9097b Jeff*1245 \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t 1246 1247 where :math:`\rho` = the atmospheric density at the surface, 1248 :math:`c_{p}` is the specific heat of air, :math:`C_{H}` is the 1249 dimensionless surface heat transfer coefficient, :math:`W_s` is the 1250 magnitude of the surface layer wind, :math:`C_u` is the dimensionless 1251 surface exchange coefficient for momentum (see diagnostic number 10), 1252 :math:`C_t` is the dimensionless surface exchange coefficient for heat 1253 and moisture (see diagnostic number 9), and :math:`\theta` is the 1254 potential temperature at the surface and at the bottom model level. 1255 1256 Surface Flux of Latent Heat (:math:`Watts/m^2`) 1257 ############################################### 1258 1259 The turbulent flux of latent heat from the surface to the atmosphere 1260 is a function of the gradient of moisture, the potential 1261 evapotranspiration fraction and the eddy exchange coefficient: 1262 1263 .. math:: 1264 0bad585a21 Navi*1265 {\bf EFLUX} = \rho \beta L C_{H} W_s (q_{\rm surface} - q_{Nrphys}) 8679f9097b Jeff*1266 \hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t 1267 1268 where :math:`\rho` = the atmospheric density at the surface, 1269 :math:`\beta` is the fraction of the potential evapotranspiration 1270 actually evaporated, L is the latent heat of evaporation, :math:`C_{H}` 1271 is the dimensionless surface heat transfer coefficient, :math:`W_s` is 1272 the magnitude of the surface layer wind, :math:`C_u` is the 1273 dimensionless surface exchange coefficient for momentum (see diagnostic 1274 number 10), :math:`C_t` is the dimensionless surface exchange 1275 coefficient for heat and moisture (see diagnostic number 9), and 0bad585a21 Navi*1276 :math:`q_{\rm surface}` and :math:`q_{Nrphys}` are the specific humidity at 8679f9097b Jeff*1277 the surface and at the bottom model level, respectively. 1278 1279 Heat Conduction Through Sea Ice (:math:`Watts/m^2`) 1280 ################################################### 1281 1282 Over sea ice there is an additional source of energy at the surface due 1283 to the heat conduction from the relatively warm ocean through the sea 1284 ice. The heat conduction through sea ice represents an additional energy 1285 source term for the ground temperature equation. 1286 1287 .. math:: {\bf QICE} = \frac{C_{ti}}{H_i} (T_i-T_g) 1288 1289 where :math:`C_{ti}` is the thermal conductivity of ice, :math:`H_i` is 1290 the ice thickness, assumed to be :math:`3 \hspace{.1cm} m` where sea ice 1291 is present, :math:`T_i` is 273 degrees Kelvin, and :math:`T_g` is the 1292 temperature of the sea ice. 1293 1294 NOTE: QICE is not available through model version 5.3, but is 1295 available in subsequent versions. 1296 1297 1298 Net upward Longwave Flux at the surface (:math:`Watts/m^2`) 1299 ########################################################### 1300 1301 .. math:: 1302 1303 \begin{aligned} 1304 {\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ 1305 & = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow\end{aligned} 1306 1307 where Nrphys+1 indicates the lowest model edge-level, or 1308 :math:`p = p_{surf}`. :math:`F_{LW}^\uparrow` is the upward Longwave 1309 flux and :math:`F_{LW}^\downarrow` is the downward Longwave flux. 1310 1311 1312 Net downard shortwave Flux at the surface (:math:`Watts/m^2`) 1313 ############################################################# 1314 1315 .. math:: 1316 1317 \begin{aligned} 1318 {\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ 1319 & = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow\end{aligned} 1320 1321 where Nrphys+1 indicates the lowest model edge-level, or 1322 :math:`p = p_{surf}`. :math:`F_{SW}^\downarrow` is the downward 1323 Shortwave flux and :math:`F_{SW}^\uparrow` is the upward Shortwave flux. 1324 1325 Richardson number (:math:`dimensionless`) 1326 ######################################### 1327 1328 The non-dimensional stability indicator is the ratio of the buoyancy 1329 to the shear: 1330 1331 .. math:: 1332 1333 {\bf RI} = \frac{ \frac{g}{\theta_v} \pp {\theta_v}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 } 1334 = \frac{c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} }{ (\pp{u}{z})^2 + (\pp{v}{z})^2 } 1335 1336 where we used the hydrostatic equation: 1337 1338 .. math:: {\pp{\Phi}{P^ \kappa}} = c_p \theta_v 1339 1340 Negative values indicate unstable buoyancy **AND** shear, small positive 1341 values (:math:`<0.4`) indicate dominantly unstable shear, and large 1342 positive values indicate dominantly stable stratification. 1343 1344 CT - Surface Exchange Coefficient for Temperature and Moisture (dimensionless) 1345 ############################################################################### 1346 1347 The surface exchange coefficient is obtained from the similarity 1348 functions for the stability dependant flux profile relationships: 1349 1350 .. math:: 1351 1352 {\bf CT} = -\frac{( \overline{w^{\prime}\theta^{\prime}} ) }{ u_* \Delta \theta } = 1353 -\frac{( \overline{w^{\prime}q^{\prime}} ) }{ u_* \Delta q } = 1354 \frac{ k }{ (\psi_{h} + \psi_{g}) } 1355 1356 where :math:`\psi_h` is the surface layer non-dimensional temperature 1357 change and :math:`\psi_g` is the viscous sublayer non-dimensional 1358 temperature or moisture change: 1359 1360 .. math:: 1361 1362 \psi_{h} = \int_{\zeta_{0}}^{\zeta} \frac{\phi_{h} }{ \zeta} d \zeta \hspace{1cm} and 1363 \hspace{1cm} \psi_{g} = \frac{ 0.55 (Pr^{2/3} - 0.2) }{ \nu^{1/2} } 1364 (h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} 1365 1366 and: :math:`h_{0} = 30z_{0}` with a maximum value over land of 0.01 1367 1368 :math:`\phi_h` is the similarity function of :math:`\zeta`, which 1369 expresses the stability dependance of the temperature and moisture 1370 gradients, specified differently for stable and unstable layers 1371 according to . k is the Von Karman constant, :math:`\zeta` is the 1372 non-dimensional stability parameter, Pr is the Prandtl number for air, 1373 :math:`\nu` is the molecular viscosity, :math:`z_{0}` is the surface 1374 roughness length, :math:`u_*` is the surface stress velocity (see 1375 diagnostic number 67), and the subscript ref refers to a reference 1376 value. 1377 1378 CU - Surface Exchange Coefficient for Momentum (dimensionless) 1379 ############################################################## 1380 1381 The surface exchange coefficient is obtained from the similarity 1382 functions for the stability dependant flux profile relationships: 1383 1384 .. math:: {\bf CU} = \frac{u_* }{ W_s} = \frac{ k }{ \psi_{m} } 1385 1386 where :math:`\psi_m` is the surface layer non-dimensional wind shear: 1387 1388 .. math:: \psi_{m} = {\int_{\zeta_{0}}^{\zeta} \frac{\phi_{m} }{ \zeta} d \zeta} 1389 1390 :math:`\phi_m` is the similarity function of :math:`\zeta`, which 1391 expresses the stability dependance of the temperature and moisture 1392 gradients, specified differently for stable and unstable layers 1393 according to . k is the Von Karman constant, :math:`\zeta` is the 1394 non-dimensional stability parameter, :math:`u_*` is the surface stress 1395 velocity (see diagnostic number 67), and :math:`W_s` is the magnitude of 1396 the surface layer wind. 1397 1398 ET - Diffusivity Coefficient for Temperature and Moisture (m^2/sec) 1399 ################################################################### 1400 1401 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the 1402 turbulent heat or moisture flux for the atmosphere above the surface 1403 layer can be expressed as a turbulent diffusion coefficient :math:`K_h` 1404 times the negative of the gradient of potential temperature or moisture. 1405 In the :cite:`helflab:88` adaptation of this closure, :math:`K_h` takes the form: 1406 1407 .. math:: 1408 1409 {\bf ET} = K_h = -\frac{( \overline{w^{\prime}\theta_v^{\prime}}) }{ \pp{\theta_v}{z} } 1410 = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} 1411 \\ \frac{ q^2 }{ q_e } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. 