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Energy Exascale Earth System Model v2.0.1

First patch release of v2.0.0 Changes since v2.0.0 [Important change] Fix ocean threading bug seen in debug cases on Chrysalis with Intel 20.0.4. Was introduced around time of v2.0.0 tag. Does not change v2.0.0 answers on Chrysalis because those didn't use threading or debugging. [EAM] Add semi-lagrangian tracer transport for theta-l (F90 and C++), add new algorithm for finding tropopause, add DSCREAM to allow v2 and SCREAM settings in same code such as adjust_ps [EAM-MMF] 60L default, allow C++ back end of RRTMGP (EAM too). [EAMxx] add nu-top functionality, fix forcing functor, add ttype9 and dcmip2012 tests 2.1, 2.2, and 3 HOMME: remove obsolete remap algs, option to specify dynamics alg indep of tracer, new sponge layer, add imex tests [ELM] Add topography-based subgrid (topounits), add FATES-ELM Nitro., Phos. and CH4 coupling, add land-use ts for NARRM, add lulc for SSP3 RCP7, Fix nutrient fertilization exp test and carbon isotope flux, Fix xactive lnd dry deposition, add lake water storage option, fix plant hydraulics 2d params, fix carbon budget calc, fix soil nutrient conc. bug, fix mosart dam bug, add test for new ELM, MOSART features, fix bug in O3 dry dep stomatal resistances, fix plant hydraulics restart BFB error, update mkmapdata. [MOSART] fix bug for reading the latitude from an unstructured input file, fix oversat in bubble test. [MPAS-ocean] Add CFC11, CFC12 tracers, add 2D spherical transport tests, fix del4 tracer mixing, add MARBL ocean tracer mixing, modify harmonic analysis options, add GPU port of vmix routines, fix calc of ML-averaged BV freq. [MPAS-seaice] Change extents of initial polar disks for oRRS18to6v3 grid, fix ice BGC with MARBL, update spherical test cases, fix DON coupling, Remove Cf from sea ice constants. [MPAS-landice] add CRYO1850-4xCO2 compset [CIME] add GCP, ANL GCE, Spock, Perlmutter, deprecate config_compilers.xml, fix and clean-up cmake macros, fix slurm bindings, refactor CIME internal testing, cleanup SCORPIO perf data, allow position independent compset naming, [also] update v2 benchmarking suite, extend e3sm_prod with throughput and memory checks

E3SM Project, DOE↗

Energy Exascale Earth System Model v2.1.0

First release of version 2.1 of the Energy Exascale Earth System Model. [ATM] The atmosphere component remains EAM. There are no major changes in the default configuration since 2.0. New features include: A semi-lagrangian tracer transport for theta-l dycore, a new algorithm for finding the tropopause, new RRM mesh configurations. Add and update SSP370 and SSP585 cases. Restore the FIDEAL case. [LAND] The land component is ELM. There are no major changes in the default configuration since 2.0. Several option features have been added including: implementation of topography-based subgrid structure (topounits) and accompanying parameterizations and atmospheric forcing downscaling methods; a new plant hydraulics scheme; two-way land-river hydrological coupling through the infiltration of floodplain water; an implementation of perennial crops; updates to the SNICAR-AD snow radiative transfer model; and implementation of soil erosion and sediment yield in ELM-Erosion. Each of these new changes is modular in design and can be turned on or off as the user specifies; they are currently being tested in different “BGC” configurations. [OCEAN] The ocean component remains MPAS-Ocean. Major change since version 2.0 include the addition of the Fox-Kemper et al. 2011 parameterization for submesocale eddies, a correction for barotropic thickness consistency that reduces divergence noise, and the addition of an ocean carbon conservation analysis member. [SEAICE] The sea-ice component remains MPAS-Seaice. Major changes since version 2.0 include: A correction to how shortwave parameters are interpolated in the snicar-ad 5-band radiation scheme, the addition of a sea ice carbon conservation analysis member, updates to the default sea ice biogeochemistry namelist parameters to be consistent with version 2.0 improvements to nitrogen cycling and a correction in the ice-ocean dissolved organic nitrogen coupling. [LAND ICE] The land-ice component remains MPAS-Albany-landIce (MALI). Major changes since 2.0 include an update to the MALI version and the Greenland mesh.[RIVER] The river model is MOSART. There are no major changes in the default configuration since 2.0. A major new optional feature is two-way river-ocean hydrological coupling between MOSART and MPAS-O. This change can be turned on or off as the user specifies, and is being tested in different configurations. [COUPLER] The coupler remains cpl7/MCT. Major changes since version 2.0 include: Carbon budget calculated when heat/water budgets active. Fix a bug in land-atm fluxes for tri-grid configurations. [OTHER] a small bug in the zenith angle calculation was fixed in the data models.

