Potential Evaporation

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 279 Experts worldwide ranked by ideXlab platform

L.p.h. Van Beek - One of the best experts on this subject based on the ideXlab platform.

  • selecting the optimal method to calculate daily global reference Potential Evaporation from cfsr reanalysis data for application in a hydrological model study
    Hydrology and Earth System Sciences, 2012
    Co-Authors: F. C. Sperna Weiland, C. Tisseuil, Hans H. Dürr, Mathieu Vrac, L.p.h. Van Beek
    Abstract:

    Potential Evaporation (PET) is one of the main inputs of hydrological models. Yet, there is limited consensus on which PET equation is most applicable in hydrological climate impact assessments. In this study six different methods to derive global scale reference PET daily time series from Climate Forecast System Reanalysis (CFSR) data are compared: Penman-Monteith, Priestley-Taylor and original and re-calibrated versions of the Hargreaves and Blaney-Criddle method. The calculated PET time series are (1) evaluated against global monthly Penman-Monteith PET time series calculated from CRU data and (2) tested on their usability for modeling of global discharge cycles. A major finding is that for part of the investigated basins the selection of a PET method may have only a minor influence on the resulting river flow. Within the hydrological model used in this study the bias related to the PET method tends to decrease while going from PET, AET and runoff to discharge calculations. However, the performance of individual PET methods appears to be spatially variable, which stresses the necessity to select the most accurate and spatially stable PET method. The lowest root mean squared differences and the least significant deviations (95% significance level) between monthly CFSR derived PET time series and CRU derived PET were obtained for a cell-specific re-calibrated Blaney-Criddle equation. However, results show that this re-calibrated form is likely to be unstable under changing climate conditions and less reliable for the calculation of daily time series. Although often recommended, the Penman-Monteith equation applied to the CFSR data did not outperform the other methods in a evaluation against PET derived with the Penman-Monteith equation from CRU data. In arid regions (e.g. Sahara, central Australia, US deserts), the equation resulted in relatively low PET values and, consequently, led to relatively high discharge values for dry basins (e.g. Orange, Murray and Zambezi). Furthermore, the Penman-Monteith equation has a high data demand and the equation is sensitive to input data inaccuracy. Therefore, we recommend the re-calibrated form of the Hargreaves equation which globally gave reference PET values comparable to CRU derived values for multiple climate conditions. The resulting gridded daily PET time series provide a new reference dataset that can be used for future hydrological impact assessments in further research, or more specifically, for the statistical downscaling of daily PET derived from raw GCM data. The dataset can be downloaded from http://opendap.deltares.nl/thredds/dodsC/opendap/deltares/FEWS-IPCC .

  • Selecting the optimal method to calculate daily global reference Potential Evaporation from CFSR reanalysis data
    Hydrology and Earth System Sciences Discussions, 2011
    Co-Authors: F. C. Sperna Weiland, C. Tisseuil, Hans H. Dürr, Mathieu Vrac, L.p.h. Van Beek
    Abstract:

    Abstract. Potential Evaporation (PET) is one of the main inputs of hydrological models. Yet, there is limited consensus on which PET equation is most applicable in hydrological climate impact assessments. In this study six different methods to derive global scale reference PET time series from CFSR reanalysis data are compared: Penman-Monteith, Priestley-Taylor and original and modified versions of the Hargreaves and Blaney-Criddle method. The calculated PET time series are (1) evaluated against global monthly Penman-Monteith PET time series calculated from CRU data and (2) tested on their usability for modeling of global discharge cycles. The lowest root mean squared differences and the least significant deviations (95 % significance level) between monthly CFSR derived PET time series and CRU derived PET were obtained for the cell specific modified Blaney-Criddle equation. However, results show that this modified form is likely to be unstable under changing climate conditions and less reliable for the calculation of daily time series. Although often recommended, the Penman-Monteith equation did not outperform the other methods. In arid regions (e.g., Sahara, central Australia, US deserts), the equation resulted in relatively low PET values and, consequently, led to relatively high discharge values for dry basins (e.g., Orange, Murray and Zambezi). Furthermore, the Penman-Monteith equation has a high data demand and the equation is sensitive to input data inaccuracy. Therefore, we preferred the modified form of the Hargreaves equation, which globally gave reference PET values comparable to CRU derived values. Although it is a relative efficient empirical equation, like Blaney-Criddle, the equation considers multiple spatial varying meteorological variables and consequently performs well for different climate conditions. In the modified form of the Hargreaves equation the multiplication factor is uniformly increased from 0.0023 to 0.0031 to overcome the global underestimation of CRU derived PET obtained with the original equation. It should be noted that the bias in PET is not linearly transferred to actual evapotranspiration and runoff, due to limited soil moisture availability and precipitation. The resulting gridded daily PET time series provide a new reference dataset that can be used for future hydrological impact assessments or, more specifically, for the statistical downscaling of daily PET derived from raw GCM data.