1412 1413 where :math:`q` is the turbulent velocity, or 1414 :math:`\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} 1415 energy}`, :math:`q_e` is the turbulence velocity derived from the more 1416 simple level 2.0 model, which describes equilibrium turbulence, 1417 :math:`\ell` is the master length scale related to the layer depth, 1418 :math:`S_H` is a function of :math:`G_H` and :math:`G_M`, the 1419 dimensionless buoyancy and wind shear parameters, respectively, or a 1420 function of :math:`G_{H_e}` and :math:`G_{M_e}`, the equilibrium 1421 dimensionless buoyancy and wind shear parameters. Both :math:`G_H` and 1422 :math:`G_M`, and their equilibrium values :math:`G_{H_e}` and 1423 :math:`G_{M_e}`, are functions of the Richardson number. 1424 1425 For the detailed equations and derivations of the modified level 2.5 1426 closure scheme, see :cite:`helflab:88`. 1427 1428 In the surface layer, :math:`{\bf {ET}}` is the exchange coefficient 1429 for heat and moisture, in units of :math:`m/sec`, given by: 1430 1431 .. math:: {\bf ET_{Nrphys}} = C_t * u_* = C_H W_s 1432 1433 where :math:`C_t` is the dimensionless exchange coefficient for heat and 1434 moisture from the surface layer similarity functions (see diagnostic 1435 number 9), :math:`u_*` is the surface friction velocity (see diagnostic 1436 number 67), :math:`C_H` is the heat transfer coefficient, and 1437 :math:`W_s` is the magnitude of the surface layer wind. 1438 1439 1440 EU - Diffusivity Coefficient for Momentum (m^2/sec) 1441 ################################################### 1442 1443 In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the 1444 turbulent heat momentum flux for the atmosphere above the surface layer 1445 can be expressed as a turbulent diffusion coefficient :math:`K_m` times 1446 the negative of the gradient of the u-wind. In the :cite:`helflab:88` adaptation of this 1447 closure, :math:`K_m` takes the form: 1448 1449 .. math:: 1450 1451 {\bf EU} = K_m = -\frac{( \overline{u^{\prime}w^{\prime}} ) }{ \pp{U}{z} } 1452 = \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} 1453 \\ \frac{ q^2 }{ q_e } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. 1454 1455 where :math:`q` is the turbulent velocity, or 1456 :math:`\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} 1457 energy}`, :math:`q_e` is the turbulence velocity derived from the more 1458 simple level 2.0 model, which describes equilibrium turbulence, 1459 :math:`\ell` is the master length scale related to the layer depth, 1460 :math:`S_M` is a function of :math:`G_H` and :math:`G_M`, the 1461 dimensionless buoyancy and wind shear parameters, respectively, or a 1462 function of :math:`G_{H_e}` and :math:`G_{M_e}`, the equilibrium 1463 dimensionless buoyancy and wind shear parameters. Both :math:`G_H` and 1464 :math:`G_M`, and their equilibrium values :math:`G_{H_e}` and 1465 :math:`G_{M_e}`, are functions of the Richardson number. 1466 1467 For the detailed equations and derivations of the modified level 2.5 1468 closure scheme, see :cite:`helflab:88`. 1469 1470 In the surface layer, :math:`{\bf {EU}}` is the exchange coefficient 1471 for momentum, in units of :math:`m/sec`, given by: 1472 1473 .. math:: {\bf EU_{Nrphys}} = C_u * u_* = C_D W_s 1474 1475 where :math:`C_u` is the dimensionless exchange coefficient for momentum 1476 from the surface layer similarity functions (see diagnostic number 10), 1477 :math:`u_*` is the surface friction velocity (see diagnostic number 67), 1478 :math:`C_D` is the surface drag coefficient, and :math:`W_s` is the 1479 magnitude of the surface layer wind. 1480 1481 1482 1483 TURBU - Zonal U-Momentum changes due to Turbulence (m/sec/day) 1484 ############################################################## 1485 1486 The tendency of U-Momentum due to turbulence is written: 1487 1488 .. math:: 1489 0bad585a21 Navi*1490 {\bf TURBU} = {\pp{u}{t}}_{\rm turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} 8679f9097b Jeff*1491 = {\pp{}{z} }{(K_m \pp{u}{z})} 1492 1493 The Helfand and Labraga level 2.5 scheme models the turbulent flux of 1494 u-momentum in terms of :math:`K_m`, and the equation has the form of a 1495 diffusion equation. 1496 1497 TURBV - Meridional V-Momentum changes due to Turbulence (m/sec/day) 1498 ################################################################### 1499 1500 The tendency of V-Momentum due to turbulence is written: 1501 1502 .. math:: 1503 0bad585a21 Navi*1504 {\bf TURBV} = {\pp{v}{t}}_{\rm turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} 8679f9097b Jeff*1505 = {\pp{}{z} }{(K_m \pp{v}{z})} 1506 1507 The Helfand and Labraga level 2.5 scheme models the turbulent flux of 1508 v-momentum in terms of :math:`K_m`, and the equation has the form of a 1509 diffusion equation. 1510 1511 1512 TURBT - Temperature changes due to Turbulence (deg/day) 1513 ####################################################### 1514 1515 The tendency of temperature due to turbulence is written: 1516 1517 .. math:: 1518 0bad585a21 Navi*1519 {\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{\rm turb} = 8679f9097b Jeff*1520 P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} 1521 = P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} 1522 1523 The Helfand and Labraga level 2.5 scheme models the turbulent flux of 1524 temperature in terms of :math:`K_h`, and the equation has the form of a 1525 diffusion equation. 1526 1527 1528 TURBQ - Specific Humidity changes due to Turbulence (g/kg/day) 1529 ############################################################### 1530 1531 The tendency of specific humidity due to turbulence is written: 1532 1533 .. math:: 1534 0bad585a21 Navi*1535 {\bf TURBQ} = {\pp{q}{t}}_{\rm turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} 8679f9097b Jeff*1536 = {\pp{}{z} }{(K_h \pp{q}{z})} 1537 1538 The Helfand and Labraga level 2.5 scheme models the turbulent flux of 1539 temperature in terms of :math:`K_h`, and the equation has the form of a 1540 diffusion equation. 1541 1542 1543 MOISTT - Temperature Changes Due to Moist Processes (deg/day) 1544 ############################################################# 1545 1546 .. math:: {\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} 1547 1548 where: 1549 1550 .. math:: 1551 1552 \left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha \frac{m_B}{c_p} \Gamma_s \right)_i 1553 \hspace{.4cm} and 1554 \hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = \frac{L}{c_p} (q^*-q) 1555 1556 and 1557 1558 .. math:: \Gamma_s = g \eta \pp{s}{p} 1559 1560 The subscript :math:`c` refers to convective processes, while the 1561 subscript :math:`ls` refers to large scale precipitation processes, or 1562 supersaturation rain. The summation refers to contributions from each 1563 cloud type called by RAS. The dry static energy is given as :math:`s`, 1564 the convective cloud base mass flux is given as :math:`m_B`, and the 1565 cloud entrainment is given as :math:`\eta`, which are explicitly defined 1566 in :numref:`para_phys_pkg_fizhi_mc`, the description of the convective 1567 parameterization. The fractional adjustment, or relaxation parameter, 1568 for each cloud type is given as :math:`\alpha`, while :math:`R` is the 1569 rain re-evaporation adjustment. 