ECP↗

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗

Simulation of the Pinatubo aerosol cloud in general circulation model

The global transport and dispersion of the Pinatubo aerosol cloud are simulated by means of a high-resolution stratospheric version of the NCAR Community Climate Model (CCM2) with an annual cycle. A passive tracer was injected into the model stratosphere over the Philippine Islands on June 15, and the transport was simulated for 180 d using an accurate semi-Lagrangian advection scheme. The simulated volcanic aerosol cloud initially drifted westward and expanded in longitude and latitude. The bulk of the aerosol cloud dispersed zonally to form a continuous belt in longitude, and remained confined to the tropics, centered near the 20-mb level for the entire 180-d model run, although a small amount was transported episodically into the upper troposphere in association with convective disturbances. Aerosol transported to the troposphere was dispersed within a few weeks into the Northern Hemisphere extratropics. In the Southern Hemisphere, the aerosol was mixed into the region equatorward of the core of the polar night jet during the first 50 d, but penetration into southern polar latitudes was delayed until the final warming in November.

Boville, Byron A.↗

Simulation of the modern arctic climate by the NCAR CCM1

The National Center of Atmospheric Research (NCAR) Community Climate Model Version 1 (CCM1's) simulation of the modern arctic climate is evaluated by comparing a five-year seasonal cycle simulation with the European Center for Medium-Range Weather Forecasts (ECMWF) global analyses. The sea level pressure (SLP), storm tracks, vertical cross section of height, 500-hPa height, total energy budget, and moisture budget are analyzed to investigate the biases in the simulated arctic climate. The results show that the model simulates anomalously low SLP, too much storm activity, and anomalously strong baroclinicity to the west of Greenland and vice versa to the east of Greenland. This bias is mainly attributed to the model's topographic representation of Greenland. First, the broadened Greenland topography in the model distorts the path of cyclone waves over the North Atlantic Ocean. Second, the model oversimulates the ridge over Greenland, which intensifies its blocking effect and steers the cyclone waves clockwise around it and hence produces an artificial circum-Greenland trough. These biases are significantly alleviated when the horizontal resolution increases to T42. Over the Arctic basin, the model simulates large amounts of low-level (stratus) clouds in winter and almost no stratus in summer, which is opposite to the observations. This bias is mainly due to the location of the simulated SLP features and the negative anomaly of storm activity, which prevent the transport of moisture into this region during summer but favor this transport in winter. The moisture budget analysis shows that the model's net annual precipitation (P-E) between 70 deg N and the North Pole is 6.6 times larger than the observations and the model transports six times more moisture into this region. The bias in the advection term is attributed to the positive moisture fixer scheme and the distorted flow pattern. However, the excessive moisture transport into the Arctic basin does not solely result from the advection term. The contribution by the moisture fixer is as large as from advection. By contrast, the semi-Lagrangian transport scheme used in the CCM2 significantly improves the moisture simulation for this region; however, globally the error is as serious as for the positive moisture fixer scheme. Finally, because the model has such serious problems in simulating the present arctic climate, its simulations of past and future climate change for this region are questionable.

