Project For Intercomparison Of Land-surface Parameterization Schemes Research Articles

Development of a Coupled Land Surface and Groundwater Model

Abstract Traditional land surface models (LSMs) used for numerical weather simulation, climate projection, and as inputs to water management decision support systems, do not treat the LSM lower boundary in a fully process-based fashion. LSMs have evolved from a leaky-bucket approximation to more sophisticated land surface water and energy budget models that typically have a specified bottom layer flux to depict the lowest model layer exchange with deeper aquifers. The LSM lower boundary is often assumed zero flux or the soil moisture content is set to a constant value; an approach that while mass conservative, ignores processes that can alter surface fluxes, runoff, and water quantity and quality. Conversely, groundwater models (GWMs) for saturated and unsaturated water flow, while addressing important features such as subsurface heterogeneity and three-dimensional flow, often have overly simplified upper boundary conditions that ignore soil heating, runoff, snow, and root-zone uptake. In the present study, a state-of-the-art LSM (Common Land Model) and a variably saturated GWM (ParFlow) have been coupled as a single-column model. A set of simulations based on synthetic data and data from the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS), version 2(d), 18-yr dataset from Valdai, Russia, demonstrate the temporal dynamics of this coupled modeling system. The soil moisture and water table depth simulated by the coupled model agree well with the Valdai observations. Differences in prediction between the coupled and uncoupled models demonstrate the effect of a dynamic water table on simulated watershed flow. Comparison of the coupled model predictions with observations indicates certain cold processes such as frozen soil and freeze/thaw processes have an important impact on predicted water table depth. Comparisons of soil moisture, latent heat, sensible heat, temperature, runoff, and predicted groundwater depth between the uncoupled and coupled models demonstrate the need for improved groundwater representation in land surface schemes.

Intercomparison of land-surface parameterization schemes: sensitivity of surface energy and water fluxes to model parameters

In this study, sensitivities of 10 land-surface schemes (LSS) to five prescribed model parameters (i.e. the maximum soil moisture content (MSMC), effective available water content (EAWC), Clapp-Hornberger B parameter, leaf area index (LAI), and minimum stomatal resistance) are investigated based on the fractional factorial analysis method. The sensitivities of four model responses (i.e. evapotranspiration, total runoff, sensible heat flux, and soil moisture in the total zone) are evaluated as functions of these five parameters considering both individual and parameter interaction effects. To facilitate these sensitivity analyses, which are conducted for three hydroclimatic scenarios, two indices are introduced along with a criterion for measuring relative parameter effects. The two new indices are single response effect index and multiple response effect index. Results show that for the majority of LSS, the four model responses are generally most sensitive to the MSMC parameter, followed by the Clapp-Hornberger B parameter under the three different hydroclimatic scenarios. The effects of MSMC, the Clapp-Hornberger B parameter, and EAWC on the model responses are generally much larger than those of LAI and minimum stomatal resistance among most of the 10 schemes. This implies that the variations associated with the soil properties possibly due to the measurement uncertainties and/or spatial heterogeneity may play a more significant role in partitioning water and energy budgets than those associated with vegetation properties in the current generation of land-surface model parameterizations. Results also show that large sensitivities of model responses exist in relation to the choice of LSS when using the same parameter values, and in relation to the hydroclimatic scenario when using the same parameter and LSS. The differences can be sometimes quite large. In addition, the effects of parameter interactions are generally weaker than those of single parameters. The preliminary conclusions obtained from this study offer some insight on why large response differences between schemes occurred every time in the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phases 1, 2(a), 2(b), and 2(c) intercomparison studies, and perhaps on why each scheme performs better at its own testing site(s) than at the PILPS sites.