1570 1571 MOISTQ - Specific Humidity Changes Due to Moist Processes (g/kg/day) 1572 #################################################################### 1573 1574 .. math:: {\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} 1575 1576 where: 1577 1578 .. math:: 1579 1580 \left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha \frac{m_B}{L}(\Gamma_h-\Gamma_s) \right)_i 1581 \hspace{.4cm} and 1582 \hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) 1583 1584 and 1585 1586 .. math:: \Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} 1587 1588 The subscript :math:`c` refers to convective processes, while the 1589 subscript :math:`ls` refers to large scale precipitation processes, or 1590 supersaturation rain. The summation refers to contributions from each 1591 cloud type called by RAS. The dry static energy is given as :math:`s`, 1592 the moist static energy is given as :math:`h`, the convective cloud base 1593 mass flux is given as :math:`m_B`, and the cloud entrainment is given as 1594 :math:`\eta`, which are explicitly defined in :numref:`para_phys_pkg_fizhi_mc`, 1595 the description of the convective parameterization. The fractional 1596 adjustment, or relaxation parameter, for each cloud type is given as 1597 :math:`\alpha`, while :math:`R` is the rain re-evaporation adjustment. 1598 1599 1600 RADLW - Heating Rate due to Longwave Radiation (deg/day) 1601 ######################################################## 1602 1603 The net longwave heating rate is calculated as the vertical divergence 1604 of the net terrestrial radiative fluxes. Both the clear-sky and 1605 cloudy-sky longwave fluxes are computed within the longwave routine. The 1606 subroutine calculates the clear-sky flux, :math:`F^{clearsky}_{LW}`, 1607 first. For a given cloud fraction, the clear line-of-sight probability 1608 :math:`C(p,p^{\prime})` is computed from the current level pressure 1609 :math:`p` to the model top pressure, :math:`p^{\prime} = p_{top}`, and 1610 the model surface pressure, :math:`p^{\prime} = p_{surf}`, for the 1611 upward and downward radiative fluxes. (see Section 1612 [sec:fizhi:radcloud]). The cloudy-sky flux is then obtained as: 1613 0bad585a21 Navi*1614 .. math:: F_{LW} = C(p,p') \cdot F^{clearsky}_{LW} 8679f9097b Jeff*1615 1616 Finally, the net longwave heating rate is calculated as the vertical 1617 divergence of the net terrestrial radiative fluxes: 1618 0bad585a21 Navi*1619 .. math:: \pp{\rho c_p T}{t} = - \p{z} F_{LW}^{NET} 8679f9097b Jeff*1620 1621 or 1622 0bad585a21 Navi*1623 .. math:: {\bf RADLW} = \frac{g}{c_p \pi} \p{\sigma} F_{LW}^{NET} 8679f9097b Jeff*1624 1625 where :math:`g` is the accelation due to gravity, :math:`c_p` is the 1626 heat capacity of air at constant pressure, and 1627 1628 .. math:: F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow 1629 1630 1631 RADSW - Heating Rate due to Shortwave Radiation (deg/day) 1632 ######################################################### 1633 1634 The net Shortwave heating rate is calculated as the vertical divergence 1635 of the net solar radiative fluxes. The clear-sky and cloudy-sky 1636 shortwave fluxes are calculated separately. For the clear-sky case, the 1637 shortwave fluxes and heating rates are computed with both CLMO (maximum 1638 overlap cloud fraction) and CLRO (random overlap cloud fraction) set to 1639 zero (see Section [sec:fizhi:radcloud]). The shortwave routine is then 1640 called a second time, for the cloudy-sky case, with the true 1641 time-averaged cloud fractions CLMO and CLRO being used. In all cases, a 1642 normalized incident shortwave flux is used as input at the top of the 1643 atmosphere. 1644 1645 The heating rate due to Shortwave Radiation under cloudy skies is 1646 defined as: 1647 0bad585a21 Navi*1648 .. math:: \pp{\rho c_p T}{t} = - \p{z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT} 8679f9097b Jeff*1649 1650 or 1651 0bad585a21 Navi*1652 .. math:: {\bf RADSW} = \frac{g}{c_p \pi} \p{\sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} 8679f9097b Jeff*1653 1654 where :math:`g` is the accelation due to gravity, :math:`c_p` is the 1655 heat capacity of air at constant pressure, RADSWT is the true incident 1656 shortwave radiation at the top of the atmosphere (See Diagnostic #48), 1657 and 1658 1659 .. math:: F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow 1660 1661 1662 PREACC - Total (Large-scale + Convective) Accumulated Precipition (mm/day) 1663 ########################################################################### 1664 1665 For a change in specific humidity due to moist processes, 1666 :math:`\Delta q_{moist}`, the vertical integral or total precipitable 1667 amount is given by: 1668 1669 .. math:: 1670 1671 {\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} 1672 \frac{dp}{g} = \frac{1}{g} \int_0^1 \Delta q_{moist} dp 1673 1674 A precipitation rate is defined as the vertically integrated moisture 1675 adjustment per Moist Processes time step, scaled to :math:`mm/day`. 1676 1677 1678 PRECON - Convective Precipition (mm/day) 1679 ######################################## 1680 1681 For a change in specific humidity due to sub-grid scale cumulus 1682 convective processes, :math:`\Delta q_{cum}`, the vertical integral or 1683 total precipitable amount is given by: 1684 1685 .. math:: 1686 1687 {\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} 1688 \frac{dp}{g} = \frac{1}{g} \int_0^1 \Delta q_{cum} dp 1689 1690 A precipitation rate is defined as the vertically integrated moisture 1691 adjustment per Moist Processes time step, scaled to :math:`mm/day`. 1692 1693 TUFLUX - Turbulent Flux of U-Momentum (Newton/m^2) 1694 ################################################## 1695 1696 The turbulent flux of u-momentum is calculated for 1697 :math:`diagnostic \hspace{.2cm} purposes 1698 \hspace{.2cm} only` from the eddy coefficient for momentum: 1699 1700 .. math:: 1701 1702 {\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = 1703 {\rho } {(- K_m \pp{U}{z})} 1704 1705 where :math:`\rho` is the air density, and :math:`K_m` is the eddy 1706 coefficient. 1707 1708 TVFLUX - Turbulent Flux of V-Momentum (Newton/m^2) 1709 ################################################### 1710 1711 The turbulent flux of v-momentum is calculated for 1712 :math:`diagnostic \hspace{.2cm} purposes 1713 \hspace{.2cm} only` from the eddy coefficient for momentum: 1714 1715 .. math:: 1716 1717 {\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = 1718 {\rho } {(- K_m \pp{V}{z})} 1719 1720 where :math:`\rho` is the air density, and :math:`K_m` is the eddy 1721 coefficient. 1722 1723 1724 TTFLUX - Turbulent Flux of Sensible Heat (Watts/m^2) 1725 #################################################### 1726 1727 The turbulent flux of sensible heat is calculated for 1728 :math:`diagnostic \hspace{.2cm} purposes 1729 \hspace{.2cm} only` from the eddy coefficient for heat and moisture: 1730 1731 .. math:: 1732 1733 {\bf TTFLUX} = c_p {\rho } 1734 P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} 1735 = c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} 1736 1737 where :math:`\rho` is the air density, and :math:`K_h` is the eddy 1738 coefficient. 1739 1740 1741 TQFLUX - Turbulent Flux of Latent Heat (Watts/m^2) 1742 ################################################### 1743 1744 The turbulent flux of latent heat is calculated for 1745 :math:`diagnostic \hspace{.2cm} purposes 1746 \hspace{.2cm} only` from the eddy coefficient for heat and moisture: 1747 1748 .. math:: 1749 1750 {\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = 1751 {L {\rho }(- K_h \pp{q}{z})} 1752 1753 where :math:`\rho` is the air density, and :math:`K_h` is the eddy 1754 coefficient. 1755 1756 1757 CN - Neutral Drag Coefficient (dimensionless) 1758 ############################################# 1759 1760 The drag coefficient for momentum obtained by assuming a neutrally 1761 stable surface layer: 1762 1763 .. math:: {\bf CN} = \frac{ k }{ \ln(\frac{h }{z_0}) } 1764 1765 where :math:`k` is the Von Karman constant, :math:`h` is the height of 1766 the surface layer, and :math:`z_0` is the surface roughness. 1767 1768 WINDS - Surface Wind Speed (meter/sec) 1769 ###################################### 1770 1771 The surface wind speed is calculated for the last internal turbulence 1772 time step: 1773 1774 .. math:: {\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} 1775 1776 where the subscript :math:`Nrphys` refers to the lowest model level. 