Bromwich, David H.↗

Isentropic mass exchange between the Tropics and extratropics in the stratosphere

The isentropic mass exchange between the Tropics and extratropics in the stratosphere is investigated with a semi-Lagrangian transport model for the periods from 1 June to 31 October 1992 and from 1 December 1992 to 30 April 1993 using winds from the U.K. Meteorological Office data assimilation system. Calculations with an idealized, initially zonally symmetric tracer show that in the middle and upper stratosphere the bulk of tropical air is transported into the midlatitudes of the winter hemisphere although there exist quasi-permeable barriers in the subtropics. The transport takes place in the form of planetary-scale 'tongues' of material that are drawn poleward in association with the episodic amplification of planetary-scale waves in high latitudes of the winter hemisphere. Once air of tropical origin is transported to the midlatitudes it is irreversibly mixed with the midlatitude air in the 'surf zone.' Air of tropical origin can, however, hardly penetrate into the interior of the winter polar vortex until the breakdown of the vortex. Transport of tropical air into the midlatitudes of the summer hemisphere is strongly inhibited. In the lower stratosphere, tropical air is transported into the northern and southern midlatitudes. During the period from 1 June to 31 October 1992, the amount of tropical air transported into the Northern Hemisphere is, however, much smaller than that transported into the Southern Hemisphere, and there exist strong gradients in the tracer field in the equatorial region, indicating that there is a quasi-permeable barrier to cross-equator mass exchange. During the period from 1 December 1992 to 30 April 1993, on the other hand, roughly the same amounts of tropical air are transported into the Southern Hemisphere, and there exist strong gradients in the tracer field in the equatorial region, indicating that there is a quasi-permeable barrier to cross-equator mass exchange. During the period from 1 December 1992 to 30 April 1993, on the other hand, roughly the same amounts of tropical air are transported into the northern midlatitudes and into the southern midlatitudes, and there exist no significant transport barriers in the equatorial area.

Chen, Ping↗

A quasi-permeable barrier in the equatorial lower stratosphere

Analyses of global isentropic maps of potential vorticity from the United Kingdom Meteorological Office (UKMO) data assimilation system reveal that there is a region of strong meridional potential vorticity (PV) gradients in the equatorial lower stratosphere. A semi-Lagrangian tracer transport model is used to show that this region of strong PV gradients acts as a quasipermeable barrier to cross-equator mass exchange on isentropic surfaces.

Chen, Ping↗

Examination of tracer transport in the NCAR CCM2 by comparison of CFCl3 simulations with ALE/GAGE observations

The latest version of the National Center for Atmospheric Research (NCAR) community climate model (CCM2) contains a semi-Lagrangian tracer transport scheme for the purpose of advecting water vapor and for including chemistry in the climate model. One way to diagnose the CCM2 transport is to simulate CFCl3 in the CCM2 since it has a well-known industry-based source distribution and a photochemical sink and to compare the model results to Atmospheric Lifetime Experiment/Global Atmospheric Gases Experiment ALE/GAGE observations around the globe. In this paper we focus on this comparison and discuss the synoptic scale issues of tracer transport where appropriate. We compare the model and observations on both 12-hour and monthly timescales. The higher-frequency events allow us to diagnose the synoptic scale transport in the CCM2 associated with the observational sites and to determine uncertainties in our high-resolution source distribution. We find that the CCM2 does simulate many of the key features such as pollution events and some seasonal transports, but there are still some dynamical features of tracer transport such as the storm track dynamics and cross-equatorial flow that merit further study in both the model and the real atmosphere.

Hartley, Dana E.↗

Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing

An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength; which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other studies, it is found that the breaking waves undergo "self-acceleration," such that the zonal-mean intrinsic frequency remains approximately constant in spite of large changes in the background wind. It is also shown that many of the features obtained in the calculations can be understood in terms of linear wave theory. In particular, linear theory provides insights into the wavelength of the waves that break at high altitudes, the onset and evolution of breaking. the horizontal extent of the breaking region and its position relative to the forcing, and the minimum and maximum altitudes where breaking occurs. Wave breaking ceases at the altitude where the background dissipation rate (which in our model is a proxy for molecular diffusion) becomes greater than the rate of dissipation due to wave breaking, This altitude, in effect, the model turbopause, is shown to depend on a relatively small number of parameters that characterize the waves and the background state.

