ETRM Model¶
How Dual Crop Coefficients are calculated¶
See recharge.etrm_processes.Processes._do_dual_crop_coefficient()
The well-established FAO Penman-Monteith dual crop coefficient(DCC) method finds a reference evapotranspiration value from which actual transpiration can be derived. See GADGET documentation for a description of tall crop reference ET (etrs). By accounting for soil water, actual evapotranspiration (eta) can be estimated by calculating a stress factor coefficient Ks, a basal vegetation transpiration coefficient Kcb, and a bare surface evaporation coefficient Ke, and multiplying them by etrs. This method is known as the dual-crop-coefficient method (Allan et al., 1998). Jensen and others (1990) found that of 20 ET estimation methods, results varied considerably in varying climates and showed the need for rigorous and expensive calibration methods when a method developed in one climate was then applied to another. The FAO Penman-Monteith was devised in the 1990s as a method that needed less rigorous local calibration than other, more empirical and local methods such as the BCM and INFIL. The operational goal of the method is to find a constrained and reasonable estimate of ET with a minimum of climate data inputs. The method contains many possible variations to allow for the continuation of the ET calculation despite missing or incomplete data. Jabloun and Sahli (2008) found that use of FAO-56 recommended methods of calculating ET with missing data produced results close to those found using complete data.
This dual crop coefficient makes use of a modified skin layer evaporation mechanism, as described in Allen (2011). This has the cost of added uncertainty in the skin layer thickness and rew terms but the benefit of modeling the rapid evaporation that occurs after a small wetting event, which is limited only by available energy.
The initial calculations are a roundabout way of finding the fraction of the ground that is covered by vegetation (fcov) and that which is not (few). The exponent is intended to account for the effect that plant height has on shading the ground. The equation has the implicit assumption that kcb is controlled by the fraction of vegetative cover, which at this time is calculated with the NDVI. In a locale with only bare soil, fcov = 0.01, few = 0.99.
To find transpiration, the DCC calculates a root-zone transpiration stress coefficient, Ks. Ks depends on the amount of water in the root zone relative to water capacity, taw. If the root zone is in a state of maximum water (i.e., at field capacity), there is no limit on transpiration by the soil. Therefore Ks is one. As the root zone is depleted of water by transpiration, the soil dries, increasing the depletion (dr). As the difference between depletion and taw increases, Ks decreases, causing a reduction in the rate of transpiration. The basal crop coefficient (kcb) is simply the ratio of ET from a specific crop compared to the reference ET given current meteorological conditions. Kcb ranges from zero for a dry soil losing no water to ET, to perhaps 1.20 for a well watered crop transpiring at a high rate. The final factor needed to estimate transpiration is the tall crop reference ET (etrs). This is the rate of ET for a well watered crop of alfalfa, 0.5 m height, in good growing conditions. See GADGET documentation for details and derivation.
To find evaporation, the ETRM makes use of the common differentiation of stage one and stage two evaporation. Stage one evaporation is the vaporization of water of which the rate is controlled principally by atmospheric conditions. Thus, available energy in the form of radiation and sensible heat, and the aerodynamic effects of wind and surface texture. This process is not controlled by soil water content; the conditions immediately above the soil control the rate of evaporation. Stage two evaporation is controlled by the process of diffusion of water vapor through the soil. The water vapor pressure gradient upwards from damp soil to drier soil at the surface controls the rate at which water leaves the soil. Therefore, if the soil is very wet at some depth, but very dry at a shallower depth, the process will occur at a greater rate than if the underlying soil was drier, as the gradient is greater. The ETRM attempts to model this process.
How snow and snow melt are calculated¶
See recharge.etrm_processes.Processes._do_snow()
The ETRM snow model takes a simple approach to modeling the snow cycle. PRISM temperature and precipitation are used to account for snowfall. The mean of the maximum and minimum daily temperature is found; any precipitation falling during a day when this mean temperature is less than 0 C is assumed to be sored as snow. While other snow-modeling techniques assume that a transition zone exists over which the percent of precipitation falling as snow varies over a range of elevation or temperature, the ETRM assumes all precipitation on any given day falls either entirely as snow or as rain. The storage mechanism in the ETRM simply stores the snow as a snow water equivalent (SWE). No attempt is made to model the temporal and spatially-varying density and texture of snow during its duration in the snow pack, nor to model the effect the snow has on the underlying soil layers. In the ETRM, ablation of snow by sublimation and the movement of snow by wind is ignored. In computing the melting rate of snowpack in above-freezing conditions, a balance has been sought between the use of available physical parameters in a simple and computationally efficient model and the representation of important physical parameters. The ETRM uses incident shortwave radiation (Rsw), a modeled albedo with a temperature-dependent rate of decay, and air temperature (T air) to find snow melt. Flint and Flint (2008) used Landsat images to calibrate their soil water balance model, and found that a melting temperature of 0C had to be adjusted to 1.5C to accurately represent the time-varying snowpack in the Southwest United States; we have implemented this adjustment in the ETRM.