1777 1778 The air/surface virtual temperature difference measures the stability of 1779 the surface layer: 1780 1781 .. math:: {\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} 1782 1783 where 1784 1785 .. math:: 1786 1787 \theta_{v{Nrphys+1}} = \frac{ T_g }{ P^{\kappa}_{surf} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} 1788 and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) 1789 1790 :math:`\beta` is the surface potential evapotranspiration coefficient 1791 (:math:`\beta=1` over oceans), :math:`q^*(T_g,P_s)` is the saturation 1792 specific humidity at the ground temperature and surface pressure, level 1793 :math:`Nrphys` refers to the lowest model level and level 1794 :math:`Nrphys+1` refers to the surface. 1795 1796 1797 TG - Ground Temperature (deg K) 1798 ################################ 1799 1800 The ground temperature equation is solved as part of the turbulence 1801 package using a backward implicit time differencing scheme: 1802 1803 .. math:: 1804 1805 {\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} 0bad585a21 Navi*1806 C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{\rm ice} - H - LE 8679f9097b Jeff*1807 1808 where :math:`R_{sw}` is the net surface downward shortwave radiative 1809 flux, :math:`R_{lw}` is the net surface upward longwave radiative flux, 0bad585a21 Navi*1810 :math:`Q_{\rm ice}` is the heat conduction through sea ice, :math:`H` is the 8679f9097b Jeff*1811 upward sensible heat flux, :math:`LE` is the upward latent heat flux, 1812 and :math:`C_g` is the total heat capacity of the ground. :math:`C_g` is 1813 obtained by solving a heat diffusion equation for the penetration of the 1814 diurnal cycle into the ground (), and is given by: 1815 1816 .. math:: 1817 1818 C_g = \sqrt{ \frac{\lambda C_s }{ 2 \omega } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} 0bad585a21 Navi*1819 \frac{86400.}{2\pi} } 8679f9097b Jeff*1820 1821 Here, the thermal conductivity, :math:`\lambda`, is equal to 1822 :math:`2x10^{-3}` :math:`\frac{ly}{sec} 1823 \frac{cm}{K}`, the angular velocity of the earth, :math:`\omega`, is 1824 written as :math:`86400` :math:`sec/day` divided by :math:`2 \pi` 1825 :math:`radians/ 1826 day`, and the expression for :math:`C_s`, the heat capacity per unit 1827 volume at the surface, is a function of the ground wetness, :math:`W`. 1828 1829 1830 TS - Surface Temperature (deg K) 1831 ################################# 1832** Warning **
Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 1834.
1833 The surface temperature estimate is made by assuming that the model’s 1834 lowest layer is well-mixed, and therefore that :math:`\theta` is 1835 constant in that layer. The surface temperature is therefore: 1836 1837 .. math:: {\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} 1838 1839 1840 DTG - Surface Temperature Adjustment (deg K) 1841 ############################################ 1842 1843 The change in surface temperature from one turbulence time step to the 1844 next, solved using the Ground Temperature Equation (see diagnostic 1845 number 30) is calculated: 1846 1847 .. math:: {\bf DTG} = {T_g}^{n} - {T_g}^{n-1} 1848 1849 where superscript :math:`n` refers to the new, updated time level, and 1850 the superscript :math:`n-1` refers to the value at the previous 1851 turbulence time level. 1852 1853 1854 QG - Ground Specific Humidity (g/kg) 1855 ##################################### 1856 1857 The ground specific humidity is obtained by interpolating between the 1858 specific humidity at the lowest model level and the specific humidity of 1859 a saturated ground. The interpolation is performed using the potential 1860 evapotranspiration function: 1861 1862 .. math:: {\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) 1863 1864 where :math:`\beta` is the surface potential evapotranspiration 1865 coefficient (:math:`\beta=1` over oceans), and :math:`q^*(T_g,P_s)` is 1866 the saturation specific humidity at the ground temperature and surface 1867 pressure. 1868 1869 1870 QS - Saturation Surface Specific Humidity (g/kg) 1871 ################################################ 1872 1873 The surface saturation specific humidity is the saturation specific 1874 humidity at the ground temprature and surface pressure: 1875 1876 .. math:: {\bf QS} = q^*(T_g,P_s) 1877 1878 TGRLW - Instantaneous ground temperature used as input to the Longwave radiation subroutine (deg) 1879 ################################################################################################# 1880 1881 .. math:: {\bf TGRLW} = T_g(\lambda , \phi ,n) 1882 1883 where :math:`T_g` is the model ground temperature at the current time 1884 step :math:`n`. 1885 1886 ST4 - Upward Longwave flux at the surface (Watts/m^2) 1887 ##################################################### 1888 1889 .. math:: {\bf ST4} = \sigma T^4 1890 1891 where :math:`\sigma` is the Stefan-Boltzmann constant and T is the 1892 temperature. 1893 1894 1895 OLR - Net upward Longwave flux at :math:`p=p_{top}` (Watts/m^2) 1896 ################################################################ 1897 1898 .. math:: {\bf OLR} = F_{LW,top}^{NET} 1899 1900 where top indicates the top of the first model layer. In the GCM, 1901 :math:`p_{top}` = 0.0 mb. 1902 1903 1904 OLRCLR - Net upward clearsky Longwave flux at :math:`p=p_{top}` (Watts/m^2) 1905 ########################################################################### 1906 1907 .. math:: {\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} 1908 1909 where top indicates the top of the first model layer. In the GCM, 1910 :math:`p_{top}` = 0.0 mb. 1911 1912 1913 LWGCLR - Net upward clearsky Longwave flux at the surface (Watts/m^2) 1914 ###################################################################### 1915 1916 .. math:: 1917 1918 \begin{aligned} 1919 {\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ 1920 & = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow\end{aligned} 1921 1922 where Nrphys+1 indicates the lowest model edge-level, or 1923 :math:`p = p_{surf}`. :math:`F(clearsky)_{LW}^\uparrow` is the upward 1924 clearsky Longwave flux and the :math:`F(clearsky)_{LW}^\downarrow` is 1925 the downward clearsky Longwave flux. 1926 1927 1928 LWCLR - Heating Rate due to Clearsky Longwave Radiation (deg/day) 1929 ################################################################# 1930 1931 The net longwave heating rate is calculated as the vertical divergence 1932 of the net terrestrial radiative fluxes. Both the clear-sky and 1933 cloudy-sky longwave fluxes are computed within the longwave routine. The 1934 subroutine calculates the clear-sky flux, :math:`F^{clearsky}_{LW}`, 1935 first. For a given cloud fraction, the clear line-of-sight probability 1936 :math:`C(p,p^{\prime})` is computed from the current level pressure 1937 :math:`p` to the model top pressure, :math:`p^{\prime} = p_{top}`, and 1938 the model surface pressure, :math:`p^{\prime} = p_{surf}`, for the 1939 upward and downward radiative fluxes. (see Section 1940 [sec:fizhi:radcloud]). The cloudy-sky flux is then obtained as: 1941 0bad585a21 Navi*1942 .. math:: F_{LW} = C(p,p') \cdot F^{clearsky}_{LW} 8679f9097b Jeff*1943 1944 Thus, **LWCLR** is defined as the net longwave heating rate due to the 1945 vertical divergence of the clear-sky longwave radiative flux: 1946 0bad585a21 Navi*1947 .. math:: \pp{\rho c_p T}{t}_{clearsky} = - \p{z} F(clearsky)_{LW}^{NET} 8679f9097b Jeff*1948 1949 or 1950 0bad585a21 Navi*1951 .. math:: {\bf LWCLR} = \frac{g}{c_p \pi} \p{\sigma} F(clearsky)_{LW}^{NET} 8679f9097b Jeff*1952 1953 where :math:`g` is the accelation due to gravity, :math:`c_p` is the 1954 heat capacity of air at constant pressure, and 1955 1956 .. math:: F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow 1957 1958 1959 TLW - Instantaneous temperature used as input to the Longwave radiation subroutine (deg) 1960 ######################################################################################## 1961 1962 .. math:: {\bf TLW} = T(\lambda , \phi ,level, n) 1963 1964 where :math:`T` is the model temperature at the current time step 1965 :math:`n`. 