Prusa, Joseph M.↗

Transport of Passive Tracers in Baroclinic Wave Life Cycles

The transport of passive tracers in idealized baroclinic wave life cycles is studied using output from the National Center for Atmospheric Research Community Climate Model (CCM2). Two life cycles, LCn and LCs, are simulated, starting with baroclinically unstable initial conditions similar to those used by Thorncroft et al. in their study of two life cycle paradigms. The two life cycles LCn and LCs have different initial horizontal wind shear structures that result in distinctive nonlinear development. In terms of potential vorticity-potential temperature (PV-theta) diagnostics, the LCn case is characterized by thinning troughs that are advected anti-cyclonically and equatorward, while the LCs case has broadening troughs that wrap up cyclonically and poleward. Four idealized passive tracers are included in the model to be advected by the semi-Lagrangian transport scheme of the CCM2, and their evolutions are investigated throughout the life cycles. Tracer budgets are analyzed in terms of the transformed Eulerian mean constituent transport formalism in pressure coordinates and also in isentropic coordinates. Results for both LCn and LCs show transport that is downgradient with respect to the background structure of the tracer field, but with a characteristic spatial structure that maximizes in the middle to high latitudes. For the idealized tropospheric tracers in this study, this represents a net upward and poleward transport that enhances concentrations at high latitudes. These results vary little with the initial distribution of the constituent field. The time tendency of the tracer is influenced most strongly by the eddy flux term. with the largest transport occurring during the nonlinear growth stage of the life cycle. The authors also study the transport of a lower-stratospheric tracer, to examine stratosphere-troposphere exchange for baroclinic waves.

Stone, Elizabeth M.↗

Coupled-Circulation-Chemistry Studies with the Finite-Volume CCM: Trace Gas Transport in the Tropopause Region

A joint project between the Data Assimilation Office at NASA GSFC and NCAR involves linking the physical packages from the Community Climate Model (CCM) with the flux-form semi-Lagrangian dynamical core developed by Lin and Rood in the DAO. A further development of this model includes the implementation of a chemical package developed by Douglass and colleagues in the Atmospheric Chemistry and Dynamics Branch at NASA GSFC. Results from this coupled dynamics-radiation-chemistry model will be presented, focussing on trace gas transport in the tropopause region.

Pawson, Steven↗

Towards a Comprehensive Dynamic-chemistry Assimilation for Eos-Chem: Plans and Status in NASA's Data Assimilation Office

In order to support the EOS-Chem project, a comprehensive assimilation package for the coupled chemical-dynamical system is being developed by the Data Assimilation Office at NASA GSFC. This involves development of a coupled chemistry/meteorology model and of data assimilation techniques for trace species and meteorology. The model is being developed using the flux-form semi-Lagrangian dynamical core of Lin and Rood, the physical parameterizations from the NCAR Community Climate Model, and atmospheric chemistry modules from the Atmospheric Chemistry and Dynamics branch at NASA GSFC. To date the following results have been obtained: (i) multi-annual simulations with the dynamics-radiation model show the credibility of the package for atmospheric simulations; (ii) initial simulations including a limited number of middle atmospheric trace gases reveal the realistic nature of transport mechanisms, although there is still a need for some improvements. Samples of these results will be shown. A meteorological assimilation system is currently being constructed using the model; this will form the basis for the proposed meteorological/chemical assimilation package. The latter part of the presentation will focus on areas targeted for development in the near and far terms, with the objective of Providing a comprehensive assimilation package for the EOS-Chem science experiment. The first stage will target ozone assimilation. The plans also encompass a reanalysis (ReSTS) for the 1991-1995 period, which includes the Mt. Pinatubo eruption and the time when a large number of UARS observations were available. One of the most challenging aspects of future developments will be to couple theoretical advances in tracer assimilation with the practical considerations of a real environment and eventually a near-real-time assimilation system.

