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Balachandrudu Narapusetty
and
Nicole Mölders

Abstract

The soil module of the Hydro–Thermodynamic Soil–Vegetation Scheme is evaluated by soil temperature observations and independent theoretical numerical results. To gain the latter, a Galerkin weak finite-element (GWFE) scheme is implemented for solving the heat and water balance equations that are originally solved by a Crank–Nicholson finite-difference (CNFD) scheme. The GWFE scheme captures discontinuities well and has a high phase fidelity. When/where frozen ground thaws and under moderate advection-dominated regimes, peak temperatures simulated with the CNFD scheme are up to seven days off compared with observations and the results of the GWFE scheme. If freeze–thaw cycles repeat for more than a month, CNFD predictions will oscillate ±1 K around the observations but will converge to the observations and results of the GWFE scheme afterward. Under diffusion-dominated regimes, CNFD runs perform well with similar quality to the GWFE predictions. Comparisons of the results of both numerical schemes substantiate that the long spinup time of CNFD simulations results from the numerical scheme and not from the initialization procedure and that the diffusive nature of the CNFD scheme and not parameterized physical processes causes phase shifts. GWFE requires 1.6–2.8 more CPU time than CNFD in this study. Unless CPU time is an issue, the GWFE scheme is recommended because of its high phase fidelity and short spinup.

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Balachandrudu Narapusetty
and
Nicole Mölders

Abstract

The Hydro–Thermodynamic Soil–Vegetation Scheme (HTSVS) coupled in a two-way mode with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (NCAR) Mesoscale Meteorological Model (MM5) is evaluated for a typical snowmelt episode in the Baltic region by means of observations at 25 soil temperature, 355 snow-depth, and 344 precipitation sites that have, in total, 1000, 1775, and 1720 measurements, respectively. The performance with respect to predicted near-surface meteorological fields is evaluated using reanalysis data. Snow depth depends on snow metamorphism, sublimation, and snowfall. Because in the coupled model these processes are affected by the predicted surface radiation fluxes and cloud and precipitation processes, sensitivity studies are performed with two different cloud microphysical schemes and/or radiation schemes. Skill scores are calculated as a quality measure for the coupled model’s performance for a typical forecast range of 120 h for a typical spring (snowmelt) weather situation in the Baltic region. Discrepancies between predicted and observed snow-depth changes relate to the coupling. Enhanced water supply to the atmosphere, which results from water that was assumed to be open in MM5 but was actually ice covered in nature, finally leads to an overestimation of snowfall (input to HTSVS) and changes in snow depth (output). The resolution-dependent discrepancies between the terrain height in the model and real world also lead to snowfall where none occurred. For heavy snowfall the performance of the coupled model with respect to predicted snow-depth changes becomes nearly independent of the choice of the cloud microphysical and radiation schemes. As compared with observed changes in snow depth, the coupled model simulation using the Schultz scheme in conjunction with the radiation scheme from the Community Climate Model, version 2, (CCM2) predicts snow-depth changes of less than 2.5 mm considerably better than the other combinations that were tested. For thick snowpacks, the accuracy of the snow-depth decrease resulting from metamorphism strongly depends on the initial value of snow density. The coupled model acceptably captures the soil temperature diurnal cycles, the observed soil temperature increase with time, and the soil temperature behavior with depth. In general, discrepancies between simulated and observed soil temperatures decrease with soil depth. Simulations performed with the so-called CLOUD radiation scheme capture soil temperature minima and maxima better than do simulations performed with the CCM2 scheme.

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Balachandrudu Narapusetty
,
Timothy DelSole
, and
Michael K. Tippett

Abstract

This paper shows theoretically and with examples that climatological means derived from spectral methods predict independent data with less error than climatological means derived from simple averaging. Herein, “spectral methods” indicates a least squares fit to a sum of a small number of sines and cosines that are periodic on annual or diurnal periods, and “simple averaging” refers to mean averages computed while holding the phase of the annual or diurnal cycle constant. The fact that spectral methods are superior to simple averaging can be understood as a straightforward consequence of overfitting, provided that one recognizes that simple averaging is a special case of the spectral method. To illustrate these results, the two methods are compared in the context of estimating the climatological mean of sea surface temperature (SST). Cross-validation experiments indicate that about four harmonics of the annual cycle are adequate, which requires estimation of nine independent parameters. In contrast, simple averaging of daily SST requires estimation of 366 parameters—one for each day of the year, which is a factor of 40 more parameters. Consistent with the greater number of parameters, simple averaging poorly predicts samples that were not included in the estimation of the climatological mean, compared to the spectral method. In addition to being more accurate, the spectral method also accommodates leap years and missing data simply, results in a greater degree of data compression, and automatically produces smooth time series.

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