1966 1967 1968 SHLW - Instantaneous specific humidity used as input to the Longwave radiation subroutine (kg/kg) 1969 ################################################################################################# 1970 1971 .. math:: {\bf SHLW} = q(\lambda , \phi , level , n) 1972 1973 where :math:`q` is the model specific humidity at the current time step 1974 :math:`n`. 1975 1976 1977 OZLW - Instantaneous ozone used as input to the Longwave radiation subroutine (kg/kg) 1978 ##################################################################################### 1979 1980 .. math:: {\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) 1981 1982 where :math:`\rm OZ` is the interpolated ozone data set from the 1983 climatological monthly mean zonally averaged ozone data set. 1984 1985 1986 CLMOLW - Maximum Overlap cloud fraction used in LW Radiation (0-1) 1987 ################################################################## 1988 1989 **CLMOLW** is the time-averaged maximum overlap cloud fraction that has been 1990 filled by the Relaxed Arakawa/Schubert Convection scheme and will be 1991 used in the Longwave Radiation algorithm. These are convective clouds 1992 whose radiative characteristics are assumed to be correlated in the 1993 vertical. For a complete description of cloud/radiative interactions, 1994 see Section [sec:fizhi:radcloud]. 1995 1996 .. math:: {\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) 1997 1998 1999 CLDTOT - Total cloud fraction used in LW and SW Radiation (0-1) 2000 ############################################################### 2001 2002 **CLDTOT** is the time-averaged total cloud fraction that has been 2003 filled by the Relaxed Arakawa/Schubert and Large-scale Convection 2004 schemes and will be used in the Longwave and Shortwave Radiation 2005 packages. For a complete description of cloud/radiative interactions, 2006 see Section [sec:fizhi:radcloud]. 2007 2008 .. math:: {\bf CLDTOT} = F_{RAS} + F_{LS} 2009 2010 where :math:`F_{RAS}` is the time-averaged cloud fraction due to 2011 sub-grid scale convection, and :math:`F_{LS}` is the time-averaged cloud 2012 fraction due to precipitating and non-precipitating large-scale moist 2013 processes. 2014 2015 2016 CLMOSW - Maximum Overlap cloud fraction used in SW Radiation (0-1) 2017 ################################################################## 2018 2019 **CLMOSW** is the time-averaged maximum overlap cloud fraction that has been 2020 filled by the Relaxed Arakawa/Schubert Convection scheme and will be 2021 used in the Shortwave Radiation algorithm. These are convective clouds 2022 whose radiative characteristics are assumed to be correlated in the 2023 vertical. For a complete description of cloud/radiative interactions, 2024 see Section [sec:fizhi:radcloud]. 2025 2026 .. math:: {\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) 2027 2028 2029 CLROSW - Random Overlap cloud fraction used in SW Radiation (0-1) 2030 ################################################################# 2031 2032 **CLROSW** is the time-averaged random overlap cloud fraction that has been 2033 filled by the Relaxed Arakawa/Schubert and Large-scale Convection 2034 schemes and will be used in the Shortwave Radiation algorithm. These are 2035 convective and large-scale clouds whose radiative characteristics are 2036 not assumed to be correlated in the vertical. For a complete description 2037 of cloud/radiative interactions, see Section [sec:fizhi:radcloud]. 2038 2039 .. math:: {\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) 2040 2041 2042 RADSWT - Incident Shortwave radiation at the top of the atmosphere (Watts/m^2) 2043 ############################################################################## 2044 2045 .. math:: {\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z 2046 2047 where :math:`S_0`, is the extra-terrestial solar contant, :math:`R_a` is 2048 the earth-sun distance in Astronomical Units, and :math:`cos \phi_z` is 2049 the cosine of the zenith angle. It should be noted that **RADSWT**, as 2050 well as **OSR** and **OSRCLR**, are calculated at the top of the 2051 atmosphere (p=0 mb). However, the **OLR** and **OLRCLR** diagnostics are 2052 currently calculated at :math:`p= p_{top}` (0.0 mb for the GCM). 2053 2054 2055 EVAP - Surface Evaporation (mm/day) 2056 ################################### 2057 2058 The surface evaporation is a function of the gradient of moisture, the 2059 potential evapotranspiration fraction and the eddy exchange coefficient: 2060 0bad585a21 Navi*2061 .. math:: {\bf EVAP} = \rho \beta K_{h} (q_{\rm surface} - q_{Nrphys}) 8679f9097b Jeff*2062 2063 where :math:`\rho` = the atmospheric density at the surface, 2064 :math:`\beta` is the fraction of the potential evapotranspiration 2065 actually evaporated (:math:`\beta=1` over oceans), :math:`K_{h}` is the 2066 turbulent eddy exchange coefficient for heat and moisture at the surface 2067 in :math:`m/sec` and :math:`q{surface}` and :math:`q_{Nrphys}` are the 2068 specific humidity at the surface (see diagnostic number 34) and at the 2069 bottom model level, respectively. 2070 2071 2072 DUDT - Total Zonal U-Wind Tendency (m/sec/day) 2073 ############################################### 2074 2075 **DUDT** is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, 2076 Diabatic, and Analysis forcing. 2077 2078 .. math:: {\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} 2079 2080 2081 DVDT - Total Zonal V-Wind Tendency (m/sec/day) 2082 ############################################### 2083 2084 **DVDT** is the total time-tendency of the Meridional V-Wind due to 2085 Hydrodynamic, Diabatic, and Analysis forcing. 2086 2087 .. math:: {\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} 2088 2089 2090 DTDT - Total Temperature Tendency (deg/day) 2091 ############################################ 2092 2093 **DTDT** is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, 2094 and Analysis forcing. 2095 2096 .. math:: 2097 2098 \begin{aligned} 0bad585a21 Navi*2099 {\bf DTDT} & = \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ 2100 & + \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} \end{aligned} 8679f9097b Jeff*2101 2102 2103 DQDT - Total Specific Humidity Tendency (g/kg/day) 2104 ################################################### 2105 2106 **DQDT** is the total time-tendency of Specific Humidity due to Hydrodynamic, 2107 Diabatic, and Analysis forcing. 2108 2109 .. math:: 2110 2111 {\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} 2112 + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} 2113 2114 2115 USTAR - Surface-Stress Velocity (m/sec) 2116 ######################################## 2117 2118 The surface stress velocity, or the friction velocity, is the wind speed 2119 at the surface layer top impeded by the surface drag: 2120 2121 .. math:: 2122 2123 {\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} 2124 C_u = \frac{k}{\psi_m} 2125 2126 :math:`C_u` is the non-dimensional surface drag coefficient (see 2127 diagnostic number 10), and :math:`W_s` is the surface wind speed (see 2128 diagnostic number 28). 2129 2130 2131 Z0 - Surface Roughness Length (m) 2132 ################################# 2133 2134 Over the land surface, the surface roughness length is interpolated to 2135 the local time from the monthly mean data of . Over the ocean, the 2136 roughness length is a function of the surface-stress velocity, 2137 :math:`u_*`. 