Pawson, Steven↗

Age-of-Air, Tape Recorder, and Vertical Transport Schemes

A numerical-analytic investigation of the impacts of vertical transport schemes on the model simulated age-of-air and the so-called 'tape recorder' will be presented using an idealized 1-D column transport model as well as a more realistic 3-D dynamical model. By comparing to the 'exact' solutions of 'age-of-air' and the 'tape recorder' obtainable in the 1-D setting, useful insight is gained on the impacts of numerical diffusion and dispersion of numerical schemes used in global models. Advantages and disadvantages of Eulerian, semi-Lagrangian, and Lagrangian transport schemes will be discussed. Vertical resolution requirement for numerical schemes as well as observing systems for capturing the fine details of the 'tape recorder' or any upward propagating wave-like structures can potentially be derived from the 1-D analytic model.

Lin, S.-J.↗

Climatology of the Finite-Volume CCM and Sensitivity Studies

A new model has been developed in the Data Assimilation Office at NASA Goddard Space Flight Center. It is intended for data assimilation and general circulation modeling, including representations of radiatively active trace gases such as stratospheric ozone. The model is based on the flux-form semi-Lagrangian' dynamical core, developed by Lin and Rood. In collaboration with the National Center for Atmospheric Research, the physical parametrization package from the Community Climate model, Version 3, has been included. This paper will discuss the climatology of a multi-year integration of the model, with observed boundary conditions (sea-surface temperature, sea ice, and incoming solar radiation). The standard model version has a resolution of 2.5 degrees longitude, 2 degrees latitude and has 55 levels between the surface and 80km. The mean climate and interannual variability of this model will be discussed, with emphasis on the middle atmosphere. The sensitivity to horizontal resolution will be examined, as will the impact of increasing and decreasing the vertical resolution. Changes which differ significantly from the interannual variations of the control run will be highlighted. Impacts of using long-term mean boundary conditions or values which vary from year to year will be discussed. Changes in the tropospheric circulation induced by lowering the upper boundary of the model will be discussed. The emphasis of the paper is on the climatology of the middle atmosphere and its impacts on the troposphere, with particular attention given to the climatologically important region near the tropopause.

Pawson, Steven↗

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Lin, Shian-Jiann↗

Implementation of the NCAR Community Land Model (CLM) in the NASA/NCAR finite-volume Global Climate Model (fvGCM)

In this study, the NCAR CLM version 2.0 land-surface model was integrated into the NASA/NCAR fvGCM. The CLM was developed collaboratively by an open interagency/university group of scientists and based on well-proven physical parameterizations and numerical schemes that combine the best features of BATS, NCAR-LSM, and IAP94. The CLM design is a one-dimensional point model with 1 vegetation layer, along with sub-grid scale tiles. The features of the CLM include 10-uneven soil layers with water, ice, and temperature states in each soil layer, and five snow layers, with water flow, refreezing, compaction, and aging allowed. In addition, the CLM utilizes two-stream canopy radiative transfer, the Bonan lake model and topographic enhanced streamflow based on TOPMODEL. The DAO fvGCM uses a genuinely conservative Flux-Form Semi-Lagrangian transport algorithm along with terrain- following Lagrangian control-volume vertical coordinates. The physical parameterizations are based on the NCAR Community Atmosphere Model (CAM-2). For our purposes, the fvGCM was run at 2 deg x 2.5 deg horizontal resolution with 55 vertical levels. The 10-year climate from the fvGCM with CLM2 was intercompared with the climate from fvGCM with LSM, ECMWF and NCEP. We concluded that the incorporation of CLM2 did not significantly impact the fvGCM climate from that of LSM. The most striking difference was the warm bias in the CLM2 surface skin temperature over desert regions. We determined that the warm bias can be partially attributed to the value of the drag coefficient for the soil under the canopy, which was too small resulting in a decoupling between the ground surface and the canopy. We also discovered that the canopy interception was high compared to observations in the Amazon region. A number of experiments were then performed focused on implementing model improvements. In order to correct the warm bias, the drag coefficient for the soil under the canopy was considered a function of LAI (Leaf Area Index). Analysis of the results revealed that there was a substantial impact, and the warm and dry bias in the CLM2 was significantly reduced. For the interception scheme, the canopy throughfall was increased to allow for more infiltration of precipitation into the soil, resulting in increased low-level moisture and a decrease in the interception loss ratio (canopy evaporation to precipitation).

Radakovich, Jon D.↗