Land-Surface Model Introduction A land-urface model mut be able to accurately depict the interaction of the atmophere with the underlying urface land a well a the interaction of the ub-urface, or ubtrate, with the urface. In pecific, land-urface model need to accurately predict heat and moiture tranfer within the ubtrate a well a between the urface and atmophere; momentum interaction with the urface i generally viewed a the domain of urface layer model. It mut alo provide input to urface layer and radiation parameterization to compute urface enible and latent heat fluxe a well a reflected, aborbed, and emitted hortwave and longwave radiation at the urface. To be able to accurately predict heat and moiture tranfer, however, a land-urface model require atmopheric input. For example, precipitation infiltration can increae oil moiture wherea oil moiture can decreae via evaporation and tranpiration to the atmophere above. In total, a landurface model require wind, temperature, precipitation, and radiative forcing input. Conequently, land-urface model are typically coupled to an atmopheric model. There are two uch contruct: Direct Coupling: A land-urface model run imultaneouly with an atmopheric model. Indirect Coupling: A tand-alone land-urface model integrate urface information with input from a tand-alone atmopheric model to develop analye of relevant land-urface field (namely, oil temperature and oil moiture). A land-urface model run in an indirectly coupled fahion i commonly referred to a a land data aimilation ytem. It i ued to aimilate oil tate obervation and therefore correct initial etimate for oil tate field that are provided by coupled atmopheric-land model forecat (that we know to intrinically be imperfect). A conceptual chematic of the relationhip between a land data aimilation ytem, land-urface model, and atmopheric model i provided in Figure 1. Figure 1. Conceptual chematic of land-urface modeling, including the framework of land data aimilation and it role in providing input to a coupled atmophere-land modeling ytem. Figure reproduced from Warner (2011), their Figure 5.6. Land-Surface Model, Page 1
Landcape mapping provide information about oil propertie, including oil type, vegetation type and cover, terrain height, and other land ue characteritic. In general, thee are read in from tatic dataet and are aumed to remain tatic over the duration of a imulation. However, propertie uch a green fraction can change on ub-eaonal and longer time cale. For uch imulation, it i deirable to be able to update uch propertie, whether uing climatological information or from an external analyi. The tatic dataet provide information to the land-urface model that it ue, alongide predicted quantitie uch a oil temperature and moiture, to compute heat and moiture tranfer-related coefficient. Procee Handled by Land-Surface Model Although heat and moiture tranfer in the ubtrate and at the urface-atmophere interface may ound traightforward to predict, it i far more complex, with far le known about it and far fewer obervation of it, than heat and moiture tranfer within the free atmophere. The major phyical procee that a land-urface model mut predict in order to accurately predict heat and moiture tranfer are depicted in Figure 2. Thee can be partitioned into three clae: thoe occurring in the ubtrate, at the ubtrate-urface interface, and immediately above the urface. Figure 2. Schematic of the major phyical procee that a land-urface model mut parameterize in order to accurately predict heat and moiture tranfer within the ubtrate and between the land and the atmophere. Figure reproduced from Warner (2011), their Figure 5.1. Land-Surface Model, Page 2
In the ubtrate, freezing, thawing, evaporation, and condenation of ubtrate water reult in the gain or lo of latent heat. Vertical heat tranport i primarily accomplihed by conduction manifet a a oil heat flux. Vegetation can uptake water, while liquid water can alo be tranported up or down by change in water table height, down by gravity, and in all direction by capillary effect. Finally, convection and molecular diffuion can tranport water vapor up or down. Thee procee all are excluively handled by a land-urface model and only indirectly rely on atmopheric model input. Land-urface model may aume that a grid box ha uniform or varying oil propertie, the choice of which will impact the treatment of thee procee within the ubtrate and jut above. At the ubtrate-urface interface, urface enible and latent heat fluxe reult in heat exchange