Shengzhi Huang - One of the best experts on this subject based on the ideXlab platform.

  • Spatio-Temporal Changes in Potential Evaporation and Possible Causes Based on SCRAQ Method: A Case Study in the Wei River Basin, China
    Journal of Coastal Research, 2018
    Co-Authors: Bo Kong, Shengzhi Huang, Lan Ma, Qiang Huang
    Abstract:

    ABSTRACT Kong, B.; Huang, S.; Ma, L., and Huang, Q., 2018. Spatio-temporal changes in Potential Evaporation and possible causes based on SCRAQ method: A case study in the Wei River Basin, China. In: Wang, D. and Guido-Aldana, P.A. (eds.), Select Proceedings from the 3rd International Conference on Water Resource and Environment (WRE2017). Journal of Coastal Research, Special Issue No. 84, pp. 94–102. Coconut Creek (Florida), ISSN 0749-0208. It is important for regional agricultural production as well as water resources planning and management to better understand the spatial and temporal variations of Potential Evaporation (PET) and their possible causes from a perspective of climate change. In this study, the spatial and temporal changes in monthly and annual PET covering 1960~2006 in the Wei River Basin (WRB), a typical arid and semi-arid region in China, were thoroughly examined based on the modified Mann-Kendall trend test method. Additionally, the slope change ratio of accumulative quantity (SCRAQ) m...

  • Spatial–temporal changes in Potential Evaporation patterns based on the Cloud model and their possible causes
    Stochastic Environmental Research and Risk Assessment, 2017
    Co-Authors: Shengzhi Huang, Jianxia Chang, Guoyong Leng
    Abstract:

    It is of importance to comprehensively investigate the spatial–temporal changes in Potential Evaporation patterns, which helps guide the long-term water resource allocation and irrigation managements. In this study, the Cloud model was adopted to quantify the average, uniformity, and stability of the annual Potential Evaporation in the Wei River Basin (WRB), a typical arid and semi-arid region in China, with the purpose of objectively and comprehensively characterizing its changing patterns. The cross wavelet analysis was then applied to explore the correlations between annual Potential Evaporation and Arctic Oscillation (AO)/El Nino Southern Oscillation (ENSO) with an aim to determine the possible causes of annual Potential Evaporation variations. Results indicated that: (1) the average of annual Potential Evaporation in the WRB first declined and then increased, and its stability also showed the same change characteristics, whilst its dispersion degree exhibited a decreasing trend, implying that Potential Evaporation has a smaller inter-annual variation; (2) the average of annual Potential Evaporation in the western basin was obviously smaller than that in the other areas, while its uniformity and stability in the Guanzhong plain and the Loess Plateau areas are larger than those in other areas, especially in the western basin where the uniformity and stability are the smallest; (3) both AO and ENSO exhibited strong correlations with annual Potential Evaporation variations, indicating that both AO and ENSO have played an important role in the annual Potential Evaporation variations in the WRB.

  • spatial temporal changes in Potential Evaporation patterns based on the cloud model and their possible causes
    Stochastic Environmental Research and Risk Assessment, 2017
    Co-Authors: Shengzhi Huang, Jianxia Chang, Guoyong Leng
    Abstract:

    It is of importance to comprehensively investigate the spatial–temporal changes in Potential Evaporation patterns, which helps guide the long-term water resource allocation and irrigation managements. In this study, the Cloud model was adopted to quantify the average, uniformity, and stability of the annual Potential Evaporation in the Wei River Basin (WRB), a typical arid and semi-arid region in China, with the purpose of objectively and comprehensively characterizing its changing patterns. The cross wavelet analysis was then applied to explore the correlations between annual Potential Evaporation and Arctic Oscillation (AO)/El Nino Southern Oscillation (ENSO) with an aim to determine the possible causes of annual Potential Evaporation variations. Results indicated that: (1) the average of annual Potential Evaporation in the WRB first declined and then increased, and its stability also showed the same change characteristics, whilst its dispersion degree exhibited a decreasing trend, implying that Potential Evaporation has a smaller inter-annual variation; (2) the average of annual Potential Evaporation in the western basin was obviously smaller than that in the other areas, while its uniformity and stability in the Guanzhong plain and the Loess Plateau areas are larger than those in other areas, especially in the western basin where the uniformity and stability are the smallest; (3) both AO and ENSO exhibited strong correlations with annual Potential Evaporation variations, indicating that both AO and ENSO have played an important role in the annual Potential Evaporation variations in the WRB.

  • spatio temporal changes in Potential Evaporation based on entropy across the wei river basin
    Water Resources Management, 2014
    Co-Authors: Shengzhi Huang, Jianxia Chang, Qiang Huang, Yimin Wang, Yutong Chen
    Abstract:

    The distribution of Potential Evaporation is highly unstable due to complex human activities and climate changes. Therefore, it is of great significance for further understanding hydrological cycle to estimate Potential Evaporation distribution. Reasonable regionalization of Potential Evaporation will help to improve the efficiency of irrigation and increase the ability of drought relief, which is of great importance to irrigation planning and management. Hence, the spatio-temporal changes in Potential Evaporation distribution at monthly and annual scales are investigated based on the modified Mann-Kendall trend test method and the entropy theory in the Wei River Basin. A nonparametric method as an attractive alternative to empirical and parametric approaches is proposed to calculate the univariate and bivariate probability distribution of Potential Evaporation. The directional information transfer index (DITI) is employed to estimate the similarity among the meteorological stations, and the k-means cluster analysis is used to classify the meteorological stations into several distribution zones with distinct features. Based on the monthly Potential Evaporation from 1960 to 2008 at 21 meteorological stations, the basin is ultimately classified into 8 zones with their own distinct spatio-temporal distribution features. In view of the distinct spatio-temporal distribution features, the DITI-based model combined with the nonparametric probability estimation method and the k-means cluster analysis offers a more precise classification of Potential Evaporation distribution zones.

Ilias Vardavas - One of the best experts on this subject based on the ideXlab platform.

  • Potential Evaporation trends over land between 1983–2008: driven by radiative fluxes or vapour-pressure deficit?
    Atmospheric Chemistry and Physics, 2011
    Co-Authors: C. Matsoukas, N. Benas, Nikolaos Hatzianastassiou, K. G. Pavlakis, Maria Kanakidou, Ilias Vardavas
    Abstract:

    We model the Penman Potential Evaporation (PE) over all land areas of the globe for the 25-yr period 1983–2008, relying on radiation transfer models (RTMs) for the shortwave and longwave fluxes. Penman's PE is determined by two factors: available energy for Evaporation and ground to atmosphere vapour transfer. Input to the PE model and RTMs comprises satellite cloud and aerosol data, as well as data from reanalyses. PE is closely linked to pan Evaporation, whose trends have sparked controversy in the community, since the factors responsible for the observed pan Evaporation trends are not determined with consensus. Our particular interest is the temporal evolution of PE, and the provided insight to the observed trends of pan Evaporation. We examine the decadal trends of PE and various related physical quantities, such as net solar flux, net longwave flux, water vapour saturation deficit and wind speed. Our findings are the following: Global warming has led to a larger water vapour saturation deficit. The periods 1983–1989, 1990–1999, and 2000–2008 were characterised by decreasing, increasing, and slightly decreasing PE, respectively. In these last 25 yr, global dimming/brightening cycles generally increased the available energy for Evaporation. PE trends seem to follow more closely the trends of energy availability than the trends of the atmospheric capability for vapour transfer, at most locations on the globe, with trends in the Northern hemisphere significantly larger than in the Southern. These results support the hypothesis that global Potential Evaporation trends are attributed primarily to secular changes in the radiation fluxes, and secondarily to vapour transfer considerations.