- where \(melt\) is snow melt (SWE, [mm]), \(a\) is albedo [-], \(R_{sw}\) is incoming shortwave radiation [W
- m-2], \(\alpha\) is the
radiation-term calibration coefficient [-], T is temperature [deg C], and \(\beta\) is the temperature correlation coefficient [-] Albedo is computed each time step, is reset following any new snowfall exceeding 3 mm SWE to 0.90, and decays
according to an equation after Rohrer (1991):
where \(a_i\) and \(a_{i - 1}\) are albedo on the current and previous day, respectively, a(min) is the minimum albedo of of 0.45 (Wiscombe and Warren: 1980), \(a_{i - 1}\) is the previous day’s albedo, and k is the decay constant. The decay constant varies depending on temperature, after Rohrer (1991).
How soil hydraulic conductivity is found and adjusted¶
See recharge.etrm_processes.Processes._do_soil_ksat_adjustment()
The only large-scale soil hydraulic conductivity (Ksat) product that covers the entire state of New Mexico (and the US) is derived from the STATSGO and SSURGO soils databases:
This project has made use of two important soil databases compiled and released by the NRCS, the Digital General Soil Map of the United States (STATSGO2) and the Soil Survey Geographic Database (SSURGO; NRCS, 2016). The STATSGO2 product is an extensive and generalized soils inventory mapped at the 1:250,000 scale, with near continuous coverage over the conterminous United States. STATSGO2 was designed to be used in regional and national-scale planning, management, and geographic analysis. SSURGO is a detailed soils data product consisting of surveys by county or hydrologic unit at a scale of 1:12,000 to 1:63,000. This larger scale provides detailed information for use by landowners, towns, and counties. Many of these surveys were conducted on foot by soil scientists, and some data include data from laboratory analysis. This product is updated frequently and represents data collected over more than 100 years of soil observations. Neither of these products covers the entire state.
Using Soil Data Viewer with Microsoft Access and ArcMap, one can build a soil saturated hydraulic conductivity layer [micrometers/sec] that must be converted to [mm/day]. This is then rasterized and resampled to model resolution.
The ETRM needs to adjust this value to account for variable precipitaion and melt rates. For example: If we have Ksat = 48 mm/day, and we assume that a rain event that ocurrs in summer will have a duration of 2 hours, we must multiply Ksat by 2 hrs/24 hrs. Thus, Ksat for our summer day is actually 48 * 2/24 = 4 mm/day. In this manner we account for precipitation intensity and only allow a maximum of 4 mm of water to enter the soil that day. Rain in excess of that amount is pushed to runoff.
In the most recent version of ETRM, a further adjustment is made: As runoff in the forest is reduced due to the roughness on the surface caused by leaf litter and such, we must allow more water to infiltrate. In effect the forest floor causes an increase in infiltration potential; we must convey this to the model via our Ksat.
Currently ETRM takes the three NLCD land cover classifications for forests (deciduous: 41, coniferous: 42, mixed: 41) and increases the Ksat (which has already been adjusted for season) by 2.0x and 3.3x for rain < 6mm and 6 mm < rain < 25 mm, respectively. See Li and others (2014).
Furthermore, the ETRM assumes snow melt has the whole day to infiltrate and thus gives cells with melt on any particular day the “max” Ksat (i.e., Ksat from the soils data).
How soil water balance is calculated¶
See recharge.etrm_processes.Processes._do_soil_water_balance()
This the most difficult part of the ETRM to maintain. The function first defines ‘water’ as all liquid water incident on the surface, i.e. rain plus snow melt. The quantities of vaporized water are then checked against the water in each soil layer. If vaporization exceeds available water (i.e. taw - dr < transp), that term is reduced and the value is updated. The function then performs a soil water balance from the ‘top’ (i.e., the rew/skin/ stage one evaporation layer) of the soil column downwards. Runoff is calculated as water in excess of soil saturated hydraulic conductivity, which has both a summer and winter value at all sites (see etrm_processes.run). The depletion is updated according to withdrawals from stage one evaporation and input of water. Water is then recalculated before being applied to in the stage two (i.e., tew) layer. This layer’s depletion is then updated according only to stage two evaporation and applied water. Finally, any remaining water is passed to the root zone (i.e., taw) layer. Depletion is updated according to losses via transpiration and inputs from water. Water in excess of taw is then allowed to pass below as recharge.
How mass balance is calculated¶
See recharge.etrm_processes.Processes._do_mass_balance()
This function is important because mass balance errors indicate a problem in the soil water balance or in the dual crop coefficient functions.
Think of the water balance as occurring at the very top of the soil column. The only water that comes in is from rain and snow melt. All other terms in the balance are subtractions from the input. Runoff, recharge, transpiration, and stage one and stage two evaporation are subtracted. Soil water storage change is another subtraction. Remember that if the previous time step’s depletion is greater than the current time step depletion, the storage change is positive. Therefore the storage change is subtracted from the inputs of rain and snow melt.