between the atmophere and oil. Moiture content can change a a reult of vegetation uptake into tem and leave, evaporation and ublimation into the atmophere, and rain, dew, nowmelt, and irrigated water infiltration from above. Runoff and other groundwater flow can alo change local moiture content. All except for irrigation require atmopheric input but alo are modulated by oil propertie intrinic to or predicted by the land-urface model. Irrigation mut be parameterized in ome fahion, if it i included at all. Runoff and groundwater flow are typically the domain of hydrological model, although land-urface model can parameterize them to varying extent. A land-urface model may include one or multiple layer of vegetation and may or may not include the urban canopy and it unique urface characteritic in thi evaluation. Immediately above the urface, moiture content i a function of precipitation, fog depoition, and water dripping from vegetation above to the urface below. Both moiture and heat are impacted by evaporation, tranpiration, now/frot melting and ublimation, and dew/frot formation. Thee procee all require atmopheric input. The treatment of now and frot at and immediately above the urface typically varie between model but ignificantly impact the urface energy budget. In the following ection, we eek to dicu the baic phyic behind each of thee procee. We tart at the atmophere-land interface and work our way down to the ubtrate. We focu le on variation between land-urface model in how pecific term and parameter are parameterized and more on model fundamental, namely the equation underlying all parameterization. A landurface model will olve for the equation that we will introduce that decribe urface and ubtrate heat and moiture tranport, with certain term etimated or parameterized. Surface Energy and Moiture Budget To firt order, urface energy balance, related to urface heating, can be expreed a: R = LE + H + G R i net radiative forcing, LE i net latent heating, H i net enible heating between the urface and the atmophere, and G i net enible heating between the ubtrate and urface. Land-urface and atmopheric characteritic influence the magnitude and ign of each term. All non-radiative heat tranfer at the urface itelf i via conduction. The net radiative forcing can be expreed a: Land-Surface Model, Page 3
R Q q 1 I I Q i the direct olar radiation incident at the urface and q i the diffue (or indirect) olar radiation incident at the urface. Thee are both computed by the hortwave radiation parameterization. α i the albedo, a meaure of the urface reflective characteritic, uch that 1 α i the tranmittance. Thi i a function of the underlying urface characteritic, both tatic and time-varying (e.g., oil moiture, whether or not now i preent, etc.). 4 I i the outgoing longwave radiation flux from the urface and i equal to T ; thu, it depend on the urface oil temperature. I i the aborbed longwave radiation emitted by the atmophere and i equal to the product of the longwave radiation incident at the urface and the tranmittance. Both of thee term are computed by the longwave radiation parameterization. Though all non-radiative heat tranfer at the urface, within the laminar ublayer, i by conduction, vertical tranport jut above the urface (e.g., within the lowet couple of meter above ground) i primarily accomplihed by turbulent vertical eddie driven by buoyancy and vertical wind hear. Both tranport occur at rate modulated by their repective diffuivitie, a meaure of the ability for energy to be tranported by diffuion. We typically repreent both by a ingle eddy diffuivity even though convection i modulated by molecular and turbulence by eddy diffuivitie. The general form of the latent and enible heat fluxe are given by: H c p K Ha T z l LE c Each i a function of the change in temperature or moiture over a finite layer at the urface. Thi i conitent with the conceptualization of urface tranport being by conduction. The ubcript of l on each partial derivative indicate that it i computed in the laminar ublayer. cp i the pecific heat of air at contant preure, q i pecific humidity, and KHa and KWa are the eddy diffuivitie in air for heat and moiture repectively. Each diffuivity i a function of the atmopheric tability, and thu varie with the meteorology and diurnal cycle, a well a the ditance from the urface. If we aume that the flux magnitude are approximately contant with height near the urface, thee expreion can be rewritten a: H c p D p H K Wa T g q z T LE lvdw qt q g lv i the latent heat of vaporization (for unfrozen oil), q(tg) i the aturation pecific humidity of the oil, qa i the atmopheric pecific humidity, Tg i the urface oil temperature, and Ta i the atmophere temperature. DH and DW are exchange coefficient for heat and moiture, repectively, and depend on tability, wind peed, and urface roughne. Both fluxe are poitive for upward l a a Land-Surface Model, Page 4