2138 2139 .. math:: {\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5}{u_*} 2140 2141 where the constants are chosen to interpolate between the reciprocal 2142 relation of for weak winds, and the piecewise linear relation of for 2143 moderate to large winds. 2144 2145 2146 FRQTRB - Frequency of Turbulence (0-1) 2147 ###################################### 2148 2149 The fraction of time when turbulence is present is defined as the 2150 fraction of time when the turbulent kinetic energy exceeds some minimum 2151 value, defined here to be :math:`0.005 \hspace{.1cm}m^2/sec^2`. When 2152 this criterion is met, a counter is incremented. The fraction over the 2153 averaging interval is reported. 2154 2155 2156 PBL - Planetary Boundary Layer Depth (mb) 2157 ######################################### 2158 2159 The depth of the PBL is defined by the turbulence parameterization to be 2160 the depth at which the turbulent kinetic energy reduces to ten percent 2161 of its surface value. 2162 0bad585a21 Navi*2163 .. math:: {\bf PBL} = P_{PBL} - P_{\rm surface} 8679f9097b Jeff*2164 2165 where :math:`P_{PBL}` is the pressure in :math:`mb` at which the 2166 turbulent kinetic energy reaches one tenth of its surface value, and 2167 :math:`P_s` is the surface pressure. 2168 2169 2170 SWCLR - Clear sky Heating Rate due to Shortwave Radiation (deg/day) 2171 ################################################################### 2172 2173 The net Shortwave heating rate is calculated as the vertical divergence 2174 of the net solar radiative fluxes. The clear-sky and cloudy-sky 2175 shortwave fluxes are calculated separately. For the clear-sky case, the 2176 shortwave fluxes and heating rates are computed with both CLMO (maximum 2177 overlap cloud fraction) and CLRO (random overlap cloud fraction) set to 2178 zero (see Section [sec:fizhi:radcloud]). The shortwave routine is then 2179 called a second time, for the cloudy-sky case, with the true 2180 time-averaged cloud fractions CLMO and CLRO being used. In all cases, a 2181 normalized incident shortwave flux is used as input at the top of the 2182 atmosphere. 2183 2184 The heating rate due to Shortwave Radiation under clear skies is defined 2185 as: 2186 0bad585a21 Navi*2187 .. math:: \pp{\rho c_p T}{t} = - \p{z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT} 8679f9097b Jeff*2188 2189 or 2190 0bad585a21 Navi*2191 .. math:: {\bf SWCLR} = \frac{g}{c_p } \p{p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} 8679f9097b Jeff*2192 2193 where :math:`g` is the accelation due to gravity, :math:`c_p` is the 2194 heat capacity of air at constant pressure, RADSWT is the true incident 2195 shortwave radiation at the top of the atmosphere (See Diagnostic #48), 2196 and 2197 2198 .. math:: F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow 2199 2200 2201 OSR - Net upward Shortwave flux at the top of the model (Watts/m^2) 2202 ################################################################### 2203 2204 .. math:: {\bf OSR} = F_{SW,top}^{NET} 2205 2206 where top indicates the top of the first model layer used in the 2207 shortwave radiation routine. In the GCM, :math:`p_{SW_{top}}` = 0 mb. 2208 2209 2210 OSRCLR - Net upward clearsky Shortwave flux at the top of the model (Watts/m^2) 2211 ############################################################################### 2212 2213 .. math:: {\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} 2214 2215 where top indicates the top of the first model layer used in the 2216 shortwave radiation routine. In the GCM, :math:`p_{SW_{top}}` = 0 mb. 2217 2218 2219 CLDMAS - Convective Cloud Mass Flux (kg/m^2) 2220 ############################################ 2221 2222 The amount of cloud mass moved per RAS timestep from all convective 2223 clouds is written: 2224 2225 .. math:: {\bf CLDMAS} = \eta m_B 2226 2227 where :math:`\eta` is the entrainment, normalized by the cloud base mass 2228 flux, and :math:`m_B` is the cloud base mass flux. :math:`m_B` and 2229 :math:`\eta` are defined explicitly in :numref:`para_phys_pkg_fizhi_mc`, the 2230 description of the convective parameterization. 2231 2232 2233 UAVE - Time-Averaged Zonal U-Wind (m/sec) 2234 ######################################### 2235 2236 The diagnostic **UAVE** is simply the time-averaged Zonal U-Wind over 2237 the **NUAVE** output frequency. This is contrasted to the instantaneous 2238 Zonal U-Wind which is archived on the Prognostic Output data stream. 2239 2240 .. math:: {\bf UAVE} = u(\lambda, \phi, level , t) 2241 2242 Note, **UAVE** is computed and stored on the staggered C-grid. 2243 2244 2245 VAVE - Time-Averaged Meridional V-Wind (m/sec) 2246 ############################################## 2247 2248 The diagnostic **VAVE** is simply the time-averaged Meridional V-Wind 2249 over the **NVAVE** output frequency. This is contrasted to the 2250 instantaneous Meridional V-Wind which is archived on the Prognostic 2251 Output data stream. 2252 2253 .. math:: {\bf VAVE} = v(\lambda, \phi, level , t) 2254 2255 Note, **VAVE** is computed and stored on the staggered C-grid. 2256 2257 2258 TAVE - Time-Averaged Temperature (Kelvin) 2259 ######################################### 2260 2261 The diagnostic **TAVE** is simply the time-averaged Temperature over 2262 the **NTAVE** output frequency. This is contrasted to the instantaneous 2263 Temperature which is archived on the Prognostic Output data stream. 2264 2265 .. math:: {\bf TAVE} = T(\lambda, \phi, level , t) 2266 2267 2268 QAVE - Time-Averaged Specific Humidity (g/kg) 2269 ############################################# 2270 2271 The diagnostic **QAVE** is simply the time-averaged Specific Humidity 2272 over the **NQAVE** output frequency. This is contrasted to the 2273 instantaneous Specific Humidity which is archived on the Prognostic 2274 Output data stream. 2275 2276 .. math:: {\bf QAVE} = q(\lambda, \phi, level , t) 2277 2278 2279 PAVE - Time-Averaged Surface Pressure - PTOP (mb) 2280 ################################################# 2281 2282 The diagnostic **PAVE** is simply the time-averaged Surface Pressure - 2283 PTOP over the **NPAVE** output frequency. This is contrasted to the 2284 instantaneous Surface Pressure - PTOP which is archived on the 2285 Prognostic Output data stream. 2286 2287 .. math:: 2288 2289 \begin{aligned} 2290 {\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ 2291 & = & p_s(\lambda, \phi, level , t) - p_T\end{aligned} 2292 2293 QQAVE - Time-Averaged Turbulent Kinetic Energy (m/sec)^2 2294 ######################################################## 2295 2296 The diagnostic **QQAVE** is simply the time-averaged prognostic 2297 Turbulent Kinetic Energy produced by the GCM Turbulence parameterization 2298 over the **NQQAVE** output frequency. This is contrasted to the 2299 instantaneous Turbulent Kinetic Energy which is archived on the 2300 Prognostic Output data stream. 2301 2302 .. math:: {\bf QQAVE} = qq(\lambda, \phi, level , t) 2303** Warning **
Wide character in print at /usr/local/share/lxr/source line 1030, <$git> line 2305.
