Evaluation of WRF planetary boundary layer parameterization schemes for simulation of monsoon depressions over India

Abstract

This study evaluates the fidelity of five planetary boundary layer (PBL) parameterization schemes in the advanced weather research and forecasting model for simulating monsoon depressions (MDs) over India. Five PBL schemes include; nonlocal first-order medium-range forecasting (MRF) and Yonsei University (YSU); hybrid first-order Asymmetric Convective Model version 2 (ACM2), and local one-and-a-half-order Bougeault–Lacarrére (BouLac) and Mellor–Yamada–Nakanishi–Niino (MYNN2). PBL schemes show significant impact on rainfall along with dynamical and thermodynamical parameters associated with MDs at the surface as well as at the upper levels. MRF simulates a relatively shallower, warmer and drier boundary layer compared to others. Results reveal that strong upper-level divergence and high moisture content within the lower levels are favorable for the occurrence of heavy rain associated with MDs. However, stronger wind shear within the mid-troposphere weakens the system and reduces the rain intensity. Based on the results and keeping the rainfall product in view, it is found that nonlocal PBL schemes (MRF and ACM2) have better forecast skills score than local PBL schemes (BouLac and MYNN2) over the Indian region.

Appendices

Appendix 1: Methods for dichotomous forecasts

	Observed
		Yes	No
Forecast	Yes	a	b
	No	c	d

Here, ‘a’ represents the event forecast to occur and did occur, i.e., hits, ‘b’ represent the event forecast to occur but did not occur, i.e., false alarms, ‘c’ represent the event forecast no to occur but did occur, i.e., misses, ‘d’ represent the event forecast no to occur and did not occur, i.e., correct no forecast

The standard verification methods used for rainfall validation are discussed as below

1.1 Equitable Threat Score (ETS)

Equitable Threat Score (ETS) is defined as the fraction of correctly predicted observed and/or forecast events after removing the contribution from hits by chance ($a_{\text{ref}}$) and is defined by

$${\begin{aligned}{\text{Equitable}}\;{\text{Threat}}\;{\text{Score}}\; \left( {\text{ETS}} \right) &= \frac{{a - a_{\text{ref}} }}{{a - a_{\text{ref}} + b + c}}\\ a_{\text{ref}} &= \frac{(a + b) \times (a + c)}{a + b + c + d}\end{aligned}}.$$

(1)

ETS vary between − 1/3 and 1, with perfect score equal to 1. ETS equal to zero represents no skill.

1.2 False alarm rate (FAR)

False alarm rate (FAR) is the ratio of the number of events actually did not occur (b) to the number of forecasted ‘yes’, i.e., a + b, and is defined as

$${\text{FAR}} = \frac{b}{a + b}.$$

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The smaller FAR indicates higher accuracy of forecast. FAR vary between 0 and 1 and zero indicates the perfect score.

1.3 Heidke Skill Score (HSS)

$${\text{HSS}} = \frac{2(ad - bc)}{(a + c)(c + d) + (a + b)(b + d)}.$$

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1.4 Percent correct (PC)

Percent correct (PC) is defined as the ratio of number of correct events (a + d) to the total number of events.

$${\text{PC}} = \frac{a + d}{a + b + c + d}$$

(4)

It ranges between 0 and 1. Larger PC indicates the more accurate forecast. Hence, PC equal to 1 is the perfect score.

1.5 Probability of detection (POD)

Probability of detection (POD) indicates the fraction of observed ‘yes’ events forecasted correctly (a) to the number of observed ‘yes’ events (a + c) and is defined as

$${\text{POD}} = \frac{a}{a + c}$$

(5)

POD ignores the event forecast to occur but did not occur actually, i.e., b and is sensitive to event forecast to occur and did occur actually, i.e., a. Larger POD values indicate the less number of events that were forecasted not to occur but did occur, i.e., c. It varies between 0 and 1 and POD equals to 1 is the perfect score.

1.6 Critical Success Index (CSI)

It is also known as threat score. It measures the fraction of observed and/or forecast events and indicated how well the forecasted ‘yes’, i.e., a, events, correspond to the observed ‘yes’, i.e., a + b + c, events and is defined as

$${\text{Critical}}\;{\text{Success}}\;{\text{Index}}\;\left( {\text{CSI}} \right) = \frac{a}{a + b + c} .$$

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It varies between 0 and 1, where 0 indicates no skill and 1 indicates the perfect score.

Appendix 2: Performance indicators for meteorological parameters

2.1 Index of agreement (IOA)

The index of agreement (IOA) measures the degree to which the model predictions are free from error and is expressed as (Willmott 1981)

$${\text{IOA}} = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{N} \left( {O_{i} - P_{i} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{N} \left( {\left| {P_{i} - \overline{O} } \right| + \left| {O_{i} - \overline{O} } \right|} \right)^{2} }}.$$

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Here, $O_{i}$, $P_{i}$, $\overline{O}$, and $\overline{P}$ are observed data, predicted data, mean observed and mean predicted data, respectively. IOA has a theoretical range of 0 and 1, where 1 indicates the perfect match and 0 connotes the complete disagreement between observed and predicted values

2.2 Bias

Bias measures the sign of the errors of the predicted values and is defined as

$${\text{Bias}} = \overline{P} - \overline{O} .$$

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Positive (negative) value of bias implies overpredicted (underpredicted) model values.

2.3 Fractional bias (FB)

Fractional bias (FB) is the normalized bias and is defined as

$${\text{FB}} = \frac{{\overline{O} - \overline{P} }}{{0.5(\overline{O} + \overline{P} )}}.$$

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FB varies between + 2 and − 2. Negative FB shows overestimation, whereas positive FB shows underestimation by model.

2.4 Root mean square error (RMSE)

Root mean square error (RMSE) measures the difference between the predicted and observed values and is defined as

$${\text{RMSE}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{N} \left( {P_{i} - O_{i} } \right)^{2} }}{N}} .$$

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