tranfer; they have larger magnitude when the temperature or moiture change between land and atmophere i larget. In general, they alo have larger magnitude for fater wind peed and when the atmophere i more turbulent (e.g., tronger vertical wind hear and lower tability), uch that the exchange coefficient magnitude are larger. Senible and latent heat fluxe are often olved by a urface layer rather than land-urface model, although they rely on land-urface model input of urface oil moiture, urface oil temperature, and urface ue characteritic. To firt order, the urface water budget can be expreed a: P ET RO D t Θ i the dimenionle volumetric oil water content, P i water input (i.e., precipitation, nowmelt, depoition, and irrigation), ET i evapotranpiration, RO i lateral runoff, and D i infiltration (or drainage) to the ubtrate. P i obtained from the atmopheric model. Land-urface model eek to parameterize ET, RO, and D, and each typically employ lightly different formulation to do o. Subtrate Heat Tranport Vertical heat tranport within the ubtrate i modulated by the thermal conductivity, or the ability of the ubtance (oil, with compoition variation in time and pace) to tranfer heat, and the heat capacity, or the amount of heat required to raie the temperature of a unit volume by 1 K. We refer to the former a k and the latter a C. Both depend upon oil compoition, including both pecified (e.g., oil type) and predicted (e.g., oil moiture, oil denity) factor. The heat capacity i cloely related to the pecific heat c, or the amount of heat required to raie the temperature of a unit ma by 1 K. Two parameter can be derived from thee quantitie. The thermal diffuivity K control the rate at which a temperature change propagate through a medium, while the thermal admittance µ i the rate at which a urface can accept or releae heat energy. k k C K C The thermal diffuivity can be viewed a analogou to an exchange coefficient. For the thermal admittance, the admittance of both the oil and atmophere are important. A higher admittance i aociated with a reduced temperature change becaue heat i tranferred efficiently rather than tored locally (where it could affect a temperature change). Soil moiture impoe a particularly large influence on thermal conductivity and heat capacity and, by extenion, thermal diffuivity and thermal admittance, a depicted in Figure 3. Moiter oil have both a greater ability to conduct heat and require more thermal energy to warm by 1 K than drier oil. Thu, both k and C increae with increaing oil moiture content. Thu reult in the thermal admittance alo increaing with increaing oil moiture content. However, heat capacity Land-Surface Model, Page 5
increae more rapidly than thermal conductivity at high oil moiture content, reulting in thermal diffuivity having maximum value at intermediate value of oil moiture. Figure 3. Dependence of (a) thermal conductivity, (b) heat capacity, (c) thermal diffuivity, and (d) thermal admittance on oil moiture. Figure reproduced from Warner (2011), their Figure 5.2. Vertical heat tranport within the ubtrate i primarily by conduction, or molecular diffuion, and i down-gradient from high to low value. It can be expreed by: H k T ubtrate The rate at which ubtrate temperature change i related to the vertical convergence of thi heat flux and to the heat capacity; i.e., i more heat being fluxed into or out of the layer, and how much of that heat i aociated with a 1 K change in the ubtrate temperature? z T t 1 C H z C ubtrate 1 k z T ubtrate z If we make the crude approximation that thermal conductivity i contant with height with in the ubtrate i.e., oil compoition i contant with height, given it control on thermal conductivity then we can write: T ubtrate t k C 2 T ubtrate 2 z Thi relationhip indicate that the change in ubtrate temperature with time i related to it econd partial derivative with height (depth), the oil heat capacity, and the oil thermal conductivity. We can explore thi relationhip in idealized form for day and night, a depicted in Figure 4. Land-Surface Model, Page 6