The versatile integrator of surface atmospheric processes: Part 2: evaluation of three topography-based runoff schemes

Three different schemes of topography-based runoff production [versatile integrator of surface atmospheric processes (VISA)-TOP1, VISA-TOP2, and VISA-TOP3] are described for a land-surface model (LSM) developed for use with a general circulation model (GCM). The schemes' sensitivities to some key parameters are assessed for two catchments using data sets developed for the Project for Intercomparison of Land-Surface Parameterization Schemes (PILPS) Phase 2e. VISA-TOP1 differs from VISA-TOP2 only in how to treat oversaturated soil water from the soil layers. In VISA-TOP1, the oversaturated soil water is thrown out of the soil column; hence, it no longer plays a role in the ensuing soil water budgets. In VISA-TOP2, this oversaturated soil water is recharged back to the unsaturated soil layers above the water table; hence, it continues to involve in the water budgets. Unlike VISA-TOP1 and VISA-TOP2, VISA-TOP3 relaxes its dependence on the topographic parameters. The oversaturated soil water is treated the same in both VISA-TOP2 and VISA-TOP3. All three models reproduce the daily and seasonal cycles of streamflow provided that different values of the saturated hydraulic conductivity decay factor are used. The decay factor controls the timing and partitioning of subsurface runoff. In both VISA-TOP1 and VISA-TOP2, an anisotropic parameter explaining different hydraulic conductivities in the vertical and horizontal directions is critical for using the topographic index in the land-surface model. In the VISA-TOP2 scheme, the topography-controlled subsurface runoff is dominant because the oversaturated water is recharged to upper unsaturated soil layers to raise the water table. The water budgets in all these schemes show dramatically different responses to the decay factor, indicating that the calibrated parameters and the model formulations should not be separated.

Simulation of high-latitude hydrological processes in the Torne–Kalix basin: PILPS Phase 2(e): 3: Equivalent model representation and sensitivity experiments

The Project for Intercomparison of Land Surface Parameterization Schemes (PILPS) Phase 2(e) showed that in cold regions the annual runoff production in Land Surface Schemes (LSSs) is closely related to the maximum snow accumulation, which in turn is controlled in large part by winter sublimation. To help further explain the relationship between snow cover, turbulent exchanges and runoff production, a simple equivalent model (SEM) was devised to reproduce the seasonal and annual fluxes simulated by 13 LSSs that participated in PILPS Phase 2(e). The design of the SEM relates the annual partitioning of precipitation and energy in the LSSs to three primary parameters: snow albedo, effective aerodynamic resistance and evaporation efficiency. Isolation of each of the parameters showed that the annual runoff production was most sensitive to the aerodynamic resistance. The SEM was somewhat successful in reproducing the observed LSS response to a decrease in shortwave radiation and changes in wind speed forcings. SEM parameters derived from the reduced shortwave forcings suggested that increased winter stability suppressed turbulent heat fluxes over snow. Because winter sensible heat fluxes were largely negative, reductions in winter shortwave radiation resulted in an increase in annual average sensible heat.

Simulation of high latitude hydrological processes in the Torne–Kalix basin: PILPS Phase 2(e): 2: Comparison of model results with observations

Model results from 21 land-surface schemes (LSSs) designed for use in numerical weather prediction and climate models are compared with each other and with observations in the context of the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) Phase 2(e) model intercomparison experiment. This experiment focuses on simulations of land-surface water and energy fluxes in the 58,000-km 2 Torne and Kalix river systems in northern Scandinavia, during the period 1989–1998. All models participating in PILPS Phase 2(e) capture the broad dynamics of snowmelt and runoff, but large differences in snow accumulation and ablation, turbulent heat fluxes, and streamflow exist. The greatest among-model differences in energy and moisture fluxes in these high-latitude environments occur during the spring snowmelt period, reflecting different model parameterizations of snow processes. Differences in net radiation are governed by differences in the simulated radiative surface temperature during the winter months and by differences in surface albedo during the spring/early summer. Differences in net radiation are smallest during the late summer when snow is absent. Although simulated snow sublimation is small for most models, a few models show annual snow sublimation of about 100 mm. These differences in snow sublimation appear to be largely dependent on differences in snow surface roughness parameterizations. The models with high sublimation generally lose their snowpacks too early compared to observations and underpredict the annual runoff. Differences in runoff parameterizations are reflected in differences in daily runoff statistics. Although most models show a greater variability in daily streamflow than the observations, the models with the greatest variability (as much as double the observed variability), produce most of their runoff through fast response, surface runoff mechanisms. As a group, those models that took advantage of an opportunity to calibrate to selected small catchments and to transfer calibration results to the basin at large had a smaller bias and root mean squared error (RMSE) in daily streamflow simulations compared with the models that did not calibrate.