2304 Note, **QQAVE** is computed and stored at the “mass-point” locations 2305 on the staggered C-grid. 2306 2307 2308 SWGCLR - Net downward clearsky Shortwave flux at the surface (Watts/m^2) 2309 ######################################################################## 2310 2311 .. math:: 2312 2313 \begin{aligned} 2314 {\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ 2315 & = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow\end{aligned} 2316 2317 2318 where Nrphys+1 indicates the lowest model edge-level, or 2319 :math:`p = p_{surf}`. :math:`F(clearsky){SW}^\downarrow` is the downward 2320 clearsky Shortwave flux and :math:`F(clearsky)_{SW}^\uparrow` is the 2321 upward clearsky Shortwave flux. 2322 2323 2324 DIABU - Total Diabatic Zonal U-Wind Tendency (m/sec/day) 2325 ######################################################### 2326 2327 **DIABU** is the total time-tendency of the Zonal U-Wind due to Diabatic 2328 processes and the Analysis forcing. 2329 2330 .. math:: {\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} 2331 2332 2333 2334 DIABV - Total Diabatic Meridional V-Wind Tendency (m/sec/day) 2335 ############################################################## 2336 2337 **DIABV** is the total time-tendency of the Meridional V-Wind due to Diabatic 2338 processes and the Analysis forcing. 2339 2340 .. math:: {\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} 2341 2342 2343 DIABT Total Diabatic Temperature Tendency (deg/day) 2344 ################################################### 2345 2346 **DIABT** is the total time-tendency of Temperature due to Diabatic processes and 2347 the Analysis forcing. 2348 2349 .. math:: 2350 2351 \begin{aligned} 0bad585a21 Navi*2352 {\bf DIABT} & = \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ 2353 & + \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} \end{aligned} 8679f9097b Jeff*2354 2355 If we define the time-tendency of Temperature due to Diabatic 2356 processes as 2357 2358 .. math:: 2359 2360 \begin{aligned} 0bad585a21 Navi*2361 \pp{T}{t}_{Diabatic} & = \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ 2362 & + \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence}\end{aligned} 8679f9097b Jeff*2363 2364 then, since there are no surface pressure changes due to Diabatic 2365 processes, we may write 2366 2367 .. math:: \pp{T}{t}_{Diabatic} = \frac{p^\kappa}{\pi}\pp{\pi \theta}{t}_{Diabatic} 2368 2369 where :math:`\theta = T/p^\kappa`. Thus, **DIABT** may be written as 2370 2371 .. math:: {\bf DIABT} = \frac{p^\kappa}{\pi} \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) 2372 2373 2374 DIABQ - Total Diabatic Specific Humidity Tendency (g/kg/day) 2375 ############################################################ 2376 2377 **DIABQ** is the total time-tendency of Specific Humidity due to Diabatic 2378 processes and the Analysis forcing. 2379 2380 .. math:: {\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} 2381 2382 If we define the time-tendency of Specific Humidity due to Diabatic 2383 processes as 2384 2385 .. math:: \pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} 2386 2387 then, since there are no surface pressure changes due to Diabatic 2388 processes, we may write 2389 2390 .. math:: \pp{q}{t}_{Diabatic} = \frac{1}{\pi}\pp{\pi q}{t}_{Diabatic} 2391 2392 Thus, **DIABQ** may be written as 2393 2394 .. math:: {\bf DIABQ} = \frac{1}{\pi} \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) 2395 2396 2397 VINTUQ - Vertically Integrated Moisture Flux (m/sec g/kg) 2398 ########################################################## 2399 2400 The vertically integrated moisture flux due to the zonal u-wind is 2401 obtained by integrating :math:`u q` over the depth of the atmosphere at 2402 each model timestep, and dividing by the total mass of the column. 2403 2404 .. math:: {\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } 2405 2406 Using 2407 :math:`\rho \delta z = -\frac{\delta p}{g} = - \frac{1}{g} \delta p`, we 2408 have 2409 2410 .. math:: {\bf VINTUQ} = { \int_0^1 u q dp } 2411 2412 2413 VINTVQ - Vertically Integrated Moisture Flux (m/sec g/kg) 2414 ######################################################### 2415 2416 The vertically integrated moisture flux due to the meridional v-wind 2417 is obtained by integrating :math:`v q` over the depth of the atmosphere 2418 at each model timestep, and dividing by the total mass of the column. 2419 2420 .. math:: {\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } 2421 2422 Using 2423 :math:`\rho \delta z = -\frac{\delta p}{g} = - \frac{1}{g} \delta p`, we 2424 have 2425 2426 .. math:: {\bf VINTVQ} = { \int_0^1 v q dp } 2427 2428 2429 VINTUT - Vertically Integrated Heat Flux (m/sec deg) 2430 #################################################### 2431 2432 The vertically integrated heat flux due to the zonal u-wind is 2433 obtained by integrating :math:`u T` over the depth of the atmosphere at 2434 each model timestep, and dividing by the total mass of the column. 2435 2436 .. math:: {\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } 2437 2438 Or, 2439 2440 .. math:: {\bf VINTUT} = { \int_0^1 u T dp } 2441 2442 2443 VINTVT - Vertically Integrated Heat Flux (m/sec deg) 2444 #################################################### 2445 2446 The vertically integrated heat flux due to the meridional v-wind is 2447 obtained by integrating :math:`v T` over the depth of the atmosphere at 2448 each model timestep, and dividing by the total mass of the column. 2449 2450 .. math:: {\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } 2451 2452 Using :math:`\rho \delta z = -\frac{\delta p}{g}`, we have 2453 2454 .. math:: {\bf VINTVT} = { \int_0^1 v T dp } 2455 2456 2457 CLDFRC - Total 2-Dimensional Cloud Fracton (0-1) 2458 ################################################ 2459 2460 If we define the time-averaged random and maximum overlapped cloudiness 2461 as CLRO and CLMO respectively, then the probability of clear sky 2462 associated with random overlapped clouds at any level is (1-CLRO) while 2463 the probability of clear sky associated with maximum overlapped clouds 2464 at any level is (1-CLMO). The total clear sky probability is given by 2465 (1-CLRO)\*(1-CLMO), thus the total cloud fraction at each level may be 2466 obtained by 1-(1-CLRO)\*(1-CLMO). 2467 2468 At any given level, we may define the clear line-of-site probability by 2469 appropriately accounting for the maximum and random overlap cloudiness. 2470 The clear line-of-site probability is defined to be equal to the product 2471 of the clear line-of-site probabilities associated with random and 2472 maximum overlap cloudiness. The clear line-of-site probability 2473 :math:`C(p,p^{\prime})` associated with maximum overlap clouds, from the 2474 current pressure :math:`p` to the model top pressure, 2475 :math:`p^{\prime} = p_{top}`, or the model surface pressure, 2476 :math:`p^{\prime} = p_{surf}`, is simply 1.0 minus the largest maximum 2477 overlap cloud value along the line-of-site, ie. 2478 2479 .. math:: 1-MAX_p^{p^{\prime}} \left( CLMO_p \right) 2480 2481 Thus, even in the time-averaged sense it is assumed that the maximum 2482 overlap clouds are correlated in the vertical. The clear line-of-site 2483 probability associated with random overlap clouds is defined to be the 2484 product of the clear sky probabilities at each level along the 2485 line-of-site, ie. 2486 2487 .. math:: \prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right) 2488 2489 The total cloud fraction at a given level associated with a line- 2490 of-site calculation is given by 2491 2492 .. math:: 2493 2494 1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) 2495 \prod_p^{p^{\prime}} \left( 1-CLRO_p \right) 2496 2497 The 2-dimensional net cloud fraction as seen from the top of the 2498 atmosphere is given by 2499 2500 .. math:: 2501 2502 {\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) 2503 \prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) 2504 2505 For a complete description of cloud/radiative interactions, see 2506 Section [sec:fizhi:radcloud]. 2507 2508 2509 QINT - Total Precipitable Water (gm/cm^2) 2510 ######################################### 2511 2512 The Total Precipitable Water is defined as the vertical integral of the 2513 specific humidity, given by: 2514 2515 .. math:: 2516 2517 \begin{aligned} 0bad585a21 Navi*2518 {\bf QINT} & = \int_{surf}^{top} \rho q dz \\ 2519 & = \frac{\pi}{g} \int_0^1 q dp 8679f9097b Jeff*2520 \end{aligned} 2521 2522 where we have used the hydrostatic relation 2523 :math:`\rho \delta z = -\frac{\delta p}{g}`. 