  • Potential Evaporation trends over land between 1983 2008 driven by radiative fluxes or vapour pressure deficit
    Atmospheric Chemistry and Physics, 2011
    Co-Authors: C. Matsoukas, N. Benas, Nikolaos Hatzianastassiou, K. G. Pavlakis, Maria Kanakidou, Ilias Vardavas
    Abstract:

    We model the Penman Potential Evaporation (PE) over all land areas of the globe for the 25-yr period 1983–2008, relying on radiation transfer models (RTMs) for the shortwave and longwave fluxes. Penman's PE is determined by two factors: available energy for Evaporation and ground to atmosphere vapour transfer. Input to the PE model and RTMs comprises satellite cloud and aerosol data, as well as data from reanalyses. PE is closely linked to pan Evaporation, whose trends have sparked controversy in the community, since the factors responsible for the observed pan Evaporation trends are not determined with consensus. Our particular interest is the temporal evolution of PE, and the provided insight to the observed trends of pan Evaporation. We examine the decadal trends of PE and various related physical quantities, such as net solar flux, net longwave flux, water vapour saturation deficit and wind speed. Our findings are the following: Global warming has led to a larger water vapour saturation deficit. The periods 1983–1989, 1990–1999, and 2000–2008 were characterised by decreasing, increasing, and slightly decreasing PE, respectively. In these last 25 yr, global dimming/brightening cycles generally increased the available energy for Evaporation. PE trends seem to follow more closely the trends of energy availability than the trends of the atmospheric capability for vapour transfer, at most locations on the globe, with trends in the Northern hemisphere significantly larger than in the Southern. These results support the hypothesis that global Potential Evaporation trends are attributed primarily to secular changes in the radiation fluxes, and secondarily to vapour transfer considerations.

  • Potential Evaporation trends over land between 1983-2008: driven by radiative or turbulent fluxes?
    Atmospheric Chemistry and Physics, 2011
    Co-Authors: C. Matsoukas, N. Benas, Nikolaos Hatzianastassiou, K. G. Pavlakis, Maria Kanakidou, Ilias Vardavas
    Abstract:

    Abstract. We model the Penman Potential Evaporation (PE) over all land areas of the globe for the 25-year period 1983–2008, relying on radiation transfer models (RTMs) for the shortwave and longwave fluxes. Penman's PE is determined by two factors: available energy for Evaporation and ground to atmosphere vapour transfer. Input to the PE model and RTMs comprises satellite cloud and aerosol data, as well as data from reanalyses. PE is closely linked to pan Evaporation, whose trends have sparked controversy in the community, since the factors responsible for the observed pan Evaporation trends are not determined with consensus. Our particular interest is the temporal evolution of PE, and the provided insight to the observed trends of pan Evaporation. We examine the interannual trends of PE and various related physical quantities, such as net solar flux, net longwave flux, water vapour saturation deficit and wind speed. Our findings are the following: Global warming has led to a larger water vapour saturation deficit. Global dimming/brightening cycles in the last 25 years slightly increased the available energy for Evaporation. PE trends seem to follow closely the trends of energy availability and not the trends of the atmospheric capability for vapour transfer, almost everywhere on the globe, with trends in the Northern hemisphere significantly larger than in the Southern. These results support the hypothesis that secular changes in the radiation fluxes, and not vapour transfer considerations, are responsible for Potential Evaporation trends.

F. C. Sperna Weiland - One of the best experts on this subject based on the ideXlab platform.

  • selecting the optimal method to calculate daily global reference Potential Evaporation from cfsr reanalysis data for application in a hydrological model study
    Hydrology and Earth System Sciences, 2012
    Co-Authors: F. C. Sperna Weiland, C. Tisseuil, Hans H. Dürr, Mathieu Vrac, L.p.h. Van Beek
    Abstract:

    Potential Evaporation (PET) is one of the main inputs of hydrological models. Yet, there is limited consensus on which PET equation is most applicable in hydrological climate impact assessments. In this study six different methods to derive global scale reference PET daily time series from Climate Forecast System Reanalysis (CFSR) data are compared: Penman-Monteith, Priestley-Taylor and original and re-calibrated versions of the Hargreaves and Blaney-Criddle method. The calculated PET time series are (1) evaluated against global monthly Penman-Monteith PET time series calculated from CRU data and (2) tested on their usability for modeling of global discharge cycles. A major finding is that for part of the investigated basins the selection of a PET method may have only a minor influence on the resulting river flow. Within the hydrological model used in this study the bias related to the PET method tends to decrease while going from PET, AET and runoff to discharge calculations. However, the performance of individual PET methods appears to be spatially variable, which stresses the necessity to select the most accurate and spatially stable PET method. The lowest root mean squared differences and the least significant deviations (95% significance level) between monthly CFSR derived PET time series and CRU derived PET were obtained for a cell-specific re-calibrated Blaney-Criddle equation. However, results show that this re-calibrated form is likely to be unstable under changing climate conditions and less reliable for the calculation of daily time series. Although often recommended, the Penman-Monteith equation applied to the CFSR data did not outperform the other methods in a evaluation against PET derived with the Penman-Monteith equation from CRU data. In arid regions (e.g. Sahara, central Australia, US deserts), the equation resulted in relatively low PET values and, consequently, led to relatively high discharge values for dry basins (e.g. Orange, Murray and Zambezi). Furthermore, the Penman-Monteith equation has a high data demand and the equation is sensitive to input data inaccuracy. Therefore, we recommend the re-calibrated form of the Hargreaves equation which globally gave reference PET values comparable to CRU derived values for multiple climate conditions. The resulting gridded daily PET time series provide a new reference dataset that can be used for future hydrological impact assessments in further research, or more specifically, for the statistical downscaling of daily PET derived from raw GCM data. The dataset can be downloaded from http://opendap.deltares.nl/thredds/dodsC/opendap/deltares/FEWS-IPCC .

  • Selecting the optimal method to calculate daily global reference Potential Evaporation from CFSR reanalysis data
    Hydrology and Earth System Sciences Discussions, 2011
    Co-Authors: F. C. Sperna Weiland, C. Tisseuil, Hans H. Dürr, Mathieu Vrac, L.p.h. Van Beek
    Abstract:

    Abstract. Potential Evaporation (PET) is one of the main inputs of hydrological models. Yet, there is limited consensus on which PET equation is most applicable in hydrological climate impact assessments. In this study six different methods to derive global scale reference PET time series from CFSR reanalysis data are compared: Penman-Monteith, Priestley-Taylor and original and modified versions of the Hargreaves and Blaney-Criddle method. The calculated PET time series are (1) evaluated against global monthly Penman-Monteith PET time series calculated from CRU data and (2) tested on their usability for modeling of global discharge cycles. The lowest root mean squared differences and the least significant deviations (95 % significance level) between monthly CFSR derived PET time series and CRU derived PET were obtained for the cell specific modified Blaney-Criddle equation. However, results show that this modified form is likely to be unstable under changing climate conditions and less reliable for the calculation of daily time series. Although often recommended, the Penman-Monteith equation did not outperform the other methods. In arid regions (e.g., Sahara, central Australia, US deserts), the equation resulted in relatively low PET values and, consequently, led to relatively high discharge values for dry basins (e.g., Orange, Murray and Zambezi). Furthermore, the Penman-Monteith equation has a high data demand and the equation is sensitive to input data inaccuracy. Therefore, we preferred the modified form of the Hargreaves equation, which globally gave reference PET values comparable to CRU derived values. Although it is a relative efficient empirical equation, like Blaney-Criddle, the equation considers multiple spatial varying meteorological variables and consequently performs well for different climate conditions. In the modified form of the Hargreaves equation the multiplication factor is uniformly increased from 0.0023 to 0.0031 to overcome the global underestimation of CRU derived PET obtained with the original equation. It should be noted that the bias in PET is not linearly transferred to actual evapotranspiration and runoff, due to limited soil moisture availability and precipitation. The resulting gridded daily PET time series provide a new reference dataset that can be used for future hydrological impact assessments or, more specifically, for the statistical downscaling of daily PET derived from raw GCM data.

Jianxia Chang - One of the best experts on this subject based on the ideXlab platform.