Timescales of land surface evapotranspiration response in the PILPS phase 2(c)

Present-day land surface schemes used in weather prediction and climate models include parameterizations of physical processes whose complex nonlinear interactions can lead to models of unknown spatial and temporal characteristics. This paper describes the timescales of the evapotranspiration response of 16 land surface schemes which participated in the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) Phase 2(c) Red-Arkansas River experiment. The basins were represented by 61, 1°×1° grid boxes. Ten years of hourly meteorological data were used to force 16 land surface schemes off line. The evapotranspiration responses of the models are characterized by an impulse response function (or unit kernel) which is described by a two-parameter model, representing the fast response of evaporation from the canopy surface or bare soil and a slower one due to transpiration. The analysis of the results shows significant differences among the various LSS in their characteristic timescales across the basins.

Land‐surface simulations improve atmospheric modeling

Because weather and climate near the land surface influence most of our social and economic activities, realistic simulation of continental near‐surface climate is important for day‐to‐day decision‐making and for policy development relating to—for example—climate change.The need for correct and validated land‐surface processes in atmospheric simulations, acknowledged by many scientists in the past few decades, has prompted the development of a large number of land‐surface parameterization schemes with varying degrees of complexity designed to improve the prediction of near‐surface climate in global atmospheric models. The Project for Intercomparison of Land‐Surface Parameterization Schemes (PUPS) offers a methodology for intercomparing and analyzing land‐surface simulations that benefits the atmospheric modeling community worldwide.

Use of the Richards equation in land surface parameterizations

Accurately modeling infiltration and soil moisture within land surface parameterization schemes (LSPs) of coupled land surface‐atmosphere models is essential for producing realistic simulations of energy and moisture fluxes and for partitioning precipitation into infiltration, surface runoff, and drainage to groundwater. This report compares simulations of soil moisture, runoff, infiltration, and drainage to groundwater for a bare clay loam using three approaches: a finite difference solution of the vertically integrated Richards equation (an approach commonly used in LSPs), a highly resolved (spatially and temporally) finite element solution of Richards equation, and an analytical kinematic wave solution of Richards equation. Comparisons show that depth‐averaged soil moisture simulated using the vertically integrated Richards equation is only similar to those of the finite element solution for vertical spatial discretizations finer than those employed by most state‐of‐the‐art land surface‐atmosphere transfer schemes. The vertically integrated Richards equation overpredicts soil moisture in the near‐surface soil column and underpredicts drainage to groundwater. The infiltration formulation is found to be critical in partitioning precipitation into runoff, soil moisture, and drainage. Different infiltration formulations and vertical spatial discretizations may partly explain the very different land surface moisture and energy fluxes reported by the LSPs evaluated as part of the Project for Intercomparison of Land Surface Parameterization Schemes (PILPS) Phase 2(b) experiment.

An application of a large scale conceptual hydrological model over the Elbe region

Abstract. This paper investigates the ability of the VIC-2L model coupled to a routing model to reproduce streamflow in the catchment of the lower Elbe River, Germany. The VIC-2L model, a hydrologically-based land surface scheme (LSS) which has been tested extensively in the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS), is put up on the rotated grid of 1/6 degree of the atmospheric regional scale model (REMO) used in the Baltic Sea Experiment (BALTEX). For a 10 year period, the VIC-2L model is forced in daily time steps with measured daily means of precipitation, air temperature, pressure, wind speed, air humidity and daily sunshine duration. VIC-2L model output of surface runoff and baseflow is used as input for the routing model, which transforms modelled runoff into streamflow, which is compared to measured streamflow at selected gauge stations. The water balance of the basin is investigated and the model results on daily, monthly and annual time scales are discussed. Discrepancies appear in time periods where snow and ice processes are important. Extreme flood events are analyzed in more dital. The influence of calibration with respect to runoff is examined.