2524 2525 2526 U2M Zonal U-Wind at 2 Meter Depth (m/sec) 2527 ########################################## 2528 2529 The u-wind at the 2-meter depth is determined from the similarity 2530 theory: 2531 2532 .. math:: 2533 2534 {\bf U2M} = \frac{u_*}{k} \psi_{m_{2m}} \frac{u_{sl}}{W_s} = 2535 \frac{ \psi_{m_{2m}} }{ \psi_{m_{sl}} }u_{sl} 2536 2537 where :math:`\psi_m(2m)` is the non-dimensional wind shear at two 2538 meters, and the subscript :math:`sl` refers to the height of the top of 2539 the surface layer. If the roughness height is above two meters, 2540 :math:`{\bf U2M}` is undefined. 2541 2542 2543 V2M - Meridional V-Wind at 2 Meter Depth (m/sec) 2544 ################################################ 2545 2546 The v-wind at the 2-meter depth is a determined from the similarity 2547 theory: 2548 2549 .. math:: 2550 2551 {\bf V2M} = \frac{u_*}{k} \psi_{m_{2m}} \frac{v_{sl}}{W_s} = 2552 \frac{ \psi_{m_{2m}} }{ \psi_{m_{sl}} }v_{sl} 2553 2554 where :math:`\psi_m(2m)` is the non-dimensional wind shear at two 2555 meters, and the subscript :math:`sl` refers to the height of the top of 2556 the surface layer. If the roughness height is above two meters, 2557 :math:`{\bf V2M}` is undefined. 2558 2559 2560 T2M - Temperature at 2 Meter Depth (deg K) 2561 ########################################## 2562 2563 The temperature at the 2-meter depth is a determined from the similarity 2564 theory: 2565 2566 .. math:: 2567 2568 {\bf T2M} = P^{\kappa} (\frac{\theta*}{k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = 2569 P^{\kappa}(\theta_{surf} + \frac{ \psi_{h_{2m}}+\psi_g }{ \psi_{h_{sl}}+\psi_g } 2570 (\theta_{sl} - \theta_{surf}) ) 2571 2572 where: 2573 2574 .. math:: \theta_* = - \frac{ (\overline{w^{\prime}\theta^{\prime}}) }{ u_* } 2575 2576 where :math:`\psi_h(2m)` is the non-dimensional temperature gradient 2577 at two meters, :math:`\psi_g` is the non-dimensional temperature 2578 gradient in the viscous sublayer, and the subscript :math:`sl` refers to 2579 the height of the top of the surface layer. If the roughness height is 2580 above two meters, :math:`{\bf T2M}` is undefined. 2581 2582 2583 Q2M - Specific Humidity at 2 Meter Depth (g/kg) 2584 ############################################### 2585 2586 The specific humidity at the 2-meter depth is determined from the 2587 similarity theory: 2588 2589 .. math:: 2590 2591 {\bf Q2M} = P^{\kappa} \frac({q_*}{k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = 2592 P^{\kappa}(q_{surf} + \frac{ \psi_{h_{2m}}+\psi_g }{ \psi_{h_{sl}}+\psi_g } 2593 (q_{sl} - q_{surf})) 2594 2595 where: 2596 2597 .. math:: q_* = - \frac{ (\overline{w^{\prime}q^{\prime}}) }{ u_* } 2598 2599 where :math:`\psi_h(2m)` is the non-dimensional temperature gradient 2600 at two meters, :math:`\psi_g` is the non-dimensional temperature 2601 gradient in the viscous sublayer, and the subscript :math:`sl` refers to 2602 the height of the top of the surface layer. If the roughness height is 2603 above two meters, :math:`{\bf Q2M}` is undefined. 2604 2605 2606 U10M - Zonal U-Wind at 10 Meter Depth (m/sec) 2607 ############################################# 2608 2609 The u-wind at the 10-meter depth is an interpolation between the surface 2610 wind and the model lowest level wind using the ratio of the 2611 non-dimensional wind shear at the two levels: 2612 2613 .. math:: 2614 2615 {\bf U10M} = \frac{u_*}{k} \psi_{m_{10m}} \frac{u_{sl}}{W_s} = 2616 \frac{ \psi_{m_{10m}} }{ \psi_{m_{sl}} }u_{sl} 2617 2618 where :math:`\psi_m(10m)` is the non-dimensional wind shear at ten 2619 meters, and the subscript :math:`sl` refers to the height of the top of 2620 the surface layer. 2621 2622 2623 V10M - Meridional V-Wind at 10 Meter Depth (m/sec) 2624 ################################################## 2625 2626 The v-wind at the 10-meter depth is an interpolation between the surface 2627 wind and the model lowest level wind using the ratio of the 2628 non-dimensional wind shear at the two levels: 2629 2630 .. math:: 2631 2632 {\bf V10M} = \frac{u_*}{k} \psi_{m_{10m}} \frac{v_{sl}}{W_s} = 2633 \frac{ \psi_{m_{10m}} }{ \psi_{m_{sl}} }v_{sl} 2634 2635 where :math:`\psi_m(10m)` is the non-dimensional wind shear at ten 2636 meters, and the subscript :math:`sl` refers to the height of the top of 2637 the surface layer. 2638 2639 2640 T10M - Temperature at 10 Meter Depth (deg K) 2641 ############################################ 2642 2643 The temperature at the 10-meter depth is an interpolation between the 2644 surface potential temperature and the model lowest level potential 2645 temperature using the ratio of the non-dimensional temperature gradient 2646 at the two levels: 2647 2648 .. math:: 2649 2650 {\bf T10M} = P^{\kappa} (\frac{\theta*}{k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = 2651 P^{\kappa}(\theta_{surf} + \frac{\psi_{h_{10m}}+\psi_g}{\psi_{h_{sl}}+\psi_g} 2652 (\theta_{sl} - \theta_{surf})) 2653 2654 where: 2655 2656 .. math:: \theta_* = - \frac{ (\overline{w^{\prime}\theta^{\prime}}) }{ u_* } 2657 2658 where :math:`\psi_h(10m)` is the non-dimensional temperature gradient 2659 at two meters, :math:`\psi_g` is the non-dimensional temperature 2660 gradient in the viscous sublayer, and the subscript :math:`sl` refers to 2661 the height of the top of the surface layer. 2662 2663 2664 Q10M - Specific Humidity at 10 Meter Depth (g/kg) 2665 ################################################# 2666 2667 The specific humidity at the 10-meter depth is an interpolation between 2668 the surface specific humidity and the model lowest level specific 2669 humidity using the ratio of the non-dimensional temperature gradient at 2670 the two levels: 2671 2672 .. math:: 2673 2674 {\bf Q10M} = P^{\kappa} (\frac{q_*}{k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = 2675 P^{\kappa}(q_{surf} + \frac{\psi_{h_{10m}}+\psi_g}{\psi_{h_{sl}}+\psi_g} 2676 (q_{sl} - q_{surf})) 2677 2678 where: 2679 2680 .. math:: q_* = - \frac{ (\overline{w^{\prime}q^{\prime}}) }{ u_* } 2681 2682 where :math:`\psi_h(10m)` is the non-dimensional temperature gradient 2683 at two meters, :math:`\psi_g` is the non-dimensional temperature 2684 gradient in the viscous sublayer, and the subscript :math:`sl` refers to 2685 the height of the top of the surface layer. 2686 2687 2688 DTRAIN - Cloud Detrainment Mass Flux (kg/m^2) 2689 ############################################# 2690 2691 The amount of cloud mass moved per RAS timestep at the cloud 2692 detrainment level is written: 2693 2694 .. math:: {\bf DTRAIN} = \eta_{r_D}m_B 2695 2696 where :math:`r_D` is the detrainment level, :math:`m_B` is the cloud 2697 base mass flux, and :math:`\eta` is the entrainment, defined in :numref:`para_phys_pkg_fizhi_mc`. 2698 2699 2700 QFILL - Filling of negative Specific Humidity (g/kg/day) 2701 ######################################################## 2702 2703 Due to computational errors associated with the numerical scheme used 2704 for the advection of moisture, negative values of specific humidity may 2705 be generated. The specific humidity is checked for negative values after 2706 every dynamics timestep. If negative values have been produced, a 2707 filling algorithm is invoked which redistributes moisture from below. 2708 Diagnostic **QFILL** is equal to the net filling needed to eliminate 2709 negative specific humidity, scaled to a per-day rate: 2710 2711 .. math:: {\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} 2712 2713 where 2714 2715 .. math:: q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} 2716 2717 Key subroutines, parameters and files 2718 +++++++++++++++++++++++++++++++++++++ 2719 2720 2721 Dos and don'ts 2722 ++++++++++++++ 2723 2724 2725 Fizhi Reference 2726 +++++++++++++++ 2727 2728 2729 Experiments and tutorials that use fizhi 2730 ++++++++++++++++++++++++++++++++++++++++ 2731 2732 - Global atmosphere experiment with realistic SST and topography in 2733 fizhi-cs-32x32x10 verification directory. 2734 2735 - Global atmosphere aqua planet experiment in fizhi-cs-aqualev20 2736 verification directory. 2737 2738
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