  • Spatial–temporal changes in Potential Evaporation patterns based on the Cloud model and their possible causes
    Stochastic Environmental Research and Risk Assessment, 2017
    Co-Authors: Shengzhi Huang, Jianxia Chang, Guoyong Leng
    Abstract:

    It is of importance to comprehensively investigate the spatial–temporal changes in Potential Evaporation patterns, which helps guide the long-term water resource allocation and irrigation managements. In this study, the Cloud model was adopted to quantify the average, uniformity, and stability of the annual Potential Evaporation in the Wei River Basin (WRB), a typical arid and semi-arid region in China, with the purpose of objectively and comprehensively characterizing its changing patterns. The cross wavelet analysis was then applied to explore the correlations between annual Potential Evaporation and Arctic Oscillation (AO)/El Nino Southern Oscillation (ENSO) with an aim to determine the possible causes of annual Potential Evaporation variations. Results indicated that: (1) the average of annual Potential Evaporation in the WRB first declined and then increased, and its stability also showed the same change characteristics, whilst its dispersion degree exhibited a decreasing trend, implying that Potential Evaporation has a smaller inter-annual variation; (2) the average of annual Potential Evaporation in the western basin was obviously smaller than that in the other areas, while its uniformity and stability in the Guanzhong plain and the Loess Plateau areas are larger than those in other areas, especially in the western basin where the uniformity and stability are the smallest; (3) both AO and ENSO exhibited strong correlations with annual Potential Evaporation variations, indicating that both AO and ENSO have played an important role in the annual Potential Evaporation variations in the WRB.

  • spatial temporal changes in Potential Evaporation patterns based on the cloud model and their possible causes
    Stochastic Environmental Research and Risk Assessment, 2017
    Co-Authors: Shengzhi Huang, Jianxia Chang, Guoyong Leng
    Abstract:

    It is of importance to comprehensively investigate the spatial–temporal changes in Potential Evaporation patterns, which helps guide the long-term water resource allocation and irrigation managements. In this study, the Cloud model was adopted to quantify the average, uniformity, and stability of the annual Potential Evaporation in the Wei River Basin (WRB), a typical arid and semi-arid region in China, with the purpose of objectively and comprehensively characterizing its changing patterns. The cross wavelet analysis was then applied to explore the correlations between annual Potential Evaporation and Arctic Oscillation (AO)/El Nino Southern Oscillation (ENSO) with an aim to determine the possible causes of annual Potential Evaporation variations. Results indicated that: (1) the average of annual Potential Evaporation in the WRB first declined and then increased, and its stability also showed the same change characteristics, whilst its dispersion degree exhibited a decreasing trend, implying that Potential Evaporation has a smaller inter-annual variation; (2) the average of annual Potential Evaporation in the western basin was obviously smaller than that in the other areas, while its uniformity and stability in the Guanzhong plain and the Loess Plateau areas are larger than those in other areas, especially in the western basin where the uniformity and stability are the smallest; (3) both AO and ENSO exhibited strong correlations with annual Potential Evaporation variations, indicating that both AO and ENSO have played an important role in the annual Potential Evaporation variations in the WRB.

  • spatio temporal changes in Potential Evaporation based on entropy across the wei river basin
    Water Resources Management, 2014
    Co-Authors: Shengzhi Huang, Jianxia Chang, Qiang Huang, Yimin Wang, Yutong Chen
    Abstract:

    The distribution of Potential Evaporation is highly unstable due to complex human activities and climate changes. Therefore, it is of great significance for further understanding hydrological cycle to estimate Potential Evaporation distribution. Reasonable regionalization of Potential Evaporation will help to improve the efficiency of irrigation and increase the ability of drought relief, which is of great importance to irrigation planning and management. Hence, the spatio-temporal changes in Potential Evaporation distribution at monthly and annual scales are investigated based on the modified Mann-Kendall trend test method and the entropy theory in the Wei River Basin. A nonparametric method as an attractive alternative to empirical and parametric approaches is proposed to calculate the univariate and bivariate probability distribution of Potential Evaporation. The directional information transfer index (DITI) is employed to estimate the similarity among the meteorological stations, and the k-means cluster analysis is used to classify the meteorological stations into several distribution zones with distinct features. Based on the monthly Potential Evaporation from 1960 to 2008 at 21 meteorological stations, the basin is ultimately classified into 8 zones with their own distinct spatio-temporal distribution features. In view of the distinct spatio-temporal distribution features, the DITI-based model combined with the nonparametric probability estimation method and the k-means cluster analysis offers a more precise classification of Potential Evaporation distribution zones.