Assembly fetes world climate research area and its leader

Both a relatively new world‐climate research area and a person instrumental in bringing it about were feted at the International Union of Geodesy and Geophysics (IUGG) Assembly this past July. The research area has been embodied in the Project for Intercomparison of Land‐Surface Parameterization Schemes (PILPS), which actually began in 1992. Its leader, Ann Henderson‐Sellers, was awarded a doctor of science degree in recognition of her 21 years of work in climate model predictions.Said Henderson‐Sellers: “I am very pleased to be able to look back on an era in which this discipline's research develops from the simplest conceivable land‐surface scheme, literally a hole in the soil, to today's highly complex schemes, which include leaves, stomates, roots, and even ecological transitions.”

Surface energy balance complexity in GCM land surface models

A large number of land surface models (LSMs) have been designed for use in atmospheric general circulation models (GCMs) and GCM modellers therefore have a large number of options when selecting an LSM for their GCM. This study provides information to aid LSM design choices. A framework within which sensitivity to LSM design can be tested is presented and a series of experiments carried out to investigate how general aspects of surface energy balance parametrisation affect land-atmosphere evaporation. Firstly, it is shown that a combination of surface energy balance complexity and aerodynamic parametrisation can be used to explain the gross simulation differences obtained in the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS). Secondly, a simple surface energy balance parametrisation with a constant surface resistance is found to be as appropriate as more complex method for simulating annual, monthly and seasonally averaged diurnal cycles of evaporation. However, complex aspects of surface energy balance parametrisation (canopy interception, bare ground evaporation and canopy resistance) are shown to contain substantial geographic and daily functionality that is not present in the simpler parametrisation.

Validation Study of the CAPS Model Land Surface Scheme Using the 1987 Cabauw/PILPS Dataset

Abstract An updated complete and comprehensive description of the land surface parameterization scheme in the Coupled Atmosphere–Plant–Soil (CAPS) model is presented. The CAPS model has been in development at Oregon State University and Phillips Laboratory since 1981. The CAPS model was originally designed for a global atmospheric model, but it has also been used as a stand-alone model for a variety of applications. The land surface scheme in the CAPS model is one of the two dozen schemes that participated in the Project for Intercomparison of Land Surface Parameterization Schemes (PILPS). Some unique features of the CAPS scheme are given in detail. A comprehensive dataset of one year (1987), including atmospheric forcing data and validation data from Cabauw, has been provided for PILPS by the Royal Netherlands Meteorological Institute. Using the Cabauw data, a validation study for the CAPS scheme has been carried out. The scheme’s self-consistencies in terms of surface energy balance and water budget are...

The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) Phase 2(c) Red–Arkansas River basin experiment:: 1. Experiment description and summary intercomparisons

Sixteen land-surface schemes participating in the Project for the Intercomparison of Land-surface Schemes (PILPS) Phase 2(c) were run using 10 years (1979–1988) of forcing data for the Red–Arkansas River basins in the Southern Great Plains region of the United States. Forcing data (precipitation, incoming radiation and surface meteorology) and land-surface characteristics (soil and vegetation parameters) were provided to each of the participating schemes. Two groups of runs are presented. (1) Calibration–validation runs, using data from six small catchments distributed across the modeling domain. These runs were designed to test the ability of the schemes to transfer information about model parameters to other catchments and to the computational grid boxes. (2) Base-runs, using data for 1979–1988, designed to evaluate the ability of the schemes to reproduce measured energy and water fluxes over multiple seasonal cycles across a climatically diverse, continental-scale basin. All schemes completed the base-runs but five schemes chose not to calibrate. Observational data (from 1980–1986) including daily river flows and monthly basin total evaporation estimated through an atmospheric budget analysis, were used to evaluate model performance. In general, the results are consistent with earlier PILPS experiments in terms of differences among models in predicted water and energy fluxes. The mean annual net radiation varied between 80 and 105 W m −2 (excluding one model). The mean annual Bowen ratio varied from 0.52 to 1.73 (also excluding one model) as compared to the data-estimated value of 0.92. The run-off ratios varied from a low of 0.02 to a high of 0.41, as compared to an observed value of 0.15. In general, those schemes that did not calibrate performed worse, not only on the validation catchments, but also at the scale of the entire modeling domain. This suggests that further PILPS experiments on the value of calibration need to be carried out.