Figure 4. Idealized vertical temperature profile in the ubtrate and near the urface at night (left) and during the day (right). Thee mot formally apply to the warm eaon, when oil temperature typically decreae with increaing depth (averaged over the full diurnal cycle). Figure reproduced from Warner (2011), their Figure 5.3. In thi idealized cenario, temperature increae toward the urface during the day. Thu, the partial derivative of ubtrate temperature with height i poitive at all depth. However, it i mot poitive near the urface, where it increae mot rapidly with height. Thi reult in the econd derivative being poitive a well. For poitive-definite value of k and C, thi reult in ubtrate warming. Converely, temperature decreae toward the urface at night, and doe o mot rapidly near the urface. The partial and econd derivative of ubtrate temperature are both negative, reulting in ubtrate cooling. Thu, heat i tranported downward during the day to warm the ubtrate, while heat i tranported upward out of the oil at night to cool the ubtrate. Subtrate Moiture Tranport A noted earlier in thee note, there are ix major procee that are relevant to ubtrate moiture tranport. Two apply to water vapor: convection and molecular diffuion. Convection occur when the ubtrate temperature lape rate exceed the dry adiabatic lape rate. It permit upward water vapor tranport through dry oil by buoyant plume. Molecular diffuion diffue water vapor from higher to lower value on the molecular level; it i proportional to the vertical gradient of mixing ratio within the ubtrate. A land-urface model mut parameterize molecular diffuion, given the patial cale on which it occur, but may predict convection uing an appropriate formulation. There are four major procee that apply to ubtrate water tranport. The firt i aociated with change in water table height below the ubtrate. A water urface mut be in dynamic equilibrium with it urrounding fluid; to achieve thi, water will flow laterally from where there i an exce Land-Surface Model, Page 7
of water to where there i a relative lack of water. Thi can locally raie the water table where it i initially lower, and vice vera. Figure 5 provide a chematic of thi proce for a hypothetical cae of thundertorm inundating the oil along the uplope ide of mountain. At a later time, water i laterally tranported beneath the ubtrate toward the drier valley, raiing the water table there while lowering it lightly to the eat and wet. The rate at which thi occur can be predicted by a land-urface model with accurate repreentation of oil moiture and water table height a well a formulation for lateral tranport rate. Figure 5. Idealized illutration of thundertorm contributing to inundation and water table rie (blue) on mountain lope, after which time lateral tranport act to attempt to retore equilibrium, raiing the water table in the valley while lowering it lightly on the mountain lope (red). The econd i aociated with capillary effect, related to urface tenion and molecular bonding. Surface tenion i a meaure of how well water molecule are bonded to oil particle. It i related to the oil poroity, or how well it can be permeated by water, and to oil moiture content itelf. More porou oil have weaker molecular bonding a water molecule can more freely permeate (rather than tick to) the oil. Drier oil alo have weaker molecular bonding. Converely, trong molecular bonding allow water molecule to gradually move vertically by molecular attraction. In general, capillary effect reult in movement from moit toward dry oil, particularly between the lower, relatively dry ubtrate and the water table below it. A with vapor molecular diffuion, thee procee mut be parameterized by land-urface model. The third i aociated with downward infiltration from the urface and through the ubtrate. Thi i driven by gravity, controlled by urface tenion, and influenced by the oil moiture potential (a meaure of oil ability to retain water). High urface tenion mitigate downward infiltration and low urface tenion readily permit downward infiltration. Soil moiture potential i related to oil moiture content and poroity; it i higher for wetter oil and for le porou oil. Vertical water tranport occur more readily for high oil moiture potential; e.g., for aturated, porou oil, oil water more readily flow elewhere, but will flow le readily for drier, le porou oil. Downward infiltration relie on input from the atmophere in the form of rain, nowmelt, irrigation, and dew. Land-Surface Model, Page 8