The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phase 2(c) Red-Arkansas River basin experiment:: 2. Spatial and temporal analysis of energy fluxes

The energy components of sixteen Soil-Vegetation Atmospheric Transfer (SVAT) schemes were analyzed and intercompared using 10 years of surface meteorological and radiative forcing data from the Red-Arkansas River basin in the Southern Great Plains of the United States. Comparisons of simulated surface energy fluxes among models showed that the net radiation and surface temperature generally had the best agreement among the schemes. On an average (annual and monthly) basis, the estimated latent heat fluxes agreed (to within approximate estimation errors) with the latent heat fluxes derived from a radiosonde-based atmospheric budget method for slightly more than half of the schemes. The sensible heat fluxes had larger differences among the schemes than did the latent heat fluxes, and the model-simulated ground heat fluxes had large variations among the schemes. The spatial patterns of the model-computed net radiation and surface temperature were generally similar among the schemes, and appear reasonable and consistent with observations of related variables, such as surface air temperature. The spatial mean patterns of latent and sensible heat fluxes were less similar than for net radiation, and the spatial patterns of the ground heat flux vary greatly among the 16 schemes. Generally, there is less similarity among the models in the temporal (interannual) variability of surface fluxes and temperature than there is in the mean fields, even for schemes with similar mean fields.

The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) phase 2(c) Red–Arkansas River basin experiment:: 3. Spatial and temporal analysis of water fluxes

The water-balance components of 16 Soil–Vegetation Atmospheric Transfer (SVAT) schemes were evaluated by comparing predicted and observed streamflow, predicted evapotranspiration and evapotranspiration inferred from an atmospheric moisture budget analysis, and soil moisture storage changes for a seven-year period (1980–1986) using data from the Red–Arkansas River basins of the Southern Great Plains of the USA. The evaluations support the following suggestions: (a) The mean annual runoff of all models follows, at least generally, the strong climatic East–West gradient of precipitation, although most models predict too much runoff in the dry part of the basin. (b) The mean monthly storage change tends to be underestimated, even though all models capture reasonably well the seasonality of the evapotranspiration. (c) The wide range of conceptualizations used for generation of surface and subsurface runoff strongly affect runoff generation on seasonal, and shorter, time scales. Model responses to summer precipitation ranged from almost no summer runoff (one model) to the (more common) situation of persistent overprediction of summer runoff, especially in the driest part of the basin. (d) All models tended to underpredict evapotranspiration in summer and overpredict in winter. (e) Model-derived mean seasonal cycles of changes in soil moisture storage are qualitatively similar to those inferred from observations, but most models do not predict the decrease in April soil moisture storage and the increase in October that is inferred from observations.

The updated version of SPONSOR land surface scheme: PILPS-influenced improvements

The parameterization scheme SPONSOR (Semi-distributed ParameterizatiON Scheme of the ORography-induced hydrology) participating in PILPS (Project for Intercomparison of Land-surface Parameterization Schemes) experiments since 1993 is described in more detail than before, taking into account a range of recent modifications. Improvement of the scheme in several aspects (e.g., soil water movement) resulted in significantly improved results for the Cabauw site (used for PILPS (2a) experiments). Then, parameterization of cold seasons/regions processes (water phase transformations within soil and snow cover) was developed for PILPS (2d) experiments carried out with Valdai data. Testing of the scheme against the data of Kolyma water balance station shows that it is able to reproduce the main features of heat and water exchange at the land surface in the permafrost zone quite satisfactorily. It was found that the scheme results are rather sensitive to the soil heat conductivity, especially in the cold seasons. The original method for the calculation of this parameter was developed using a square root function. The surface temperature and dates of crossing the 0°C temperature threshold for Kolyma station were reproduced with satisfactory accuracy. The temporal variation of the deep soil layers' temperatures was modelled satisfactorily too, but the seasonal amplitude of deep soil temperatures was overestimated by the scheme. This disadvantage can possibly be improved by inclusion of vertical inhomogeneity of soil thermal and hydraulic properties in the model.

Intercomparisons of land-surface parameterizations coupled to a limited area forecast model

The goal of the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) is to improve the understanding of the interactions between the atmosphere and the continental surface in climate and weather forecast models. In PILPS Phase 4(b), selected schemes are coupled to the Limited Area Prediction System (LAPS) developed by the Australian Bureau of Meteorology. To facilitate the comparison of PILPS schemes' behavior within LAPS, a single mode of coupling is selected: explicit coupling. This type of coupling is more flexible and avoids most of the problems raised when interchanging the surface schemes. Exploratory tests are conducted. Initially, experiments are run in which the land-surface schemes use the same parameters as in their original host models. Then, in other runs, the most important surface parameters are set constant in an attempt to reduce the scatter amongst the schemes' results. In order to understand the impact of initialisation of soil moisture on the schemes' results some extreme cases (wet and dry) are performed. The partitioning between surface fluxes is studied as well as the soil moisture budget. Both regional and local results are analysed. Sensitivity between LSS is found in the precipitation field with rainfall over the Australian continent altering by about 20%, but no significant change is found in the net radiation. The scatter in the surface energy fluxes amongst the schemes is large (up to 300 W m −2 locally, during the daytime peak) but is seldom affected by the choice of surface parameters. The dynamical range of flux partitioning between extremely dry and wet initialisation varies strongly amongst the schemes. Some major shortcoming with the BUCKET approach are seen in the re-evaporation of convective precipitation over dry land, in the very large evaporation from wet surfaces and the diurnal cycle of surface temperature.

Integrating land‐surface and atmospheric models

The Project for Intercomparison of Land‐Surface Parameterization Schemes (PILPS) is a World Climate Research Programme project operating under the auspices of the Working Group on Numerical Experimentation (WGNE) and the Global Energy and Water Cycle Experiment (GEWEX). Its goal is to improve our understanding of how the modeling of land‐surface processes affects atmospheric conditions in climate and weather forecast models. PILPS will assess the range of responses of surface parameterizations to atmospheric forcing and detect the source of these differences. This effort is needed to improve the capabilities of climate and weather prediction models when surface processes strongly influence the movement of the atmosphere. Since it began in 1992 [Henderson‐Sellers et al., 1992], PILPS has initiated a number of complementary sensitivity studies designed by the land‐surface scientific community.

The Interplay between Transpiration and Runoff Formulations in Land Surface Schemes Used with Atmospheric Models

Abstract The Project for Intercomparison of Land-surface Parameterization Schemes (PILPS) has shown that different land surface models (LSMs) driven by the same meteorological forcing can produce markedly different surface energy and water budgets, even when certain critical aspects of the LSMs (vegetation cover, albedo, turbulent drag coefficient, and snowcover) are carefully controlled. To help explain these differences, the authors devised a monthly water balance model that successfully reproduces the annual and seasonal water balances of the different PILPS schemes. Analysis of this model leads to the identification of two quantities that characterize an LSM’s formulation of soil water balance dynamics: 1) the efficiency of the soil’s evaporation sink integrated over the active soil moisture range, and 2) the fraction of this range over which runoff is generated. Regardless of the LSM’s complexity, the combination of these two derived parameters with rates of interception loss, potential evaporation, ...

Sensitivity study of the CAPS model land-surface scheme using the 1987 Cabauw/PILPS data set

The land-surface scheme in the Coupled Atmosphere - Plant - Soil (CAPS) model is one of many schemes that participated in the Project for Intercomparison of Land-surface Parameterization Schemes (PILPS). The CAPS model, also called the Oregon State University/Phillips Laboratory (OSU/PL) Atmospheric Boundary Layer Model, has undergone development at Oregon State University and Phillips Laboratory since 1981. This model was originally designed for a global atmospheric model, but has also been used as a stand-alone model for a variety of applications. A comprehensive data set of one year (1987) including atmospheric forcing data from Cabauw has been provided for PILPS by the Royal Netherlands Meteorological Institute (KNMI). Using the Cabauw data, a series of sensitivity simulations have been carried out for the CAPS scheme. Sensitivities of latent and sensible heat fluxes to the parameters in four categories (atmospheric forcing, boundary conditions, vegetation, and soil type) have been tested. Our results show that those fluxes are sensitive to atmospheric forcing, especially to air temperature and specific humidity in the surface layer. The most sensitive and important parameters for the CAPS scheme are the roughness lengths for momentum, and heat and moisture, and the minimum canopy (stomatal) resistance.