The lat i water tranport by vegetation, including the extraction of ubtrate water by plant, the evaporation of urface water collected on the plant canopy, and the tranpiration of water vapor out of plant leave pore. Though the phyic of tranpiration are not ufficiently well-undertood, we know that it i largely dependent on vegetation type, vegetation denity, atmopheric moiture content, the diurnal cycle, and oil temperature and moiture (a relating to plant tree). All of thee procee rely upon accurate urface cover pecification and parameterization of the relevant phyical procee. A ubtrate oil moiture budget can be expreed in term of a vertical moiture flux, where: q t z Θ i the dimenionle volumetric oil moiture, q i pecific humidity, and Et i a parameterized lo of oil moiture to the plant canopy by evapotranpiration term. The vertical moiture flux can be expreed a: E t q z K z D z KΘ i the hydraulic conductivity aociated with infiltration; it i inverely related to oil moiture potential. DΘ i the oil water diffuivity aociated with urface tenion effect. Both are pecified by the land-urface model in light of both tatic and predicted oil characteritic. Different model will ue different formulation for thee term; example given by the coure text include: K K 2b3 D bk b3 Subcript of indicate aturation (i.e., holding the maximum amount of oil moiture) value. b i an empirically-derived coefficient. Ψ i the oil moiture potential. Note the trong relationhip to oil moiture content and to oil propertie, the latter entering through KΘ and Ψ. Practical Application A land-urface model may employ a urface layer, although many model conider urface layer parameterization to be eparate from land-urface model. In fact, model uch a the WRF-ARW model pair urface layer parameterization with planetary boundary layer parameterization rather than land-urface model. Land-urface model typically ue between one and ten ubtrate layer between the urface and a pecified depth at which the ubtrate i aid to not meaningfully impact the atmophere above on the time cale of the imulation. For example, the widely ued NOAH land-urface model, ued by the GFS and NAM model, ue four ubtrate layer for the 0-10, 10-40, 40-100, and 100-200 cm layer. The RUC land-urface model, ued by the RAP and HRRR model, ue nine ubtrate layer for the 0-1, 1-4, 4-10, 10-30, 30-60, 60-100, 100-160, and 160-300 cm layer. Land-urface model may alo ue multiple vegetation canopy and/or now layer. Land-Surface Model, Page 9
Each land-urface model ha different way in which it predict the evolution of oil temperature and oil moiture. Thi i no different than other parameterized procee. It i well-known that a multiply neted model imulation hould maintain parameterization conitency between domain, and thi i true for land-urface model a well. However, what about imulation that ue another model output for initial and lateral boundary condition? Microphyical parameterization predict model prognotic variable uch a ma mixing ratio and number concentration for variou water pecie. Some planetary boundary layer parameterization, namely local cloure cheme, predict model prognotic variable uch a turbulent kinetic energy. Yet, when another model output i ued to initialize or provide lateral boundary condition for a model imulation, thee quantitie are typically neglected, and thu it generally doe not matter if a different parameterization for thee procee i ued than wa ued with the model that provide the initial and lateral boundary condition. Cumulu and radiation parameterization update model prognotic variable uch a temperature and water vapor mixing ratio that are routinely oberved and can be updated by data aimilation. Though different parameterization for each et of procee take different approache to updating model prognotic variable, the updated variable have identical meaning between model. Thu, it generally alo doe not matter if a different parameterization for thee procee i ued than wa ued with the model that provide the initial and lateral boundary condition. In contrat, different land-urface model predict oil propertie on different level uing different method and often different repreentation for the urface and ubtrate. Conequently, numerical weather prediction model imulation are generally run uing the ame land-urface model a wa ued to generate the initial oil tate field. Alternatively, a pin-up period of at leat everal day may be ued to allow the oil tate field to adequately adjut to the particular land-urface model, although the hort duration of mot weather imulation limit the extent to which thi i done. Land-Surface Model, Page 10